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Who said: “I seem to have been only like a boy playing on the seashore, ... finding a smoother pebble or a prettier shell ... whilst the great ocean of truth lay all undiscovered before me.”
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Home > Category Index for Science Quotations > Category Index C > Category: Curvature

Curvature Quotes (8 quotes)

[Students or readers about teachers or authors.] They will listen with both ears to what is said by the men just a step or two ahead of them, who stand nearest to them, and within arm’s reach. A guide ceases to be of any use when he strides so far ahead as to be hidden by the curvature of the earth.
From Lecture (5 Apr 1917) at Hackley School, Tarrytown, N.Y., 'Choosing Books', collected in Canadian Stories (1918), 150.
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Adapting from the earlier book Gravitation, I wrote, “Spacetime tells matter how to move; matter tells spacetime how to curve.” In other words, a bit of matter (or mass, or energy) moves in accordance with the dictates of the curved spacetime where it is located. … At the same time, that bit of mass or energy is itself contributing to the curvature of spacetime everywhere.
With co-author Kenneth William Ford Geons, Black Holes, and Quantum Foam: A Life in Physics (1998, 2010), 235. Adapted from his earlier book, co-authored with Charles W. Misner and Kip S. Thorne, Gravitation (1970, 1973), 5, in which one of the ideas in Einstein’s geometric theory of gravity was summarized as, “Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve”.
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It was shortly after midday on December 12, 1901, [in a hut on the cliffs at St. John's, Newfoundland] that I placed a single earphone to my ear and started listening. The receiver on the table before me was very crude—a few coils and condensers and a coherer—no valves [vacuum tubes], no amplifiers, not even a crystal. I was at last on the point of putting the correctness of all my beliefs to test. ... [The] answer came at 12:30. ... Suddenly, about half past twelve there sounded the sharp click of the “tapper” ... Unmistakably, the three sharp clicks corresponding to three dots sounded in my ear. “Can you hear anything, Mr. Kemp?” I asked, handing the telephone to my assistant. Kemp heard the same thing as I. ... I knew then that I had been absolutely right in my calculations. The electric waves which were being sent out from Poldhu [Cornwall, England] had travelled the Atlantic, serenely ignoring the curvature of the earth which so many doubters considered a fatal obstacle. ... I knew that the day on which I should be able to send full messages without wires or cables across the Atlantic was not far distant.
Quoted in Degna Marconi, My Father, Marconi (2000), 93.
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Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
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Ploughing deep, your recipe for killing weeds, is also the recipe for almost every good thing in farming. … We now plough horizontally following the curvatures of the hills and hollows, on the dead level, however crooked the lines may be. Every furrow thus acts as a reservoir to receive and retain the waters, all of which go to the benefit of the growing plant, instead of running off into streams … In point of beauty nothing can exceed that of the waving lines and rows winding along the face of the hills and vallies.
In letter (17 Apr 1813) from Jefferson at Monticello to Charles Willson Peale. Collected in The Jefferson Papers: 1770-1826 (1900), 178-180.
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There is nothing in the world except empty curved space. Matter, charge, electromagnetism, and other fields are only manifestations of the curvature of space.
(1957) Quoted in New Scientist, 26 Sep 1974.
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To the pure geometer the radius of curvature is an incidental characteristic—like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the “cat without a grin” and the “grin without a cat” are equally set aside as purely mathematical phantasies.
In 'The Universe and the Atom' The Expanding Universe. (1933), 103.
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…The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein’s special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein’s amazing revelations have likewise sunk into the commonplaces of educated thought.
In The Theory of Relativity and its Influence on Scientific Thought (1922), 31-32
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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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