Showing posts with label Timaeus. Show all posts
Showing posts with label Timaeus. Show all posts

Saturday, December 12, 2015

The Same, The Other, And The Essence │ Theology of Arithmetic

“One, two, three [...] Let me tell you then why the creator made this world of generation. He was good [...] He took the three elements of the same, the other, and the essence, and mingled them into one form, compressing by force the reluctant and unsociable nature of the other into the same. When he had mingled them with the essence and out of three made one, he again divided this whole into as many portions as was fitting, each portion being a compound of the same, the other, and the essence. And he proceeded to divide after this manner: 

First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27]. After this he filled up the double intervals [1, 2, 4, 8] and the triple [1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one exceeding and exceeded by equal parts of its extremes [1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and 1/3 of 2 less than 2], the other being that kind of mean which exceeds and is exceeded by an equal number. Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243. And thus the whole mixture out of which he cut these portions was all exhausted by him.

This entire compound he divided lengthways into two parts, which he joined to one another at the center like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three [Sun, Mercury, Venus] he made to move with equal swiftness, and the remaining four [Moon, Saturn, Mars, Jupiter] to move with unequal swiftness to the three and to one another, but in due proportion.” Timaeus - Plato (360 BCE)


Johannes Kepler knew that "ubi materia, ibi geometria" (where there is Matter, there is Geometry), and "that the geometrical things have
provided the Creator with the model for decorating the whole world
". In Harmonices Mundi (The Harmony of the World, 1619) he related musical
consonance and the angular velocities of the planets, for example, the ratio between Jupiter’s maximum and Mars minimum speed is as 5:24. That
is equivalent to the interval of two octaves plus a minor third. The two octaves are eliminated by dividing 24 with 4, which gives the ratio
of 5:6, a minor third. From his studies of planetary harmonics Kepler also arrived at the bold conclusion that between Jupiter and Mars must
exist an unknown planet: "Intra Jovem et Martem posui planetum." (Between Jupiter and Mars I put a planet.") Some 170 years later the so-called
asteroid belt was found in the corresponding place. 

Saturday, December 5, 2015

SPX vs Galactic Center

Calculated and charted with Timing Solution
"The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."
Alfred North Whitehead










The Milky Way and the Sun of all Suns are the inspiration for the symbol of the Ouroboros, a serpent of light residing in the heavens, in the galactic central point of Sagittarius A*, and eating its own tail. Plato described the Ouroboros as the first living thing; a self-eating, circular being — the universe as an immortal, mythologically constructed entity. The current mathematical symbol for infinity may be derived from the Ouroboros, also known to ancient Egypt, China, Japan, India, Celts, Norse, Native American Indian tribes, Aztecs and Toltecs alike. In the iconography of Greco-Babylonian astrology, Hermeticism and Gnostic Christianity, the beginning and ending points of the sky are positioned where the ecliptic, the pathway of the Sun, crosses the galactic plane of the Milky Way (Plato's X). The galactic plane is tilted 60°to the ecliptic and is crossed by our Sun twice a year at the galactic equatorial node (the "Gate of God" ≈ 5° Sagittarius 17'245.283 degrees Nov 28), and the anti-galactic equatorial node (the "Gate of Man" 5° Gemini 17' 65.283 degrees May 26). Universal descriptions depict the distance between these points as the Ouroboros, the “tail-devourer” (Greek oura “tail”, boros “eating”), representing cyclic renewal of life and infinity, the concepts of eternity and eternal return, the cycle of life, death and rebirth, leading to immortality. The Sun will conjunct the Galactic Center - the mouth of the Ouroborus - on Dec 19 (Sat), just before the winter solstice.