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Home > Category Index for Science Quotations > Category Index D > Category: Dimension

Dimension Quotes (21 quotes)

Mon royaume est de la dimension de l’univers, et mon désir n’a pas de bornes. Je vais toujours, affranchissant l’esprit et pesant les mondes, sans haine, sans peur, sans pitié, sans amour, et sans Dieu. On m’appelle la Science.
My kingdom is of the dimension of the universe and my desire has no bounds. I am going about always to free the spirit and weigh the worlds, without hatred, without fear, without pity and without God. They call me Science.
French passage from La Tentation de Saint-Antoine (1874) in Œvres Complètes de Gustave Flaubert (1885), 222. English translation by Ernest Tristan and G.F. Monkshood, The Temptation of Saint Anthony (1910), 254.
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On the future of Chemistry:
Chemistry is not the preservation hall of old jazz that it sometimes looks like. We cannot know what may happen tomorrow. Someone may oxidize mercury (II), francium (I), or radium (II). A mineral in Nova Scotia may contain an unsaturated quark per 1020 nucleons. (This is still 6000 per gram.) We may pick up an extraterrestrial edition of Chemical Abstracts. The universe may be a 4-dimensional soap bubble in an 11-dimensional space as some supersymmetry theorists argued in May of 1983. Who knows?
George B. Kaufmann, 'Interview with Jannik Bjerrum and Christian Klixbull Jørgensen', Journal of Chemical Education (1985), 62, 1005.
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A mind that is stretched by a new idea can never go back to its original dimensions.
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Absolute space, of its own nature without reference to anything external, always remains homogenous and immovable. Relative space is any movable measure or dimension of this absolute space; such a measure or dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space, as in the case of space under the earth or in the air or in the heavens, where the dimension is determined from the situation of the space with respect to the earth. Absolute and relative space are the same in species and in magnitude, but they do not always remain the same numerically. For example, if the earth moves, the space of our air, which in a relative sense and with respect to the earth always remains the same, will now be one part of the absolute space into which the air passes, now another part of it, and thus will be changing continually in an absolute sense.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Definitions, Scholium, 408-9.
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All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.
Lectures on the Logic of Arithmetic (1903), Preface, 18-19.
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Biology is a science of three dimensions. The first is the study of each species across all levels of biological organization, molecule to cell to organism to population to ecosystem. The second dimension is the diversity of all species in the biosphere. The third dimension is the history of each species in turn, comprising both its genetic evolution and the environmental change that drove the evolution. Biology, by growing in all three dimensions, is progressing toward unification and will continue to do so.
In 'Systematics and the Future of Biology', Systematics and the Origin of Species: on Ernst Mayr's 100th anniversary, Volume 102, Issues 22-26 (2005), 1.
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Carbon has this genius of making a chemically stable two-dimensional, one-atom-thick membrane in a three-dimensional world. And that, I believe, is going to be very important in the future of chemistry and technology in general.
From Nobel Lecture (7 Dec 1996), 'Discovering the Fullerenes', collected in Ingmar Grenthe (ed.), Nobel Lectures, Chemistry 1996-2000 (2003).
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Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,—namely, length and width,—all solids of nature which have three dimensions,—length, width, and depth,—provided, however, that these solids are capable of rigorous definition.
The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions.
From On the Purpose of Descriptive Geometry as translated by Arnold Emch in David Eugene Smith, A Source Book in Mathematics (1929), 426.
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Diamond, for all its great beauty, is not nearly as interesting as the hexagonal plane of graphite. It is not nearly as interesting because we live in a three-dimensional space, and in diamond each atom is surrounded in all three directions in space by a full coordination. Consequently, it is very difficult for an atom inside the diamond lattice to be confronted with anything else in this 3D world because all directions are already taken up.
From Nobel Lecture (7 Dec 1996), 'Discovering the Fullerenes', collected in Ingmar Grenthe (ed.), Nobel Lectures, Chemistry 1996-2000 (2003).
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For Christmas, 1939, a girl friend gave me a book token which I used to buy Linus Pauling's recently published Nature of the Chemical Bond. His book transformed the chemical flatland of my earlier textbooks into a world of three-dimensional structures.
'What Holds Molecules Together', in I Wish I'd Made You Angry Earlier (1998), 165.
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From a mathematical standpoint it is possible to have infinite space. In a mathematical sense space is manifoldness, or combinations of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, the 10-dimension system.
As quoted in 'Electricity Will Keep The World From Freezing Up', New York Times (12 Nov 1911), SM4.
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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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If I’m concerned about what an electron does in an amorphous mass then I become an electron. I try to have that picture in my mind and to behave like an electron, looking at the problem in all its dimensions and scales.
Quoted in Timothy L. O’Brien, 'Not Invented here: Are U.S. Innovators Losing Their Competitive Edge?', New York Times (13 Nov 2005), B6.
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Maxwell's equations… originally consisted of eight equations. These equations are not “beautiful.” They do not possess much symmetry. In their original form, they are ugly. …However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls “beauty.”
In 'Quantum Heresy', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 130. Note: For two “beauty” criteria, unifying symmetry and economy of expression, see quote on this page beginning “When physicists…”
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My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect in the Unseen residing,
And thine doth like a convict sit,
With marline-spike untwisting it,
Only to find its knottiness abiding;
Since all the tools for its untying
In four-dimensional space are lying,
Wherein they fancy intersperses
Long avenues of universes,
While Klein and Clifford fill the void
With one finite, unbounded homoloid,
And think the Infinite is now at last destroyed. (1878)
A parody of Shelley as 'A Paradoxical Ode', quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (1882), 649-650.
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Scientists often invent words to fill the holes in their understanding.These words are meant as conveniences until real understanding can be found. … Words such as dimension and field and infinity … are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean.
In God’s Debris: A Thought Experiment (2004), 20-21.
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The dance is four-dimensional art in that it moves concretely in both space and time. For the onlooker, it is an art largely of visual space combined with time. But for the dancer, and this is more important, the dance is more a muscular than a visual space rhythm, a muscular time, a muscular movement and balance. Dancing is not animated sculpture, it is kinesthetic.
In Art Is Action: A Discussion of Nine Arts in a Modern World (1939), 56.
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The greatest advantage to be derived from the study of geometry of more than three dimensions is a real understanding of the great science of geometry. Our plane and solid geometries are but the beginning of this science. The four-dimensional geometry is far more extensive than the three-dimensional, and all the higher geometries are more extensive than the lower.
Geometry of Four Dimensions (1914), 13.
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The mind of God we believe is cosmic music, the music of strings resonating through 11 dimensional hyperspace. That is the mind of God.
From online article with video 'Math is the Mind of God', (29 Dec 2012) on website of bigthink.com.
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Yet I exist in the hope that these memoirs... may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.
Flatland (1899), 154.
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[S]ome physicists describe gravity in terms of ten dimensions all curled up. But those aren't real words—just placeholders, used to refer to parts of abstract equations.
In God's Debris: A Thought Experiment (2004), 20-21.
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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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