The true elements of the material world, Timaeus says, are not earth, air, fire, and water, but two sorts of right-angled triangles, the one which is half a square and the one which is half an equilateral triangle... The above two sorts of triangles, we are told, are the most beautiful forms, and therefore God used them in constructing matter. By means of these two triangles, it is possible to construct four of the five regular solids, and each atom of one of the four elements is a regular solid. Atoms of earth are cubes; of fire, tetrahedra; of air, octahedra; and of water, icosahedra. (I shall come to the dodecahedron presently.)...
The regular tetrahedron, octahedron, and icosahedron, have equilateral triangles for their faces; the dodecahedron has regular pentagons, and cannot therefore be constructed out of Plato's triangles. For this reason he does not use it in connection with the four elements.
As for the dodecahedron, Plato says only "there was yet a fifth combination which God used in the delineation of the universe." This is obscure, and suggests that the universe is a dodecahedron; but elsewhere it is said to be a sphere. The pentagram has always been prominent in magic... It seems that it owed is properties to the fact that the dodecahedron has pentagons for its faces, and is, in some sense, a symbol of the universe.
Bertrand Russell, The History of Western Philosophy
Saturday, December 01, 2007
Works Cited
These [Pythagorean] studies are not to be pursued in any utilitarian spirit, but in order to prepare [the young man's] mind for the vision of eternal things. In astronomy, for example, he is not to trouble himself too much about the actual heavenly bodies, but rather with the mathematics of the motion of ideal heavenly bodies. This may sound absurd to modern ears, but, strange to say, it proved to be a fruitful point of view in connection with empirical astronomy...
The apparent motions of the planets, until they have been very profoundly analysed, appear to be irregular and complicated, and not at all such as a Pythagorean Creator would have chosen... The problem thus arose: is there any hypothesis which will reduce the apparent disorderliness of planetary motions to order and beauty and simplicity?... Aristarchus of Samos found such a hypothesis: that all the planets, including the earth, go round the sun in circles. This view was rejected for two thousand years, party on the authority of Aristotle... It was revived by Copernicus, and its success might seem to justify Plato's aesthetic bias in astronomy. Unfortunately, however, Kepler discovered that the planets move in ellipses, not in circles, with sun at a focus, not at the centre; then Newton discovered that they do not move even in exact ellipses.
Bertrand Russell, The History of Western Philosophy
The apparent motions of the planets, until they have been very profoundly analysed, appear to be irregular and complicated, and not at all such as a Pythagorean Creator would have chosen... The problem thus arose: is there any hypothesis which will reduce the apparent disorderliness of planetary motions to order and beauty and simplicity?... Aristarchus of Samos found such a hypothesis: that all the planets, including the earth, go round the sun in circles. This view was rejected for two thousand years, party on the authority of Aristotle... It was revived by Copernicus, and its success might seem to justify Plato's aesthetic bias in astronomy. Unfortunately, however, Kepler discovered that the planets move in ellipses, not in circles, with sun at a focus, not at the centre; then Newton discovered that they do not move even in exact ellipses.
Bertrand Russell, The History of Western Philosophy
Works Cited
Philosophy, for Plato, is a kind of vision, the "vision of truth." It is not purely intellectual; it is not merely wisdom, but love of wisdom... Everyone who has done any kind of creative work has experienced, in a greater or less degree, the state of mind in which, after long labour, truth, or beauty, appears, or seems to appear, in a sudden glory...
This experience, I believe, is necessary to good creative work, but it is not sufficient; indeed the subjective certainty that it brings with it may be fatally misleading. William James describes a man who got the experience from laughing-gas; whenever he was under its influence, he knew the secret of the universe, but when he came to, he had forgotten it. At last, with immense effort, he wrote down the secret before the vision had faded. When completely recovered, he rushed to see what he had written. It was: "A smell of petroleum prevails throughout."
Bertrand Russell, The History of Western Philosophy
This experience, I believe, is necessary to good creative work, but it is not sufficient; indeed the subjective certainty that it brings with it may be fatally misleading. William James describes a man who got the experience from laughing-gas; whenever he was under its influence, he knew the secret of the universe, but when he came to, he had forgotten it. At last, with immense effort, he wrote down the secret before the vision had faded. When completely recovered, he rushed to see what he had written. It was: "A smell of petroleum prevails throughout."
Bertrand Russell, The History of Western Philosophy
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