The Harmony of Being | Geometry in Man, Nature, and Cosmos

Proportional roots: (a) the √2 proportion, (b) the √3 proportion,
and (c) the golden mean (Phi) proportion.

Loai M. Dabbour (2012) - Geometry describes the assertions of a mathematical order of the intrinsic nature of the universe. Geometry is the very basis of our reality, and we live in a coherent world governed by underlying laws. Johannes Kepler stated that geometry is underpinning the cosmos, which was based on Plato’s ideas that God created the universe according to a geometric plan. The structure of the universe is determined by and revealed as certain mathematical and geometric constants which represent a confirmation that proportions are the underlying fabric of nature. This can be seen in man, nature, and cosmos.

Root proportions based on the square.

By contemplating geometric proportions, an understanding towards the sacred truth can be obtained since geometric proportions are one of the definitive geometric qualities of life itself. The Holy Quran tells us that man has within himself all what is reflected in the universe - the best proportions. Man is the core of God’s creatures; he possesses the most harmonious proportions, reflecting of the Divine harmony of being. "We have indeed created man in best of forms" – proportions (Surah At-Tin, 95:4). Leonardo da Vinci illustrated the mathematical proportions of the human body, showing that human being exhibits clearly golden mean proportions in his body based on ratios of 1.618.The Vitruvian Man drawn by Leonardo Da Vinci is based on Vitruvius, who believed that if human proportions could be incorporated into buildings, they would become perfect in their geometry. According to Vitruvius, the distance from fingertip to fingertip should be the same as that from head to toe. The sacred mean rules can be seen in the ratios of body parts throughout the human body. The human body contains in its proportions all the important geometric geodesic measures and functions. The proportions of ideal man are at the center of a circle of invariant cosmic relationships.

Proportions of Venus’ and Earth’s mean orbits.

The mathematical harmony of the universe can be seen from the proportions of the planets in our solar system. For example, the ratio of the sacred mean can be seen in the rotations of Venus and Earth around the Sun in that for each five years that the Earth rotates around the Sun, Venus rotates around it eight times. The connection between 5 and 8, both of which are Fibonacci numbers, is the golden mean proportion (8/5 = 1.6). The result of this motion is that Venus draws a pentagon around the Sun every eight years (Figure A). Figure B shows that a circle is drawn, which represents Venus’ mean orbit. A pentagon is constructed inside it and a small circle placed through the arm-crossing points. The radius of this small circle divides the radius of the large one into golden sections and can be used to space Venus’ orbit from Earth’s orbit. It can be seen from the agreement between eightfold and fivefold geometries that eight touching circles are drawn from Venus’ mean orbit. In turn, the circumference circle is enclosing these eight circles, defining Earth’s mean orbit. The ratio of the mean orbits of Venus’s to Earth is the √2 proportion. The geometric representation of these orbits creates the golden mean proportion.

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. 

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.

“Live As On A Mountain. Let Men See.”

“Men exist for the sake of one another”

[...] Consider that everything is opinion, and opinion is in thy power. [...] He who does not know what the world is, does not know where he is. And he who does not know for what purpose the world exists, does not know who he is, nor what the world is. But he who has failed in any one of these things could not even say for what purpose he exists himself. What then dost thou think of him who avoids or seeks the praise of those who applaud, of men who know not either where they are or who they are?

 [...] Say to yourself in the early morning: I shall meet today inquisitive, ungrateful, violent, treacherous, envious, uncharitable men. All these things have come upon them through ignorance of real good and ill. [...] Men exist for the sake of one another. Teach them then or bear with them. [...] Very little is needed to make a happy life. [...] Know the joy of life by piling good deed on good deed until no rift or cranny appears between them. [...] Have I done something for the general interest? Well then I have had my reward. Let this always be present to thy mind, and never stop doing such good.  [...] He who fears death either fears to lose all sensation or fears new sensations. In reality, you will either feel nothing at all, and therefore nothing evil, or else, if you can feel any sensations, you will be a new creature, and so will not have ceased to have life. [...] Live as on a mountain. Let men see, let them know a real man who lives according to nature. If they cannot endure him, let them kill him. For that is better than to live thus." - Roman Emperor Marcus Aurelius Antoninus (121 – murdered 180 AD): Meditations

Confucius In The Age of Oligarchy

"Better light a candle
than curse the dark."

One great tradition of anti-oligarchical thinking in world culture stems from the influence of Confucius (551-479 BC). Confucianism can perhaps best be understood as a movement to save Chinese civilization from oligarchical depredations. Confucius starts from a standpoint very much like that of Plato (428-348 BC): the need to secure good government capable of promoting the general welfare. Confucius recognized that most governments in the divided and balkanized China of his time were unacceptable. 

The main political issue was the incessant private warfare of the Zhou dynasty military nobility, which served no useful purpose, but kept the country weak and divided, with no effective central government. According to Confucius, bad government derived from the fact that rulers and high officials lacked the character and qualifications to serve the common good. 

Sun Yat-Sen, Provisional President,
Republic of China (1912), the first
Republic in Asia: "Of the people, by
the people, for the people."

Confucius thought the main reason for this incompetence was the status of the rulers and hereditary aristocrats around them. He regarded most of them as parasites, and wrote in his Analects: 

“It is difficult to expect anything from men who stuff themselves with food the whole day, while never using their minds in any way at all. Even gamblers do something, and to that degree are better than these idlers.”
 
Like Plato he argued that government needs to be in the hands of the most capable and competent. Ability has nothing to do with birth, nobility, or wealth, but depends on character and knowledge alone, which in turn are the results of education. Confucius called for careers open to talent, in which appointment and advancement would be based on ability, not on property, hereditary rank and title. Contrary to this, oligarchy represents an irrational principle based on domination and repression, justified neither by merit and ability, nor by the results achieved.

“Wealth will not help a pilot to navigate his ship.”

“Out of Oligarchy arises Democracy”

Plato's Republic (Book VIII - 380 B.C.E.):

[...] What manner of government do you term oligarchy? 
A government resting on a valuation of property, in which the rich have power and the poor man is deprived of it. [...] Oligarchy is more or less exclusive; and they allow no one whose property falls below the amount fixed to have any share in the government. These changes in the constitution they effect by force of arms, if intimidation has not already done their work.

[...] How does the change from oligarchy into democracy arise?
Democracy comes into being after the poor have conquered their opponents, slaughtering some and banishing some, while to the remainder they give an equal share of freedom and power. [...] That is the nature of democracy, whether the revolution has been effected by arms, or whether fear has caused the opposite party to withdraw. [...] The people, consisting of those who work with their own hands, when assembled, is the largest and most powerful class in a democracy.