The six hexagram pairs of Great Purity
– Emblem of the revolution of the earth around the sun.
A square standing on a corner with a circle in it and a cross connecting the corners – the emblem for the number of days in the year.
Just as there are hexagram pairs of Great Harmony, so there are hexagram pairs of Great Purity. Eight hexagram pairs of Great Harmony and six hexagram pairs of Great Purity. Of the latter, only six, as the the double signs have no mirror partners.
The eight hexagram pairs of Great Harmony form the emblem of Mother Earth. But what emblem represent the six hexagram pairs of Great Purity?
If they are graphically represented in the circle of Early Heaven they form a square standing on a corner with a cross connecting the corner of this figure (Fig. 1).
The Earth-Emblem is formed by the eight hexagram pairs of Great Harmony. What may form the six hexagram-pairs resp. 12 hexagrams of Great Purity. The number twelve could mean that they have something to do with time, with the twelve lunar months in the year or the twelve double-hours a day.
Purity is something that is reserved for the sky. For the Earth the Old Chinese wished harmony, but the earth was not thought to be a place of great purity. As purity is a property of the sky, the twelve hexagrams of Great Purity could have something to do with the sky. But these hexagrams also represent graphically a square standing on a corner with a cross in it. This is in a slightly distorted way also the Emblem for Mother Earth..
According to the commentary of R. William to the second line of hexagram 2, the double sign Earth, the square is the symbol of the earth, just as the circle is the symbol of heaven.
Square and circle in ancient China played a special role in mathematics. This emerges from a mathematical work, whose title is:
„The classical arithmetic of the gnomon (gnomon to determine the low sun) and the circular path of heaven.“
It is apparently created in the 6th Century BC.
In an interview there is mentioned a theorem about the right-angled triangle, which is known in the West as the Pythagorean theorem.
Furthermore,mentioned is the importance of the circle in a square, which was obviously regarded as fundamental:
„… The art of counting“, it says there, „goes back to the circle and the square. The circle is derived from the square and the square from a rectangle …
The square belongs to the earth, the circle to the sky because the sky is round and the earth square ….“ In this text, so too the square represents the earth and the circle the sky. Square and circle are described as closely related.
The square-figure standing on a corner with a cross connecting the corners, as shown in Fig. 1, together with the circle could characterize the earth in its connection with the sky. In the figure, a measure is included, which reflects the role of Earth in its relationship to the circling of the sun.
The I Ching was used not only as an oracle and book of wisdom, but also a solar-lunar calendar, which showed the farmers the right time to pursue their activities in harmony with the DAO. For the people of earlier times living on agriculture, the knowledge of the number of days in the year and the dates of the equinoxes and solstices were of great importance and by no means self-evident.
The moon determined the length of the synodic month of 29 ½ days, the sun the length of the solar year of 365 ¼ days. The ancient Chinese calendar was not limited to the fixing of years, months and days. It also included predictions of the apparent movement of the sun, moon and five visible planets, and it also contained the prediction of solar and lunar eclipses.
Each of the six pairs of parallel lines represents a hexagram pair, a hexagram with an odd and the following hexagram with an even atomic number. There are only six hexagram-pairs, who are also pairs of lines.
The (female) hexagram with the straight atomic number of a pair contains the same trigrams as the male, but the order is reversed. The two partners mirror each other. Therefore they are a hexagram-pair of Great Purity.
Most of the 12 hexagrams of Great Purity contain a predominantly favorable prognosis.
The following table contains the names of the 12 hexagrams of Great Purity and also the 12 solar periods for which they stand:
Table 1
The six hexagram pairs of Great Purity
Hexagram Solar period
5) Waiting 5 End of Spring
6) Conflict 6 End of Spring
7) The Army 7 Early Summer
8 ) Holding Together 8 Early Summer
11) Peace 11 End of Summer
12) Standstill (Stagnation 12 End of Summer
13) Fellowship with Men 13 Early Autumn
14) Possession
in Great Measure 14 Early Autumn
35) Progress 11 End of Summer
36) Darkening of the Light 12 End of Summer
63) After Completion 15 Autumn Equinox
64) Before Completion 16 Autumn Equinox
274 = Total of the Ordinal numbers
If you look at the name of hexagram 36, which represents one of the lines in the table above, one is astounded, because her name is: „The eclipse of light.“ The combination of the atomic number and the name of hexagram 36 apparently refers to the 36 days of the year in which the light of the moon is eclipsed.
(In every lunar month the moon for three days is virtually invisible.)
(If you add up the numbers 1 to 36: 1 +2 +3 … +36, so is the result the number 666. In the West, the number is ambivalent because it is both the number of the beast of the apocalypse as well as the number of Hakathriels, the Angel of sovereignty. In the Kabbalah 666 is the number of Sorath, the solar demon who stands opposite the Archangel Michael.)
The eight hexagram-pairs of Great Harmony represent no winter- months. The same applies for the six hexagram pairs of Great Purity. The end of summer is twice represented.
If you add the atomic numbers of the twelve hexagrams of Great Purity, so is the result the number 274.
This is a very special number!
The reciprocal of 274 is the number 365, the number of days in the year.
The square around a circle is also a symbol for the connection of the earth with the sky! Why?
The figure provides the measure, on which the motion of the Earth is embedded in the solar system.
When the Earth in a year rotates once around the sun, the earth has rotated 365.24 times around itself. For the ancient Chinese, it was of course the sun, which revolves around the earth. In the centuries before our era, when the I Ching received its final form, it was known in China that the length of the solar year is 365 1 / 4 days. The part of the orbit, the Earth every day covers, is 1 / 365, 25 = 0.002737, rounded up to 0.00274 (mean value). This is also the sum of the atomic numbers of the twelve hexagrams of Great Purity.
But what has this speed, the reciprocal of the number of days per year, to do with the pictorial representation of hexagrams, forming a square? The reason for this is that you get in this way the number sequence 274 in a second way.
When you in the square in Fig. 1 draw a circle with the circumference 1 then the following applies:
The difference between square and circle circumference is
Csquare – Ccircle 4/Pi – 1 = 0.274
The difference between the circumference of the square and the circumference of the circle is thus again the number sequence 274.
The number pi is here, as mentioned, set at 3.14.
Pi is a dimensionless quantity that appears in mathematical formulas that have to do with the calculation of perimeter, area, or content of circle or sphere. In physics formulas, Pi usually arises because the fundamental forces of nature are isotropic, ie they prefer no direction in space.
The reciprocal of 0.274 is again the number sequence 365, so the number of days in the year. This relationship between square and circle was likely known in ancient China and has been supplied the reason why the twelve hexagrams of Great Purity form a square and the sum of their atomic numbers is the number sequence 274.
The number sequence 274 is itself an emblem. M. Granet, in his book „The Chinese Thinking“ repeatedly pointed out that the quantitative significance of numbers in ancient China was far behind its symbolism. If anyone has a number of great symbolic value for the position of Earth in the cosmos, then it is the number sequence 274, fewer than the average daily rate, but above all because its reciprocal is the number of days per year.
If could be deduced from the movements of heavenly bodies or from constructions a number, then it was believed, that this number was corresponding to the divine order. This may have been the case for the number sequence 274. If now, still providing for the movement of the earth around the sun, the same sequence of numbers was received as a geometric relationship between a square and the enclosed circle, then it was assumed that between the geometric figure and the apparently movement of the sun around the earth was a connection. The figure, shown here, was therefore particularly suitable for display as an emblem of the most important relationship between heaven and earth.
In the calculations here it was assumed that the number Pi (3.14), the ratio of circumference to diameter of a circle, the Chinese at the time, when the I Ching got its final form, was at least known until two digits after the decimal point. They then had in regard to Pi the same knowledge as the Greek Archimedes in the third century BC
The relationships here spoken of were probably also viewed as confirmation that it was right to choose as a symbol for Mother Earth the square and as a symbol of the heaven the circle.