To Plato each perfect solid represented the essence of its :orresponding element so, when his contemporary Theaetetus pointed out to him that the dodecahedron was the fifth regular polyhedron (there are only five), Plato postulated a fifth essence in prder to unify his geometric model of the world. In the fifth century bc Parmenides of Elea and his pupil Zeno hypothesised that the universe consisted of a single substance, “Oneness”, which was motionless and of infinite mass, enveloping all things without any space between them.
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So complex was Ptolemy’s system that in the 13th century Alfonso the Great, seeing the labors of his astronomers, is said to have remarked that had he been present at the Creation he would have given the Lord some hints about simplification. In the 17th century, Kepler thought he had found in these five forms the secret of the planets’ arrangement in the solar system. The Ptolemaic conception of the cosmos dominated both Arab and European views of the heavens until the 17th century, when Kepler, Newton and others radically re-envisioned the universe, replacing the cosmic gears with a quasi-infinite network of stellar masses held in place by the force of gravity.
The 17th century Dutch physicist Christiaan Huygens applied the idea to light, which he regarded as a disturbance of an omnipresent “luminiferous ether”. In the 12th century ad the English prelate Robert Grosseteste, who is widely considered to be one of the founding fathers of empirical science, regarded light as the most elementary substance and the primary constituent of the world. The fifth, the dodecahedron, he equated with the supposed fifth element, or quintessence, the mysterious substance of which the celestial bodies were said to be composed.
The Aristotelian picture iscompleted by the “upper activity” of he superlunary world of planets and stars, whose “physicality”, mquestionably real and tangible as it is, consists of the fifth element, quintessence. The four element system was adopted by Plato, whose Timaeus describes the sublunary world as subject to a series of transformations – birth-corruption-death – of the four elements brought into being by the Creator. Johannes Kepler, the great precursor to Isaac Newton and the founding father of modern astrophysics, envisioned the universe as God’s play: As he saw it, the aim of the astronomer was to learn to play God’s game.
In general Aristotle appropriated the Platonic model of the :osmos, but he did not adopt the idea of a correspondence between he elements and the regular solids. After Aristotle the nature of the fifth element changed repeatedly and was the subject of constant debate. There is, however, a fifth regular polyhedron, the dodecahedron, vhich consists of 12 pentagons and is therefore the three-limensional equivalent of the pentagon, considered to be a “magic” nape. Just as a windup ballerina can be made to perform a complex dance, even though her mechanism consists only of circular gears, so cosmologists for 2,000 years believed the motions of the heavenly bodies could be described by an intricate celestial clockwork.
In the 19th century, the French mathematician Jean Baptiste Joseph Fourier demonstrated that, in fact, any periodic motion can be described by a combination of circular motions. Take, for example, the Greek and medieval view that the dance of the planets and stars must be explained by a combination of strictly circular motions. The Greeks in particular put forward ideas as to its composition: in keeping with their belief in a rational, unified and harmonious universe, not only did there have to be a limited number of fundamental elements, but there must also be laws governing their combination and transformation.
Any macroscopic conception of the universe is also a conception of its microscopic structure. Of interest is the moment at the robot end-effector, which represents the point in the robot structure with the highest load resulting from the apparent forces, due to the greatest moment arm from the point of application. He turned out to be wrong, but, bizarrely, the idea of a polyhedral arrangement to the cosmos has resurfaced within the framework of general relativity, which allows for some truly extraordinary topologies, including ones in which space takes on a pseudo-crystalline structure.
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Plato thought carefully about the relationship between each element and its representative shape: for example, a cube is the most difficult shape to move, so it is associated with earth, the heaviest element; an icosahedron has more sides than any other Platonic solid (five triangles meet at each point), giving it a virtually round, fluid structure which is most clearly associated with water; and so on. “Celestial Treasury” includes an exquisite computer image of this enigmatic spatial structure from the Geometry Center at the University of Minnesota. Replete with extended foldouts and delicately detailed inserts, “Celestial Treasury” is a stunningly beautiful survey of the science, mythology and iconography of the cosmos through the ages. Ostensibly a history of (primarily Western) cosmological thinking, “Celestial Treasury” advances a far more radical agenda. болки в кръста тумор
. As with two recently ended and superb exhibitions in our own city-“Treasures of the Great Libraries of Los Angeles” at the UCLA Hammer Museum and “Devices of Wonder” at the Getty-“Celestial Treasury” demonstrates that science can be an engine not only of knowledge but also of aesthetic inspiration.