Wheels of Time

72

5 + 12 + 15 + 40

V + XII + XV + XL

The Fires of Heaven, book 5 of Wheel of Time, art by Dan Dos Santos

As we accompany each other on our journeys ― as we choose to, some while ago ― She has my back and I have Hers. That is we mutually protect, defend, save, stand up for, guard, shield, watch over, safeguard, and shelter. Together we experience, enjoy 180°x2, 360° peripheral vision, a spherical viewing as for instance, from inside and at the very centre of a G•ode.

She is Her', Ἥρα (Hḗra) 陰, and watches the 6 of this Her•mit, IX.

― Ἥρᾱ • (Hḗrā), is the Pythagorean name for nine, 9 ―

The Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers.

• The number 一 one (䷀ the monad) represented — 有 — the origin of all things, 名萬物之母。
• The number 二 two (䷁ the dyad) represented matter, 坤, sacred or 坎, ䷜ profane 29, the Two Ἥρα.
• The number 三 three was an "ideal number" because it had a beginning, middle, and 2end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo.
• The number four signified the four seasons and the four elements.
• The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month.

They believed that odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage because it was the sum of two and three.

X

Ten was regarded as the "perfect number" and the Pythagoreans honoured it by never gathering in groups larger than ten.

Pythagoras was credited with devising τετρακτύς, the Tetractys, the triangular figure of four rows that add up to the perfect number, ten. The Pythagoreans regarded τετρακτύς, the Tetractys as a symbol of utmost mystical importance. Iamblichus, in his Life of Pythagoras, states that τετρακτύς the Tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it.

τετρακτύς, Tetractys, Divine Proportion

The Pythagoreans were especially fascinated by the presence of numbers in the natural world. Perhaps their most spectacular discovery was that musical harmony is related to simple whole-number ratios. A string (such as that on a harp) produces a note with a particular pitch; a string one-half as long produces an extremely harmonious note to the first, now called the octave. A string two-thirds as long produces the next most harmonious note, now called the fifth. And one three-fourths as long produces the fourth, also very harmonious. The Pythagoreans discovered these facts empirically by experimenting with strings of different lengths. Today these harmonies are traced to the physics of vibrating strings, which move in patterns of waves. The number of waves that can fit into a given length of a string is a whole number, and these whole numbers determine the simple numerical ratios. When the numbers do not form a simple ratio, the corresponding notes interfere with each other and form discordant “beats” that are unpleasant to the ear. The full story is more complex, involving what the brain becomes accustomed to, but there is a definite rationale behind the Pythagorean discovery. This later led the German astronomer Johannes Kepler to the concept of the “music of the spheres,” a kind of heavenly harmony in which the planets effectively produced tunes as they moved across the heavens. Some of Kepler’s theories about the planets, such as the elliptical shape of their orbits, became solid science—but not this one. Nonetheless, it was influential in establishing the view that there is some kind of order in the cosmos, an idea that culminated in Isaac Newton’s law of gravity.

Pythagorean symbol

1. The first four numbers symbolize the Musica Universalis and the Cosmos as:
   1. (1) Unity (Monad)
   2. (2) Dyad – Power – Limit/Unlimited (peras/apeiron)
   3. (3) Harmony (Triad)
   4. (4) Kosmos (Tetrad).
2. The four rows add up to ten, which was the unity of a higher order (The Dekad).
3. The Tetractys symbolizes the four classical elements—fire, air, water, and earth.
4. The Tetractys represented the organization of space:
1. the first row represented zero dimensions (a point)
2. the second row represented one dimension (a line of two points)
3. the third row represented two dimensions (a plane defined by a triangle of three points)
4. the fourth row represented three dimensions (a tetrahedron defined by four points)

One of the prayers of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.

Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all.^[5]

As a portion of the secret religion, initiates were required to swear a secret oath by the Tetractys. They then served as novices for a period of silence lasting five years.

The Pythagorean oath also mentioned the Tetractys:

By that pure, holy, four-lettered name on high,
nature's eternal fountain and supply,
the parent of all souls that living be,
by him, with faith find oath, I swear to thee."

It is said that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison 1:1 and the octave 2:1. Note that the diapason, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to τετρακτύς, the Tetractys of the decad, but that the diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.

τετρακτύς, the Tetractys [also known as the decad] is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself—in seedlike form—the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the mysteries of the divine realm. So revered was this ancient symbol that it inspired ancient philosophers to swear by the name of the one who brought this gift to humanity.