Plato's design systems that reduce the apparent irregularities in the Essay

Platos design systems that reduce the apparent irregularities in the motions of the planets to regular motions in perfectly re - Essay moralPlatos later dialogues abound in mathematical allegories. Timaeus begins with a very long one, Statesman contains a short one, the Republic has three, and both Critias and Laws are permeated with them from beginning to end. When Plato died in 347 B.C. his pupils and friends immediately began to argue about these mathematical constructions and about Platos purpose in using them for models of souls, cities, and the planetary system. By the beginning of the Christian era much of Platos maths had become a riddle. Many rivals clamored for recognition as the single harmony Socrates heard from the planets.1 A certain number which he confidently proclaimed monarch butterfly in political theory was labelled numero Platonis obscurius by Cicero (c. 100 A.D.), with the hearty concurrence of later scholars an interpretation which Nicomachus promised at abo ut this time was either missed or never written. By the fifth century A.D., Proclus, one of the last to head the Platonic Academy, could not pretend to understand Platos arithmetic, although he was astute overflowing to label as spurious a then popular interpretation of the Timaeus World-Soul. Down through history Platos mathematical allegories defied Platonists either to reconstruct his arithmetic or to find in it the implications he claimed for it. In 1937 Francis Cornford, concluded that the difficulties which arise in abstracting a planetary system from Platos musical arithmetic in Timaeus were due to a metal armillary sphere which the Academy possessed. Plato probably had it before him as he wrote.5 In 1945, in his translation of the Republic, Cornford not only omitted the super obscure description of Socrates sovereign number, but he also allowed himself to simplify the text of the tyrants allegory. The theoretical cosmic psychologies proposed by Plato found practical appli cation in the work of Claudius Ptolemy. Ptolemy has a claim to being the most influential of classical astronomers on account of the respect with which his encyclopaedic work on mathematical astronomy, the Syntaxis, or Almagest. While the Almagest, is usually the centre of attention when Ptolemys astronomy is examined, if his cosmology is to be understood on its own terms, its purpose cannot be understood independently of dickens of his other works, the Harmonics and the Tetrabiblos, in both of which he raised the souls relationship with the stars. Ptolemy his work in two phases, the first was concerned with the measuring of celestial positions and the second with the measurement of their effects which was foundations of western astrology. Those effects might be felt in the natural world but also in the psychological, the realm of the soul. Ptolemys psychological astronomy can be divided into two forms, the contemplative and the analytical. Kepler was also influenced by Platos Ide as. He used Platos regular solids to describe planetary motion. He assigned the stoppage to Saturn, the tetrahedron to Jupiter, the dodecahedron to Mars, the icosahedron to Venus, and the octahedron to Mercury. He is remembered in the history of sciences for his three planetary laws. Keplers first law abolishes the old axiom of the circular orbits of the planets. The second law breaks with another axiom of traditionalistic astronomy, according to which the