Nine comments to the lost Manuscript Yi Jīng

The gobelin. The illustration is given in books by Waddell «The Buddhism of Tibet» and Carus «Chinese thought». Its dating and author are unknown. Geometry of the gobelin conforms to the structure of the Sierpinski carpet with the exception of the fact that geometric base of the Sierpinski carpet contains 9x9=81 cells (3⁴ power) around the perimeter, while the gobelin has 8x9=72 cells (the symmetry of hexagonal structure tending to the symmetry of sphere 6x12).

The pattern of Lo Shu square in the centre of the gobelin and its conformity with Tibetian numerals in Lo Shu square. Correspondence of number system in Lo Shu square with trigrams on the gobelin.

As trigrams Dui and Zen are placed towards the centre in the way different from other trigrams, they have different value and different numbering when the gobelin is rotated (the centre of Lo Shu square remains fixed).

Correspondence of trigrams numbering when the gobelin is rotated.

Numerical values of Li (fire) and Kǎn (water) trigrams changed from 5 and 1 to 3 and 7.

The ancient pattern of Ho Tu and numeric equivalent of Ho Tu pattern in accordance with trigrams numbering on the gobelin.

Correspondence of numerical values of trigrams in accordance with the rule depicted on the gobelin:

We can ask a question why the numerical value 9 found in Ho Tu pattern is not found among trigrams and why 9 can be substituted with 5. We find the answer in symbolic values of these figures in Ancient Chinese culture. 5 is symbolically reflected in five elements which are a foundation of the Universe. The first five elements together with the symbolic element of the Sky establish the Initial Triad: the Sky, a Man, the Earth on the diagram of the «Supreme Ultimate». If we count 9 elements starting with the first one (the Sky), from the right and left side we get identical structure (a square (rhombus 8x8) on the plane), indicated by the elements the Sky, Fire, Water, the Earth in the scale repeating the initial structure. Under the rule of symmetry, trigrams in HoTu pattern line up in two orders according to the numerical values.

*trigrams Dui and Kūn form stable geometric patterns – the circle and the cross – which does not make it possible for us to designate them through one figure but makes it possible to designate them through the numerical value 1 which forms a circle and a cross (1(10) and 1(5)). Two orders of trigrams form «symbols» (сян) - Тай yin, Шао ян, Тай ян, Шао yin - from two figures «М»ВОДМП and «М»ОВД(«М»)П on the diagram of the «Supreme Ultimate».

Two quadrangles with apices «М»ВДМП and «М»ОВДП form Тай yin and Тай ян. Each of two initial figures do not include two triangles. We cannot answer the following question at this moment: why in the order TIĀN, LI, KAN, XЩN, (DUI), «KŪN» on the diagram of the «Supreme Ultimate» element M – metal (hexagram Dui) is not symmetrically considered. Rules of symmetry let us factor out this element of the general graphic scheme.

Moving from one figure to another Шао ян and Шао yin are formed. Тай yin forms quadrangle with apices (clockwise) ОДМВ and quadrangle «М»ВМП, Шао ян form quadrangles (from left to right, the left quadrangle is the upper line, the right one is the lower line) «М»ВМП and «М»ПДО, Тай ян = «М»ПДО + triangle ОДВ, Шао yin = ОДВ + ОДМВ from left to right: Тай инь, Шао ян, Тай ян, Шао yin which form unified order of trigrams: KŪN - ZHИN - DUI - KAN - XЩN - TIĀN - LI - GИN (trigrams are formed downwards on scheme: 2, 3 and the 4th level of lines (Yбo): the black colour – a broken line (Zhй), the white colour – a single line (dǎn).

This structure corresponds to the Cantor set. If we put the unified order of trigrams on the diagram of the «Supreme Ultimate» we get the pattern of «Ursa Major» constellation or Sān wǔ structure (the constellation is outlined on the plane), where the beginning and the end of the constellation relate to the «Inherent truth» (Zhong fu, 中孚).

P - Phekda (3) - Sky Pearl (Tian Zi) 天用 (a pearl of irregular shape, celestial sphere), «M» - Alioth (5) – Nephrite axis (Yщ hйng 衡 ), П – Alkaid (7) – Flaring Light (Yao Guang 光), M - Dubhe (1) - Sky shift (Тянь шу) 天 Ш.

The eight line of Yi Jīng, in which a hexagon structure (a tortoise shell) and the structure of «Ursa Major» constellation are described with hieroglyph ۩, is dedicated to Sānwǔ structure as a method to prevent chaos expansion.

Using a method of forming 64 hexagrams from the diagram of “Supreme Ultimate” and unified order of trigrams: KŪN - ZHИN - DUI - KAN - XЩN - TIĀN - LI - GИN, we get certain sequence order of all 64 hexagrams that we superimpose on the “Mǎwanduī” order of hexagrams (The name is taken form the place of archeological excavations in province Hunan (China), where the oldest copy of the Book of Changes dated the II century BC was found). In the table hexagrams are set in «Mǎwanduī» order. The number above a hexagram shows its sequence number in the scheme of formation of 64 hexagrams from the «Supreme Ultimate». The figure next to a hexagram shows its number in Вэнь-вана’s order (in a form of a table). Numbers of red color shows the order of lines.

Having the order of hexagrams where «the Supreme Ultimate» and Mǎwanduī copy of «the Book of Changes» in their structure do not contradict one another we get the initial text of the Book (given version written from left to right in «European style» that might not coincide with Ancient Chinese text structure written “top-down”). Two hexagrams highlighted red are corresponded to two trigrams Kūn and Gиn.

Because of a part of hexagrams being designated with two hieroglyphs, the clearly outlined square 8x8 is not observed in the initial structure, though unconditionally the square is the graphical basis of the Book itself.

An objectivity in relation to archeological artifacts either manuscript or an element of architectural style requires professional evaluation and knowledge which is necessary for that evaluation, but «The Book of Changes» allow to mention facts easy to understand and interpret even for a person who do not know Ancient Chinese grammar. Due to that, the final chapter is devoted to following questions:

1. The meaning of the hieroglyph 10 in the second line of the Book of Changes and it’s possible connection to Ancient Hindu deity named Rudra.

2. The meaning of the hieroglyphs 4-9 in the eighth line of the Book of Changes.

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