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Chapter 3: The Geometric World of Spiritual Symbols
Section 1: The Geometric Origin of the Yi Gua
Section 2: Cultural Positioning and Scientific Perspective of the Yi
Section 3: Taiji Merkaba of Platonic Solid Nesting
Section 4: Hyperlink beyond Civilizations
In the previous chapter, we mainly discussed how cosmic consciousness and cosmic forces evolve based on Indian religious spiritual philosophy. Based on P.R. Sarkar's views combining primitive tantra and yoga practice, we further described the evolution of the macrocosm BC universe cycle and microcosmic mv life theory in a geometric way. This exploration process also occurred in ancient Yi Gua and sacred geometry civilizations.
The universe often shows us its incredible creativity. In many ancient civilizations, geometry is considered a sacred symbol of universal creation. Through simple geometric proportions, everything can be transformed into various forms. This is not just an imaginary totem that our primitive ancestors worshiped nature's mysterious power or just a spiritual symbol in religion beliefs. As a basic form for describing space, geometry is actually the structure of universal energy manifested through cosmic consciousness via universal forces. The geometric patterns that manifest from self-manifestation exist in everything as well as within human minds; when inner spirituality meets with external reality, these geometric symbols pointing towards the core of the universe become milestones for returning home while serving as a common language during our journey through this vast cosmos.
In the process of human civilization, the unpredictable and chaotic nature as well as the endless vitality of all things have made people feel both reverence and fear. With the accumulation of experience and continuous development of intelligence, humans have also discovered that there are simple and constant forms and orders in nature. These are patterns presented by space and time, where diverse phenomena are like clothes for the universe, woven from geometric shapes and numbers into energetic structures.
The primitive pure energy that is scattered without direction or purpose is like tiny fibers67 eventually being woven into this tangible world. Geometry and numbers carry information from universal consciousness, just like water in a container holding an ocean of energy. After a certain period of time has passed, the water in the container will ultimately return to the ocean.
From macrocosm to microcosm - including everything from human beings to celestial bodies - all things exist within various geometric containers68 that can be counted with numbers. Therefore, it is a tangible universe that can be expressed numerically69. Even concepts such as "infinity" imagined by humans based on limited water in containers remain fundamentally finite.
The universe creates itself through geometry and numbers to give birth to this world we see and feel. Thus it can be said that "Dao gives birth to one; one gives birth to two; two gives birth to three; three gives birth to all things." This refers respectively to spiritual consciousness, mind/soul, matter - from nothingness into existence: point-line-plane-body. The universe was created by order in geometrical structures and numbers. When the first cell of life appeared in this living organism called Universe along with its first Plank scale spacetime entity – mv (minus volume), 3D space emerged while time remained implicit inside it only accessible by mind/spiritual awareness . At the moment of creation of this singular element -mv (+mv) which represents an empty space element in material universe , there existed both +mv & -mv pairs even though they were not yet visible or apparent at that time . In numerical concepts such Yin-Yang pairs are considered singular entities just like Tai Chi symbol70 where Yin-Yang coexist harmoniously without any distinction between them ; they are inseparable parts forming whole system together . Before physical universe came into being , there was only simple state of Universal Mind+MV which used its conceptual geometrical prototype firelight (as per Sarkar's theory)to create shadowy counterpart- MV (-volume). As -MV proliferated/grew larger , single Universal Mind+MV transformed into pluralistic individualized fragmented forms existing within each -MV unit ; since both heart/mind +MV (-MV) and matter -MV (+MV) are pluralistic , the universe's heart/mind can use time to arrange relative positions of space, which is why time exists. Time is a special form of space that measures the universe's heart/mind creation. Then came wind-water-fire-earth phases in order followed by completion of this material world.
Regardless of pure material or living organisms, they are actually a unity of mind and matter. The total amount of +–mv in mind and matter is constant, only the proportion changes to make it appear as pure material, pure spirit or unity of mind and matter. Taking humans as an example: the dead body after death is pure material (body), the intermediate state before rebirth is pure spirit (disembodied soul), and the present moment when alive is unity of mind and matter (integrated body-mind). The reason why mind and matter can separate and combine is because there are +mv (-mv) in mind, -mv (+mv) in matter, yin within yang, yang within yin; this interaction between yin-yang results in change which is the basic characteristic of universal transformative force R△. In BC universe evolution cycle we can see that dominant R governing consciousness can develop towards inertial forces leading to materialization or towards pleasurable forces leading to spiritualization; this phenomenon belongs exclusively to life71.
The creation process of the universe forms space through geometry and evolves into a world of substance through different phases. As far as our existence in three-dimensional space is concerned, it can be traced back to five Platonic solids which constitute the five elements. These polyhedrons not only represent physical space but also manifest as expressions of consciousness and awareness within time-space dimensionality. If we substitute SRT△ for eight trigrams representing heaven-man-earth with triads 72 corresponding to spiritual-mental-physical aspects then Yi Gua will form a close explanatory relationship with sacred geometry revealing true structure behind space where geometry serves as key common language.
Section1: The Geometric Origin of the Yi Gua73
Through the description of the laws (Tao) of cosmic consciousness and operation of cosmic forces in Indian yoga spiritual science and philosophy, three interrelated spiritual, mental, and physical attributes of cosmic forces are analyzed: Sattvaguna (positive force), Rajoguna (dynamic force), and Tamoguna (inertial force). These are then corresponded to the three lines representing heaven, human, and earth in the Yi Gua. This leads to a deduction of the geometric structure underlying the Yi Jing. This structure resonates with Western civilization's sacred geometry known as "the flower of life," revealing an ancient connection between civilizations.
The Yi is not only a philosophical system explaining principles governing human society and universal phenomena but also a scientific framework proposing common geometric structures for macrocosmic universe, microcosmic individuals, and subatomic particles' energy. At a microscopic level lies microvita - basic elements shared by mind-matter.
From a perspective on spiritual science that integrates materialism, mentality, spirituality into one unified description for space-time structure.
This article attempts to provide comprehensive explanations based on Tai Chi Merkaba theory about how Yi Jing can be understood scientifically especially in terms of emerging Earth's new era spirituality science. It summarizes fundamental principles behind "geometric yi" aiming at stepping out from complicated forest-like learning materials towards vast geometrical wilderness where humanity shares core understanding about universal energy geometry across different ancient civilizations. It serves as an introduction from which readers can approach Tai Chi Merkaba or spirituality science through studying Yi Jing.
1.Introduction:
The universe is a constantly changing phenomenon, consisting of the combination and separation of matter, mind, and spirit. Change is its essence, as indicated by the basic principles of the Yi , which are simplicity, changeability, and constancy(三易).This represents a comprehensive understanding of the universe in all its aspects. Whether viewed from human biological physiology and neural function or cultural history or objective spatiotemporal structure, "three" has virtues such as balance, stability, and development. For humans,"three" is indeed a virtue that provides powerful assurance for existence. Therefore Laozi said: "The Tao gives birth to one; One gives birth to two; Two give birth to three; Three give birth to all things." 74After this point in time when the cosmic consciousness evolved into tangible material world it becomes easier to understand everything else once we grasp this fundamental principle because there are no more enumerations needed.
As with science, philosophy,and spiritual religion,easy can be used as a tool or method for people to recognize ,understand,and communicate with this material,mindful,and spiritual world that combines these three elements.This also manifests itself as an overall explanation for easy's trinity - heaven,humanity,and earth.It should be noted that "heaven,humanity,and earth" have different orders in general,"heaven,humanity,and earth" reflects subjective thinking while "heaven,humanity,and earth" reflects objective world conditions.The latter corresponds more directly to the structure of three lines eight diagrams from top down or six lines sixty-four diagrams from top down,such as 3-2-1 or 6-5-4-3-2-1.For understanding this heavenly-human-earthly structure within three-line diagrams,it will directly relate back to easy diagram patterns or more specifically,the establishment of easy geometric models.
Figure 3.1 shows an image combining day-month changes of the sun and moon with the traditional sequence of eight pre-heaven diagrams (Qian, Dui, Li, Zhen, Xun,Kan, Gen,and Kun) and their corresponding annual solar movements.
Figure 3.2 shows a square diagram of sixty-four pre-heaven diagrams that correspond to the day-month changes of the sun and moon in Figure 3.1.
2.Historical Retrospective of the Yi
From a historical perspective, we cannot help but ask: does the one-dimensional hexagram of the Yi have its predecessor? In other words, did two-dimensional or even three-dimensional hexagrams exist long before the one-dimensional hexagrams of Zhouyi? If the answer is yes, then we must face the question of the geometric origin of Yi.
The Book of Rites(周禮) records that during the Zhou Dynasty's ritual system, diviners (太卜)were responsible for enforcing three Yis(三易): Lianshan (Mountain Connection), Guicang (Returning to Storage), and Zhouyi. The subordinates of diviners called shi ren were in charge of carrying out this work. "All major national affairs are first divined and then cast." While Zhouyi is a book for casting and divination, representing philosophical levels from Spring and Autumn(春秋) to Warring States(戰國) periods, Xia Lianshan Yi (夏-連山易)and Shang Guicang Yi (商-龜藏易)before it have been lost without any surviving records. However, some related signs from these two can be found widely in practical techniques such as feng shui and fortune-telling in ancient non-mainstream academic fields; they just became obscure over time leaving people with much room for imagination or even more complexity and mystification. Among them, revealing the geometric essence behind Yi should be considered most important.
Han dynasty Xiangshu(漢-象數) school's Jing Fang Yi (Yi by Jing Fang京房) as well as modern unearthed silk books' Yì with their systems different from those in Zhouyi lead us back to two- or even three-dimensional geometry prior to Zhouyi which was more logically rigorous than that in Zhouyi itself. The evolution from physical 3D geometry into mathematical operations on 1D descriptions within Zhouyi resulted from human cultural language development along with enhanced abstract thinking ability - similar to how children grow up into adults - although growth does not necessarily mean that adults are closer to the truth than children. From this perspective, returning to the fundamental "geometry" level of Yi and stepping out of the dense forest of Yi studies back into the geometric wilderness facing towards the universe may be a meaningful path. This path still closely connects with modern science, which is no longer just about material but has always been about both matter and mind as results from one unified cosmic wave motion. The two driving forces for continuous progress in the path of Yi have been through rationalization by Principes, Emblems and Numbers (理象數) axioms and modeling via 3D geometry.
3.Geometric Structure of Eight Trigrams(八卦) and Three Lines(三爻)
The basic structure of Yi - Yin-Yang, three lines, eight trigrams - has already become highly symbolicized, mathematized symbols that can be grasped and applied; its ultimate goal is to become a carrier or manifestation pathway/method for "Li" in reality. In prehistoric times when human society was not yet systematized with written language systems, images were more concrete ways to convey real messages compared to numbers; they could be intuitively understood without thinking ability required. This inherent intuitive ability was filtered under human civilization's rational understanding into mystical experiences or dressed up in philosophy/religion/mythology until it gradually lost its essence.
Images are the first step in realizing universal principles; their fundamental form is geometry which represents initial cosmic energy structures manifested by universal consciousness itself operating within its own power field: heaven-human-earth tri-lines from top-down order. Generally drawing hexagrams from bottom-up reflects how Zhouyi's mathematical operations on grasses' divination reflect six-line hexagrams being cut sequentially along any line starting from one tri-line orthogonal intersection point among heaven-human-earth tri-lines forming two quadrants then four quadrants before finally cutting them into eight quadrants describing 3-, 2-, 1-dimensional correspondences with heaven-human-earth. This can be called the "heaven-human-earth tri-dimensional line" which corresponds to spirit, mind, and body as described in yoga science philosophy and spiritual practice.
Figure 3.3 SRT△ Tai Chi MKB in clockwise and counterclockwise rotation.
Figure 3.4 SRT△ regular octahedron Bagua unfolding diagram.
Figure 3.5 Three-dimensional trigrams (using Qian Gua as an example) of the three Yao Guas from one to three dimensions, please also refer to the "Hanshan Jade Tablet" section for supplementary explanations on "Lian Shan". The three-dimensional regular tetrahedral Gua is a two-dimensional plane Gua with the same spin direction observed from inside each face of the tetrahedron.Hanshan Jade Pisces is also known as Hanshan Jade Tablet.
Yin and Yang are changes in three-dimensional Yao, while Heaven-Man-Earth or Lingxin-Shen (matter) are attributes of three-dimensional Yao, which are manifestations of the three forces: positive energy (S-sattvaguna), transformational energy (R-rajoguna), and inertial energy (T-tamoguna). They are represented by white-red-black color waves, and basic physical force75 describes the last type of force.
A balanced force forms an equilateral triangle with white-red-black SRT clockwise or counterclockwise forming its sides. Through this Yi Gua construction process, geometric Yi represents a model of universal energy that differs from Song Confucian Shao Yong's pre-heavenly Yi learning Bagua establishment method constructed sequentially in one-two-three dimensions at once to establish eight quadrants for eight gua symbols; their processes are reversed.
Described using all five regular polyhedra inscribed within a sphere, Qian Kun gives birth to six children by dividing a sphere into heaven-man-earth rings sequentially according to Pre-Heavenly Yi; Pre-Heavenly Yi constructs one sphere through sequential construction of these rings. As for all five regular polyhedra, this is first reflected directly in the structure of the regular octahedron, i.e., the 12 edges of a regular octahedron form four squares each, with three squares belonging to SRT white-red-black three-dimensional Yao. Thus, a regular octahedron has its eight gua symbols established on its eight triangular faces with their sides corresponding to SRT white-red-black three-dimensional Yao forming an SRT△-based Bagua with Yin-Yang changes. This Bagua is essentially a two-dimensional plane Gua where each Gua symbol is one face of an equilateral triangle; that is, eight gua symbols from eight SRT△ plane Guas construct a regular octahedron. Corresponding to three-dimensional space using three-dimensional Yao provides Heaven-Man-Earth (Lingxin-Shen) with a field for coexistence and mutual internal interaction among material energy, mental energy, and spiritual consciousness energy. Its specific manifestation is life phenomena which include macrocosm, microcosm and subatomic world; thus returning to the geometric nature of Yi Gua is not just a result of materialism. This geometry structure constitutes neutral basic elements shared by heart-matter; among them Tai Chi represents heart while Liangyi-Sixiang-Bagua (the process described above as Qian Kun giving birth to six children and Shao Yong's Eight Trigrams generation) represents matter expansion.
Figure 3.6 Nested Platonic solids (relationship between five regular polyhedra and counterclockwise/ clockwise tetrahedral star Bagua). The hexagrams/trigrams on dodecahedrons' or icosahedrons' faces overlap projections onto those on cube/octahedron's faces respectively; see Figure 3.7.
Figure 3.7 Cube/octahedral star Tai Chi MKB nested within positive twelve-faced/equatorial twenty-faced Bagua (left/right). Note that the corresponding tetrahedral star is nested inside. There are six SRT gua symbols (six edges) for each of the twelve-faced/equatorial twenty-faced polyhedra, which correspond to each edge/gua symbol of a regular octahedron Bagua in projection.
Figure 3.8 Two mutually reverse generation processes of Bagua: Shao Yong's Pre-Heavenly Yi learning constructs one sphere through sequential construction of three rings and three Yao Guas; while Bo Jing'smethod cuts one sphere into three rings and three Yao Guas (see Figure 3.2 inscribed regular polyhedrawithin a sphere, where these three rings and three Yao Guas correspond to the twelve edges of a regular octahedron Bagua).
Figure 3.9 Yin-Four-Faced Tetrahedron combined with Yang-Four-Faced Tetrahedron forms Four-Faced Tetrahedral Star with eight small four-faced tetrahedral Gua symbols surrounding it forming an outer layer Eight-Gua system; inside this structure is nested a regular octahedral Bagua.
As a geometric structure of cosmic energy, the Yi Jing can provide a non-territorial mode of thinking for us humans who reside between heaven and earth, who exist in the macrocosm and microcosm, and for those who can learn from life's truly beneficial lessons by directing their hearts towards both matter and spirit.
Geometry is derived from space-time-mind-matter. The Eight Trigrams describe this fundamental geometric structure of universal energy in three dimensions. Based on known literature and unearthed artifacts, earlier versions of the Eight Trigrams were directly related to six out of five regular polyhedrons - specifically the octahedron and icosahedron - as well as indirectly related to the tetrahedron. According to the inverse time-space-reversal triangle (SRT) hexagram developed from it, when each regular tetrahedral trigram is placed onto one face of an octahedral trigram so that they form eight equilateral triangles around its center point, then it becomes a star-tetrahedral eight-trigram which consists of two dual compound regular tetrahedra with opposite orientations sharing a common central octahedral trigram surrounded by eight small tetrahedral trigrams at its vertices. When these twelve edges are connected together they form another regular solid called cube or hexahedron with eight corners where each corner corresponds to one vertex or line-end-point combination among all possible combinations formed by joining any two points among these twelve points.
Figure 3.10 shows the Tai Chi MKB tetrahedron star Bagua, and the principle of mirror symmetry can be seen in Figure 3.11.
4.Geometric Symmetry of the Divination Techniques of Bo Shu Yi Gua and Jing Fang Ba Gong Yi Gua
Observing from the perspective of two tetrahedrons with eight stars representing the Bagua, one can see that the four Yang tetrahedrons and four Yin tetrahedrons correspond to the eight trigrams in sequence as revealed in the Book of Changes: Qian, Gen, Kan, Zhen for Yang; Kun, Dui, Li, Xun for Yin. If viewed in reverse order using SRT△ clockwise rotation then it becomes Jing Fang's Eight Palaces Bagua sequence: Qian, Zhen, Kan, Gen for Heaven; Kun,Xun,Li,Dui for Earth. The two systems are mirror images of each other and reflect a mirror symmetry between Qian and Kun while keeping Kan and Li unchanged but swapping Gen with Zhen and Dui with Xun.
Figure 3.11: In the innate hexahedron and octahedron division, there are three axes in the middle of the Yin-Yang trigrams' mutual rotation, which correspond to the three diagonal lines of the octahedron. In contrast, in the spinning process of the silk-jing tetrahedral star and triple-symmetric hexahedron's Yin-Yang trigrams' mutual rotation, there are four axes in total on its main and secondary central axis, corresponding to either four diagonal lines of a tetrahedral star or six faces of a hexahedron. The two sets of diagonals form separate systems; statically observing all axes within this nested Yin-Yang trigram mutual rotation system yields seven (4+3) axes. However, dynamically speaking, only one set can be observed at a time - either four or three - depending on individual rational consciousness's observation of the universe. From this perspective, "innate" refers to being prior to "postnatal," with both poles of its Yin-Yang trigram mutual rotation axis being shared vertices among each quadrant rather than Qian-Kun as seen in Silk-Jing or other relative pairs between two quadrants. For Silk-Jing's Yin-Yang poles they refer to Qian-Kun (main central axis) or other relative pairs between two quadrants (secondary central axis), while for Innate they refer to Taiji points where their motion is described by SRT Wei Yao as movement along a line connecting these points across three dimensions that share six intersection points forming continuous loops around spherical Taiji M-K-B SRT rings over time. Therefore "Innate" and "Postnatal" should be understood as dynamic relative relationships rather than mechanical absolute ones. The clockwise/counterclockwise rotations shown for Taiji M-K-B sphere in Figure 3-11 are based on this system of four main and secondary central axes. For the ratio of Yin-Yang regular tetrahedron mutual rotation, please refer to relevant figures in Chapter 3 Section 3 on Fibonacci sequences.
The same situation can also be seen in the 64 hexagrams of the silk book Yi and the 64 hexagrams of Jing Fang's eight palaces based on the principle of world soul. The unearthed 64 hexagrams of silk book Yi are obtained by multiplying the eight trigrams sequence and four-axis vertices of tetrahedral star silk book eight trigrams with two opposite hexagrams, namely Qian, Kun, Gen, Dui, Kan, Li, Zhen and Xun in silk book lower trigrams multiplied by each other to form an 8x8=64 square matrix. If it is changed to multiply according to Shao Yong's pre-heavenly 64 hexagram sequence matrix self-multiplication principle and given that silk book upper trigram sequence matrix self-multiplies accordingly, this kind of Silk Book 64 Hexagram (Silk Pre-Heavenly 64 Hexagram) will correspond completely mirror-like with Jing Fang's Eight Palaces' 64 Hexagram (Jing Pre-Heavenly 64 Hexagram) (see Figure3.18 and Figure3.19 captions). That is to say that the principle of forming a standing matrix multiplication for making up a set of sixty-four divinations based on Shao Yong's pre-heavenly Yixue was one of his most important discoveries; such a standing matrix multiplication principle formed an easy-to-understand geometric representation from three-dimensional Bagua into sixty-four-, five hundred twelve-, or four thousand ninety-six-dimensional sets.
This development process can be more clearly observed through cubic Yijing observation: formally speaking as dimension decreases towards tetrahedral stars or increases towards cubes. Therefore, actual sixty-four divinations - taking Jing Fang’s Eight Palaces’ divination as an example - are directly completed on cubes; their world souls represent midpoints between point(s), line(s), plane(s), body(ies) of geometric elements in the cube. That is, eight pure hexagrams on eight vertices + one world soul and five world souls and twenty-four returning souls on twelve edges and twelve midpoints (forming a truncated cube surrounded by eight regular tetrahedrons) + two world souls, four wandering souls, and twenty-four moving souls on six faces and six midpoints + eight hexagrams at the center of the cube. Of course, this also has its mirror-like correspondence in Silk Pre-Heavenly 64 Hexagram based on pre-heavenly principle.
Figure 3.12: The Cube Silk Book of the Pre-Heaven 64 Hexagrams (the left side shows the eight hexagrams in sequence). This is a view of the Qianyang pole, and the next figure is a view of the Kunyin pole. The cube has white, red, and black colors representing celestial-human-earth attributes on top, which are equivalent to the 64 hexagrams composed of eight tetrahedral stars. Eight tetrahedral stars (i.e., eight small cubes in each palace) combine to form an octagonal cube with 64 hexagrams in each palace. The large tetrahedron on top represents the outer upper gua (such as Qian Gua's Qian-Yu-Song-Wu Wang), while the small tetrahedron below represents the inner lower gua (such as Gou-Qian Song Zhong Dian-Qian Yu Zhong Dian). These two corresponding tetrahedrons represent Guan-Gua's upper outer Qian and lower inner Xun. Therefore, there are 64 sets of six lines consisting of one large and one small corresponding position tetrahedron group (eight large tetrahedrons with vertices facing outward from each vertex of an octahedral cube; using four vertices facing inward or outward from these eight large tetrahedrons to make eight small ones; matching each big one with a little one for a total of 64 groups). There are two basic forms for external/internal guas: One is like Guan Gua mentioned earlier, where four small pyramids made by four faces facing outwards from this palace's big pyramid contain Shi Hun Yi Shi Wu Shi Gui Hun San Shi Gua totaling thirty-two guas (for example, Guan Palace includes Gou-Lv-Tong Ren-Fou); The second type consists of four smaller pyramids nested inside this palace's large pyramid, containing Shang Shi Er Shi Si Shi You Hun Gua totaling thirty-two guas (for example, Qian Palace includes Qian-Tuo-Song-Wu Wang). The tetrahedral star described here, plus the eight small pyramids facing inward and outward on the vertices and faces of the large pyramid, actually form a structure of a tetrahedral star octagon. Note that the upper outer gua of six lines corresponds to eight large tetrahedrons with vertices facing outward from each vertex of an octahedral cube (such as Qian Gua's Qian-Yu-Song-Wu Wang; Gen Palace's Gen-Da Chu-Yi-Meng; Kan Palace's Kan-Tun-Xu-Jian; Zhen Palace's Zhen-Jie-Xiao Guo-Da Zhuang; Kun Palace's Kun-Lin-Ming Yi-Sheng; Dui Palace's Dui-Cui-Da Guo-Ge; Li Palace’s Li-Ding-Jin-Kui; Xun Gong’s Xun-Jia Ren-Zhong Fu-Guan). In summary, it is consistent with the geometric structure of the tetrahedral star in terms of eight large tetrahedrons corresponding to an octahedral cube."
Figure 3.13: Cube Silk Book Pre-Heaven 64 Hexagrams Viewed from Kunyin Pole.
Figure 3.14: A truncated cube on Taiji MKB (Silk Book Pre-Heaven 64 Hexagrams) rotating clockwise/counterclockwise. This model only represents SRT three-dimensional hexagram color attributes and omits yin-yang distinctions.
Figure 3.15: Tetrahedral Star Silk Book Pre-Heaven 64 Hexagrams are closer to cubes than Tetrahedral Star Taiji MKB Eight Trigrams in shape because they consist of eight Tetrahedral Star Eight Trigrams. This figure is the same as Figure 3.12.
"The silk book's pre-heaven 64 hexagrams, which are multiplied by the upper and lower gua matrices in the silk book, are called pre-heaven 64 hexagrams (pre-64 hexagrams) to distinguish them from the original silk book's 64 hexagrams obtained by multiplying the upper and lower gua matrices. The latter can be regarded as a basic imbalance of pre-64 hexagrams based on subjective psychological needs and objective environmental changes after being balanced in advance, while choosing a possible path for returning to balance from imbalance in later stages constitutes divination based on energy geometry. This further indicates that the unearthed Yi Jing text of Silk Book is a toolbook used for divination arts and numbers, so it faithfully reflects the geometric structure of tetrahedral star octagons on eight trigrams, with its formation modified accordingly.
Figure 3.16: The Silk Book of 64 Hexagrams
Figure 3.17: The Pre-Heavenly 64 Hexagrams in the Silk Book
Figure 3.18: The Eight Palaces and Worldly Spirits of the Jing Fang School's 64 Hexagrams are equivalent to the eight trigrams sequence shown in Figure 3.16, with a four-dimensional star octagon mirror symmetry based on the pre-heavenly principle of multiplying itself to obtain a square matrix. Therefore, the Jing Fang School's 64 hexagrams are equal to its pre-heavenly counterpart, except for differences in how certain lines change (such as fourth and fifth generations, wandering spirits, and returning spirits), resulting in changes to their order. However, when considering the structure of these hexagrams on Taiji MKB cubic lattice points (as seen in Figures 3.19 and 3.21), they remain consistent overall.
Figure 3.19 shows that each palace corresponds to an opposite one; for example Qian Palace is opposite Kun Palace while Zhen Palace is opposite Kan Palace etc.. In terms of original Jing Fang School's worldly spirit hexagram line changes still being influenced by linear six-line arrangements from Yi Ching (whereby lines are arranged according to gravity direction from bottom up), whereas those same worldly spirit hexagram line changes after geometric logic reorganization via Taiji MKB become non-linear six-line arrangements based on relative positions within a geometry space rather than gravity direction (since there is no such thing as "up" or "down" without gravity). This difference between traditional Yi Ching linear arrangement versus Taiji MKB non-linear arrangement can be understood by comparing gravitational states on Earth versus weightlessness conditions in space.
The reverse ordering between traditional Yi Ching where lines go from bottom up versus Taiji MKB where lines go from top down can be seen reflected through the two mutually inverse processes of generating the eight trigrams shown in Figure 3.8, where Shao Yong's Pre-Heavenly Three Rings and Three Yao become one sphere while the Silk Book's One Sphere is divided into three rings and three yao. Although original Silk Book and Jing Fang School hexagrams still follow Yi Ching linear thinking when it comes to line changes, their construction of the eight trigrams reflects a geometric spatial thinking that follows Shao Yong's pre-heavenly 64 hexagram matrix logic.
From the historical development of Yi Ching, it can be seen as a transitional phase between geometry and mathematics; similar to how Pythagoras used numerical forms to describe atomic theory as an initial step towards building systematic science, but true systematized science only emerged after Euclidean geometry. The purpose of "Geometric Yi" is to establish spiritual science as the next stage in scientific development (as discussed in Chapter Four).
Figure 3.20: Geometrically speaking, the outer hexagrams of the 64 hexagrams of Tai Chi MKB's six Yao gua are composed of eight large tetrahedrons formed by the eight vertices of a large cube and the midpoints of three adjacent faces. These eight tetrahedrons also form the tetrahedral stars nested within the MKB cube that make up its 64 hexagrams. The eight tetrahedra in this larger star represent the upper outer gua (hexagram) while those in smaller nested tetrahedral stars within each small cube represent their lower inner gua.
This is how we can understand the structure of Tai Chi MKB's six Yao gua from an MKB Tetrahedral Star perspective (i.e., how these nested stars relate to both larger and smaller cubes). Thus, upper outer and lower inner guas correspond to these larger and smaller tetrahedral structures respectively. This can be viewed from other regular polyhedron perspectives as well, but ultimately, Tai Chi MKB's Tetrahedral Star represents a comprehensive expression of five regular polyhedron octagons; its more complete version being "Plato's Nested Tai Chi MKB" (see later chapters), which combines Tai Chi Yi Gua with Metatron solids in sacred geometry projected into four-dimensional space.
According to ancient Mingtang practices, public assembly halls or imperial courts for political meetings or religious ceremonies were designed with circular tops representing heaven and square bottoms representing earth. They had either five or nine rooms arranged according to astronomical calendars and mathematical principles such as magic squares or Nine Palaces theory. Jing Fang Eight Palaces was used as an explanation for Yi Gua system based on these concepts.
From a perspective of Tai Chi MKB Cube (wherein a cube is represented by its circumscribed sphere), there are eight small cubes containing each palace/gua/Hexagram (i.e., eight tetrahedral stars). The large tetrahedron representing the upper outer gua is fixed in position, while the smaller nested tetrahedral star representing the lower inner gua moves around within this structure. The eight fixed positions of large tetrahedra represent three Yao guas (hexagrams), which form a part of these nested Tetrahedral Stars within the larger cube. Meanwhile, eight movable small tetrahedra represent each palace/gua/Hexagram's four faces and vertices outside and inside these large tetrahedra respectively, forming their respective Tetrahedral Star structures.
Thus, according to Tai Chi MKB's geometric logic reorganization of Jing Fang Eight Palaces' 64 hexagrams into its six Yao guas (hexagrams) based on SRT△ principles, only lower inner gua undergoes changes in world soul sequence. This provides a rigorous explanation for change versus unchangeable aspects from a geometrical perspective.
The upper third Yao Gua, first fourth Yao Gua, second fifth Yao Gua and wandering returning souls are all relative to two opposite hexagrams from a geometrical standpoint; that is to say they share an identical upper outer gua but have different lower inner guas. Together they form a Merkaba-shaped Tetrahedral Star.
Figure 3.21: The distribution of the world soul (27 points) and SRT segmentation in the clockwise and counterclockwise rotation of the Tai Chi MKB cube for Jing Fang's Eight Palaces Gua. This represents the structure of Jing Fang's Eight Palaces Gua, which is actually equivalent to multiplying the eight palaces and eight trigrams sequence matrix to obtain the Tian Gan Tian Fang 64 Gua. The world soul is a viewpoint on this geometric structure rather than a basis for establishing 64 hexagrams, unlike the role of lower gua in silk books. In other words, lower gua are used to multiply with upper gua sequence matrices to form 64 hexagrams based on practical needs without considering SRT △ requirements in geometric construction; that is, they do not have SRT dimensional color but possess it as standard models in inverse clockwise and counterclockwise rotation Tai Chi MKB with SRT dimensional color.
The world soul describes the internal geometric structure of Jing Gan Tian Fang's established 64-gua Tai Chi MKB, including truncated cubes, SRT segmentation (dividing one large cube into eight small cubes for outer and inner guas), geometry control points such as three nines twenty-seven points etc. In other words, it can also be viewed as describing how a large cube divided into eight small cubes forms an octagram by analyzing its cutting pattern (conversely speaking, eight small cubes forming an octagram compose a large cube).
Observing Yin-Yang through SRT segmentation on Tai Chi MKB cubic reveals that regarding Jing Fang's Eight Palaces' sixty-four-counterclockwise rotated cubic Tai Chi MKB; its corresponding positive square R-segmentation corresponds directly to one generation/fifth generation/returning souls - i.e., four vertices from each side of half-cube form a square segmented by R-division method. This square is segmented simultaneously on the cubic Tai Chi MKB and its half-cube. Similarly, T/S segmentation corresponds to fifth generation/returning souls. The same situation applies to truncated cubes (i.e., octagrams), where SRT dimensional color segmentation of eight trigrams forms three sets of Yin-Yang pyramid shapes; this SRT dimensional color is a continuous 3-ring sphere ring Tai Chi MKB.
The distribution of sixty-four tetrahedrons' energy points representing Jing Fang's Eight Palaces Gua in clockwise rotated cubic Tai Chi MKB reveals:
- Pure eight guas from previous generations: eight vertices of the cube.
- Eight guas from third generation: center point of the cube (shared with central Tai Ji F#).
- Each side (12 sides) midpoint for one generation/fifth generation/returning soul's eight gua, two hexagrams share each point - i.e., twelve vertices for half-cube corresponding to SRT segmentation.
- Center point for each face in second/fourth/wandering souls' eight gua, four hexagrams share each point - i.e., six center points for six squares faces on half-cube.
A total of twenty-seven energy bursting points represent sixty-four tetrahedrons or 64-gua cubic Tai Chi MKB's vertexes (eight vertices), edges (twelve sides), faces (six faces), and body centers(1 cube). 8(8 trigrams)+12(24 trigrams)+6(24 trigrams)+1(8 trigrams)=27(64 hexagrams).
Observing all twenty-seven points through various surfaces shows that they are relative to both sides and middle surface as three layers per nine-point matrix(centerpoint) on every layer. Second/third/fourth/wandering souls correspond to the centerpoints of these nine-point matrices while one/fifth/gathering soul corresponds to truncated cubes' centerpoints.
Figure 3.22 Tai, Pi, Hsien, Sun, Chi-chi, Wei-chi, Yi and Heng are the central points of the three generations of eight gua in the entire 64-gua grand cube. The eight small cubes of Qian Zhen Kan Gen, Kun Xun Li Dui are the eight palaces. Each palace contains eight gua spirits. This is the pre-heavenly 64 gua of Jing Fang's Eight Palaces and its mirror symmetry with Pre-Heavenly 64 Gua from Bo Shu (Jing being clockwise reversed Taiji MKB while Bo being counterclockwise rotated Taiji MKB).
Figure 3.23 According to Zhouyi Liu Yao (six lines), it is arranged linearly as upper and lower gua (upper three lines and lower three lines). From a geometric perspective on a cube structure it can be seen as outer-inner gua (the outer guas are the eight big cubes in the grand cube while inner ones are those in small cubes). For this pre-heavenly 64-gua system based on Jing Fang's clockwise-reversed Taiji MKB method for generating them; each palace’s external hexagrams remain unchanged but only their internal hexagrams change: The first line becomes First Generation; Second Line becomes Second Generation; Lines One through Three become Third Generation just like how they were originally arranged in Jing Fang's Eight Palaces’ Guas. Then under Third Generation Gua’s internal hexagram: First Line becomes Fourth Generation; Second Line becomes Fifth Generation; Lines One through Three become Sixth generation Guas (since Sixth overlaps with Upper generation so it was replaced by Wandering Spirit or Returning Spirit); Under Upper Generations' Internal Hexagram: Third Line Becomes Wandering Spirit(Outer Change) while Second line Becomes Returning Spirit(Inner Change). The terms "Wandering Spirit" and "Returning Spirit" come from the Zhouyi Xici's statement that "Essence becomes things, changes become spirits." By rearranging Jing Fang's Eight Palaces' gua spirits according to Taiji MKB, the upper generation’s external hexagrams become Wandering Spirits which wander outside while their internal hexagrams become Returning Spirits which return inside. Changes become spirits; when a spirit is within an object it is called a Returning Spirit (inner change), and when it is outside of an object it is called a Wandering Spirit (outer change). Here, based on the logic of geometric Yi in Taiji MKB, we have reorganized and interpreted the rules for changing gua spirits in Jing Fang's Eight Palaces. See Figure 3.20.
The perfect symmetry between Bo Shu Gua (Pre-Heavenly 64 Gua generated by pre-heavenly principles) and Jing Fang's Eight Palaces Pre-Heavenly 64 Gua (Jing being clockwise reversed Taiji MKB method) directly leads us into the three-dimensional world of Yi. The main structure of Bo Shu Gua consists of tetrahedral stars (which can be seen from multiplying two gua sequences or eight-gua sequences relative to four axes in Bo Shu text below), while Jing Fang's Eight Palaces Guas are mainly constructed on cubes (which can be seen from their gua spirits). The connection between them lies in their common core - regular octahedron - which also serves as both heart chakra system in yoga cakra meridians and geometric structures for Western sacred geometry’s four elements wind/air at its corresponding position located at Zhongdan point or middle dantian in Daoist alchemy i.e., above chest near heart.
5. Evidence of the History of Flat and Three-Dimensional Gua in Hanshan Jade Tablet and Xuejiagang Six-Hole Ceramic Ball
In history, the eight trigrams were first three-dimensional geometric objects, which then evolved into two-dimensional flat geometry, and finally became one-dimensional hexagrams (gua) drawings that corresponded to the evolution of civilization from Fuxi's creation of the eight trigrams to the geometric entity's two-dimensionalization during Xia-Shang Lianshan Guicang. Finally, it evolved into a one-dimensional gua drawing (hexagram), with zero-dimension points running through the entire process in numerical form. This first created a model for understanding the universe's phenomena as a geometric entity before drawing an eight-trigram with three lines based on this geometric model. The development of Yi is closely related to geometrical elements such as surface lines and dots, reflecting its use as a tool for calculating connections between time-space entities.
Therefore, we can see that Tai Chi Yin Yang Four Images Eight Trigrams dimensions increase gradually from creation to reality; however, their expression forms decrease interestingly from three dimensions to two dimensions and then one dimension line drawings. Isn't this yin-yang? The reverse movement of Tao is a process that reverses back towards primitive eight-trigram geometry structures that will help explore universal creation.
Modern research on three-dimensional Yi has laid many good foundations for geometrical Yi; its achievements have listed most possible arrangements of gua on geometrical bodies. However, these bottleneck lies in explaining insufficiently about substantive connotations between each pair or line drawn out by these geometrical bodies; thus limiting gua within one dimension only because traditional gua only distinguishes between yin-yang without effectively distinguishing attributes belonging to heaven-man-earth properties represented merely by up-down linear arrangement positions among pairs or lines drawn out by gua. Once SRT△ and its color attributes are introduced into the three lines of heaven-man-earth, then triangular flat gua and tetrahedral solid gua will naturally form.
Modern unearthed Yi-related artifacts provide good evidence for what eight-trigram geometrical bodies really are. Here we mainly discuss "Hanshan Jade Tablet," which represents the two-dimensional plane projection unfolding of a regular octahedron's eight trigrams, and "Xuejiagang Six-Hole Ceramic Ball," which represents the spherical radial projection of a star-shaped octahedron (or cube-shaped octahedron nested in a regular octahedron).
1.Hanshan Jade Tablet
Figure 3.24: Han Shan Yu edition. Currently housed in the Palace Museum, Beijing.*
Returning to direct evidence from history about the eight trigrams' two-dimensional equilateral triangle surface on a regular octahedron, it is found in 1987 during the first archaeological excavation of Tomb No. 4 (No. 87M4) at Lingjiatan site in Da Wen Kou culture period (about more than 5000 years ago) located in Henshan County, Anhui Province where "Hanshan Jade Tablet" was discovered.
A jade turtle was found inside this tomb; its back shell and belly shell were separated with a rectangular jade piece sandwiching between them. The discovery confirmed the mythological legend of "Yuan Gui Xian Fu." It may be one of China's oldest divination tools.
The jade turtle is divided into two parts: back shell and belly shell with several corresponding circular holes drilled up-down-left-right for rope fixing purposes. When excavated, this rectangular jade piece measuring approximately palm size at length-width ratio of 11x8.2 cm thickened by 0.2-0.4 cm was sandwiching between both shells; its front side is rectangular while slightly concave on reverse side with edges ground out to form concave width by 0.4 cm deepening by 0.2 cm. Each of the two short sides has five holes drilled, while each of the two long sides has nine and four holes respectively. The front side of this jade piece is engraved with an octagonal pattern consisting of two concentric circles; the eight corners are inscribed in a small circle that is tangent to both large and small circles, dividing them into eight equal parts with arrow or gui-shaped patterns on each part's edge pointing towards one corner of this rectangular jade piece where there are also four arrows or gui-shaped patterns on its edges pointing towards four corners. Jade turtle76and this jade piece were found together, indicating that it was not a daily life item or decoration but rather an object with some religious significance.
The Hanshan Jade Tablet and the "Xuejiagang Six-Hole Ceramic Ball" are both unearthed cultural relics from the late Neolithic period more than 5000 years ago. Scholars Guo Zhicheng(郭志成) and Guo Tao(郭韜) in their book "Entering Fuxi"(走進伏羲) believe that the Hanshan Jade Tablet may be the ancient "River Diagram"(河圖), but this "River Diagram" is not the same as Liu Mu's(劉牧)widely circulated "River Diagram" or Zhu Xi's "Luoshu"(朱熹洛書). Instead, it matches Chen Tuanlong's diagram of holes on jade pieces, indicating that there is some truth to Chen Tuan long's diagram.(陳摶龍圖)
The article on Chen Tuanlong’s sequence (other texts have been lost, only one sequence remains) reveals many clues about a three-dimensional geometric Bagua structure. The Guos argue that it describes a pyramid-shaped “platform” structure, which is closer in form to the pyramids of Maya culture in America. The pyramid shape is half of a regular octahedron, meaning that many ancient pyramid-shaped buildings may reflect two upward-facing Yang pyramids of an octahedral Yin-Yang pair. In other words, these pyramid-shaped buildings represent four Yang Gua among eight Gua (as for regular octahedral Bagua), while corresponding four Yin Gua exist underground.
If we consider the relative relationship between the octahedral bagua, cubic bagua, and tetrahedral star bagua duality nesting, then half of the above pyramid-shaped regular octahedron bagua in solid geometry is precisely the result of dividing77 any one-dimensional yao among the heavenly-human-earth SRT three-dimensional hexagrams that include all five regular polyhedra.The Yin-Yang discrimination generated by spinning and cutting directly results in observing Taiji generating Liangyi(兩儀) even BaGua with fractal symmetry reflecting its transformative power R△2D trigram motion attributes; the development of Yi studies fully demonstrates this dual phenomenon on and under the table.
The Yin-Yang discrimination generated by Taiji generating Liangyi can also be obtained by cutting in a three-dimensional trigram way (regular octahedron and cubic Bagua corresponding to regular octahedrons). Therefore, this cube will be evenly divided into eight small cubes. That is, each face of the cube is cut into a cross shape with a "field" shape in the center, which corresponds to each face and the center of the entire cube. Regardless of surface or body, Yang-Yin discrimination for Cube Bagua based on cutting along edges from regular octahedral Bagua indicates that Dantian is not only a description of Cakra energy system but also an explanation for BaGua. This is why Wei Boyang's work in "Can Tong Qi" was not just comparing alchemy with Yi Jing or using Yi Jing to explain his alchemical theory; it was actually a scientific verification result. This leads us to seriously consider whether the original Platonic solid behind BaGua or Fuxi’s creation besides simulating external phenomena as “far-reaching” also reflects subjective observation results about internal phenomena called “near-reaching”. It refers not only to visible limbs, facial features or organ systems but also non-ordinary visualized deeper basic human energy systems described by meridians and DanTian. The fractal dimensionality relationship between this human microcosm energy system and macrocosm/microcosm exists entirely correlated with geometric structure of Yi Gua.
Returning focus back onto Hanshan Jade Tablet's Octagon diagram: The Octagon at the center represents projection from regular octahedron then unfolded according to its pattern as shown in figure:
Figure 3.25 shows the unfolded projection of the regular octahedron made of mountain jade. It can be seen that the cutting along each edge of the octahedron also cuts through the cube and tetrahedral star.
Guo's "Entering Fuxi" also pointed out that the octagonal diagram was widely seen in prehistoric civilizations from 2000 to 4000 BC, and this kind of image is still preserved in some ethnic customs in southwestern China today. There are also many discoveries in America, and academia generally believes that this is a type of Bagua diagram without hexagrams. According to the length and short sides of jade pieces with holes at positions 4,9 and 5,5 as well as turtle shells placed between them on top (8 holes) or bottom (5 holes), it shows that dragon diagrams are not unrelated but related to He Tu instead of Liu Zhu's Luo Shu which has been passed down for generations. In addition, four positive four-dimensional arrows or guiform patterns shown by jade pieces indicate that they represent not only simple two-dimensional patterns of regular octahedrons but also precisely eight trigrams.
The geometric structure developed by regular octahedrons and tetrahedral stars (or vice versa) corresponds to wind elements (qi, energy) among four or five great elements in Western sacred geometry and yoga Cakra chakra energy system as heart wheel geometry while mountain jades were placed between turtle shells on both front chest plates corresponding to Dan Dao position where Tai Chi is located at Zhongdan position; Qian Heaven above Kun Earth below; people inside; heart united body begins life while leaving body ends death; things travel against time all come from this heart whose meaning is self-evident.
Some studies suggest that jade pieces were used for astronomical observation timing purposes with eight arrows pointing towards eight directions where outer ones point towards winter/summer solstice sunrise/sunset while four holes on long sides represent north and nine holes on long sides represent south, and two five-hole short sides represent east and west. Some also argue that jade pieces were used as sundials. In fact, the relationship between eight directions, winter/summer solstice astronomical observation timing, lunar phase changes or sundial guibiao (a type of ancient Chinese timekeeping device), Luo Shu point numbers etc. are closely related to Bagua which is a sum of ancient civilization expressions combining astronomical calendar positioning functions.
Regarding the study of Yi Gua geometry, it mainly recognizes that the central octagonal pattern is actually projected through self-rotation of regular octahedrons and then unfolded in a special dynamic projection method similar in form and psychological intuition to modern cubist painting where intuitive emotional perception cleverly combines with strict geometric rationality into one yin-yang unity so that three-dimensional consciousness can be visualized as flat images for easy observation and grasp while flat images can also present true states beyond appearances of three-dimensional consciousness.
Figure 3.26 shows the Victorian-style tile paving by Minton Hollins & Co. in the living room of the former British Consulate General's residence in front of Danshui Red Hair Castle photographed by author.
Figure 3.27 shows Lianshan's unfolded projection diagram for regular octahedron Bagua where if each two-dimensional hexagram made up from triangles is transformed into a three-dimensional tetrahedral hexagram according to tri-gua dimensional evolution principle, then Lianshan represents an unfolded display for eight small tetrahedral hexagrams forming Merkaba (the Star Tetrahedron) corresponding to cube Bagua cut along SRT axis representing Yin-Yang pyramid shape while different combinations can be formed by cutting red R white S second-third lines instead using black T first line as cut-off point.
Figure 3.28 shows the Hanshan Jade Eagle currently stored in the Anhui Provincial Institute of Cultural Relics and Archaeology.*
The Octagonal Star, commonly seen in geometric patterns, is similar to the octagonal pattern on jade pieces but they are actually different. The former is made up of squares (such as the tile pattern in front of Tamsui Fort San Domingo shown in Figure 3.26) or regular octagons, so each side of the square forms a right angle between two pairs of triangles. On the other hand, the position between two triangles on a jade piece reflects a 60-degree angle projection after spinning from a regular tetrahedron's equilateral triangle plane projection; therefore it appears as an acute angle. This also proves that the octagonal pattern on jade pieces is a result of projecting and unfolding from a regular tetrahedron rather than directly making it with squares or octagons like how sun symbols are usually made.
The octagonal diagram on jade pieces essentially reflects Bagua (Eight Trigrams) from a regular tetrahedron instead of being used as symbols for sun or stars like how Octagonal Stars are used in many cultures. Due to their similarity, however, some researchers have mistaken this diagram for an Octagonal Star symbolizing the sun found on Jade Eagles discovered at cultural sites. But when we look at an eight-sided polygon circumscribed by circles around both diagrams' centers, it becomes clear that these two diagrams share common origins and that borrowing one another's image was involved: The central square in Bagua became replaced by circle representing Sun while retaining its outer ring.
Recent studies about Water Book Tai Chi Diagram78 should be strong evidence supporting that Bagua depicted on Jade Pieces represents Tai Chi Eight Trigrams because Water Book Tai Chi Diagram records events occurring after text trigrams were introduced (i.e., each trigram has its own name). In Water Book Tai Chi Diagrams "Bagua" is referred to as "Ba Shan," which means "eight mountains." Interestingly, the character for "mountain" in Water Book is similar to the shape of a square's side in an Octagonal Diagram. Compared with pictographic characters used in Water Book, Bagua on Jade Pieces appears more ancient and should be considered as image-based Bagua from pre-text period. It can be confirmed that Water Book's use of "Ba Shan" instead of "Bagua" connects it to Lian Shan Gui Zang (Continuous Mountain Hidden Store), which existed before Zhouyi but was not completely lost after Han Yi; rather, it continued to exist through applications such as Feng Shui, Kan Yu and Bu Gua. However, this system remained underground and non-mainstream until recently when people began to understand its principles scientifically.
Figure 3.29: Water Book Eight Mountains and Hanshan Jade Tablet.
The Water Book Tai Chi Diagram is the application of the later eight trigrams sequence, which appeared after the appearance of text-based divination. The eight mountains in "Water Book" - Lishan, Fenshan, Duishan, Jianshan, Ganshan, Genshan, Zhengshan and Hengshan - correspond to Li gua (Fire), Kun gua (Earth), Dui gua (Lake), Qian gua (Heaven), Kan gua (Water), Gen gua(Mountain) , Zhen gua(Thunder) and Xun Guo(Wind) in Zhou Yi.
Hanshan Jade Tablet at least reflects the application of pre-text-based divination. Since text-based divination had not yet appeared at that time, it actually reflected a study of principles. That is to say that the hexagram sequence on top of Hanshan Jade Tablet was open-ended; firstly it was determined as Tian Gan or Pre-Heavenly Sequence(the silk book with mirror symmetry revealed by six children born from Heaven and Earth). Secondly,it could be given any other post-heavenly hexagram sequences according to practical needs just like traditional Gui Cang starts with Kun while Lian Shan starts with Gen . This situation reflected in "Water Book" should belong to its applied studies rather than its theoretical studies.
That is to say that Water Book Tai Chi Diagram gives a post-heavenly hexagram sequence while Hanshan Jade Tablet has both pre-heavenly and post-heavenly possibilities simultaneously.This indicates that there must be an even more primitive version of Hanshan Jade Tablet which can trace back from two-dimensional octagonal diagram into three-dimensional regular octahedron.The "Eight Mountains" mentioned in Water Book explains that Hanshan Jade Tablet is indeed an octagon but does not explain the origin of Hanshan Jade Tablet. Instead, it avoids the problem of the origin of octagonal diagram, which is also the fate of traditional applied studies.
In oracle bone inscriptions, there is also a representation method for three-line hexagrams using three points to form a triangle. The dots later evolved into a horizontal stroke in oracle bone inscriptions. The problem is that they are three points forming a triangle, which may be an intermediate process from regular triangular hexagram (the face of regular octahedron) evolving into one-dimensional trigram drawing with three lines.The time course happens to be Xia(夏△), Shang (商∴) and Zhou (周≡) 79.Hanshan Jade Tablet can be said to inherit from solid stereoscopic eight trigrams and precede one-dimensional trigram drawing.
In addition,Lian Shan not only splits regular octahedron into two pyramid shapes but also unfolds each face.It can also unfold eight regular tetrahedrons in four-dimension star polytope shape.Eight regular tetrahedrons are unfolded into connected ones.This form looks more like Lian Shan.If we make an outer sphere for each tetrahedron,it becomes a string bead shape.This is exactly what Eight Dan Balls Meridian System above Central Channel represents.There are eight dan balls meridians on human body(there are actually seven in reality while Qian gua's Brahma aperture locates at about four inches or about eight fingers wide above head).Dan Dao systematically reorganizes itself as upper,middle and lower dan balls.If we understand it from this perspective,Xia Lian Shan inherits from four-dimension star polytope while Shang Gui Cang inherits from regular octahedral forms.
Guizhou Water Book has geographical connections with Taoist balls distributed in Sichuan Daxi Culture,Hubei Qujialing Culture,and Anhui Xuejiagang Culture as well as Anhui Hanshan Jade Tablet, which shows the geometric nature of its inherited Yi-gua civilization and is different from the one-dimensional trigram drawing in Zhou Yi. These geometric shapes are largely preserved in Taoist balls. By cutting them, we can get eight divided spheres representing regular octahedral sphere projection of eight guas.On this basis,six-hole and fourteen-hole Taoist balls extend into four-dimension star polytope sphere projection (radial projection of tetrahedron star on sphere by center).The Han Dynasty Taoist ball further demonstrates that the tetrahedron star is nested in a cube and corresponds to 26+1 points describing 64 hexagrams according to JKF principle(see Figure 3.34 caption).
2. Xuejiagang Six-Hole Ceramic Ball
Pushing the perspective of the three-dimensional hexagrams further forward is the "Xuejiagang Six-Hole Ceramic Ball". The octagonal diagram on the aforementioned Hanshan jade Tablet has a circumcircle, which means it is the circumscribed sphere of a regular octahedron with eight trigrams. Therefore, it would be inscribed in the circumscribed sphere of a regular cube with eight trigrams. This leads to the exploration of Xuejiagang's six-hole ceramic ball, which represents this circumscribed sphere.
Figure 3.30: Xuejiagang Six-Hole Ceramic Ball. Currently housed at Anhui Provincial Museum.
Figure 3.31: The internal dual-nested regular octahedron with eight trigrams within a regular cube with eight trigrams (left) is equivalent to Tetrahedral Star Eight Trigrams (Tai Chi Merkaba). The spherical projection of Tai Chi MKB is Spherical Ring Tai Chi MKB (nine) (right), where each point on Tetrahedral Star Eight Trigrams projects radially onto its circumscribing sphere.
Figure 3.32: The mutually perpendicular orthogonal SRT white-red-black tri-rings divide the ball into eight quadrants corresponding to each face and vertex of both Octahedral Yang Trigram and Yin Trigram Tetrahedral Stars - Qian C, Gen B, Kan A, Zhen G for Yang; Kun C, Dui D, Li E and Xun F for Yin.
Figure 3.33: Comparison between spherical projections of SRT three-dimensional Yao planes for Tai Chi MKB Nine-Ring Sphere and Tetrahedral Star Tai Chi MKB respectively. Note that only SRT two-dimensional Yao planes are shown for dodecahedra and icosahedra as in Figures 3.6 and 3.7, respectively. The spherical projection of the six-hole ceramic ball from the late Neolithic Xuejiagang culture is consistent with that of Tai Chi MKB Nine-Ring Sphere if it represents the eight trigrams, which means that the patterns on the ceramic ball are exactly what we see in Figure 3.33 - a spherical projection of Tetrahedral Star Eight Trigrams Tai Chi Merkaba.
Alternatively, as shown in Figure 3.34, replacing (a) Tetrahedral Star with (b) dual-nested regular octahedron within a cube (cuboctahedron), then cutting this cuboctahedron into eight small cubes along its edges parallel to those of an inscribed regular octahedron yields an Octagonal Cube with SRT Yao planes projected onto each face's circumscribing sphere at each hole position corresponding to one vertex of Octahedral Yang Trigram or Yin Trigram Tetrahedral Stars - Qian C, Gen B, Kan A, Zhen G for Yang; Kun C, Dui D, Li E and Xun F for Yin.
The spectral colors red-orange-yellow-green-blue-indigo-violet-white correspond to musical notes CDEFGABC and trigrams Kun-Dui-Li-Xun-Zhen-Kan-Gen-Qian.
Xuejiagang Six-Hole Ceramic Ball was excavated from Xuejiagang Culture Site in Qianshan County Anhui Province during 1979-1982 AD dating back over five thousand years ago to late Neolithic period like Hanshan Jade Tablet found earlier there as well as at other sites such as Da Xi Culture Site and Qujialing Culture Site). The six holes correspond to six vertices of a regular octahedron inscribed inside this ball which can be divided into eight equal parts by three great circles passing through these six points and orthogonal to each other, corresponding to the three axes of a rectangular coordinate system. According to Guo's view, this is the "Heavenly Sphere" mentioned in Shangshu or "Yuan Bao" from the perspective of Yi Xue (the study of I Ching), which is a three-dimensional model of ancient spherical divination.
Some researchers believe that the eight-part ball represents the eight trigrams with each triangular face pointing towards its center representing one Yao. From our analysis, even those three great circles on this ball represent SRT Yao planes for Tai Chi MKB Eight Trigrams (i.e., dual-nested regular octahedron within a cube) projected onto their circumscribing sphere as shown in Figure 3.33 - a spherical projection of Tetrahedral Star Eight Trigrams Tai Chi Merkaba.
It represents the unity between Octagonal Cube with eight trigrams and Regular Cube with eight trigrams or rather both originated from Tetrahedral Star Eight Trigrams.
Figure 3.34 Comparison of various Bagua geometric solids. Han Dynasty pottery ball (image source: "Souyi Sou" antique website)
1. The six holes correspond to the eight vertices of the regular octahedron Bagua, which is divided into three sets of yin-yang opposing two pyramids (3x2=6) according to the SRT white-red-black division of the regular octahedron. Therefore, the six holes correspond to 3 sets of 6 pyramid tops and are represented by 6 energy points on the surface of the sphere that circumscribes the regular octahedron Bagua (points where energy enters and exits). These points correspond to midpoints on each face of a cube's Bagua, i.e., intersection points between an inscribed sphere in a cube and its faces' edges. For example, for Tetrahedral Star MKB's Bagua, these energy entry/exit points appear at its eight vertexes on its circumscribing sphere; thus, there are a total of fourteen energy points for Tetrahedral Star's eight vertexes plus Cube's six midpoints.
Bagua contains eight single guas with a total number of vertices being 8 x 4 =32; after accounting for overlapping vertices shared among different guas, there are only fourteen distinct ones left (i.e., Cube's eight vertexes plus six midpoint), representing all energy entry/exit points on surfaces that circumscribe tetrahedrons', cubes', or octahedrons' baguas respectively. Dodecahedron and Icosahedron baguas can be expressed using Octahedral baguas.
Therefore, spherical Bagua integrates five Platonic solid-based baguas theoretically having similar forms as those projected onto spheres with fourteen holes like Tetrahedral Star Sphere Projection Ball. There is also another pottery ball with twenty-six holes, which is the sum of Tetrahedral Star's fourteen and Cube's twelve vertices (i.e., 12 midpoints on its edges). Twenty-six plus one equals twenty-seven, representing the sixty-four guas in Jing Fang's Eight Palaces' cube (one central point and eight guas per three generations).
2. The origin of this Han Dynasty pottery ball is unknown; if it is genuine:
Han Dynasty pottery ball → corresponds to Tetrahedral Star Bagua and Cube Bagua (Tetrahedral Star and Octahedron have a total of 14 vertexes. Additionally, all twelve edges' midpoint on a cube are marked. Thus, there are 26 points: 14 + 12 =26. Adding one center point from the sixty-four guas in Jing Fang's Eight Palaces gives us a total of twenty-seven points that establish the principle for creating sixty-four guas), indicating that geometric descriptions were indeed present in Han Dynasty silk divination system. This pottery ball represents spherical projections of Tetrahedral Star Bagua and its implied Cube.
Xuejiagang Pottery Ball has another twenty-six holes with a size of 4.4 cm while the fourteen-hole pottery ball has a size of 8.8 cm; however, we do not know what size six-hole pottery balls should be.
6. Supplementary discussion on Yuanbaojing Yi Guà:
Wei Yuansong’s(衛元嵩)80 “Yuanbaojing” (元包經)provides correspondences between its own set of sixty-four gua symbols with those used by Jing Fang’s Eight Palaces’ world soul system beyond Zhouyi framework limitations; although Yuanbaojing was written later than Zhouyi, it discusses an earlier system than Zhouyi.
Figure3 .35 "Yuanbaojing " 64Gua
Jingfang Bagua Tetrahedron Star Tai Chi Merkaba and Silk Book Bagua Tetrahedron Star Tai Chi Merkaba mirror symmetry (with the Qian Kun diameter as the central axis, the silk spinning direction is opposite to that of Kyoto)
The original bagua sequence of Yuanbao is Kun Qian, Dui Gen, Li Kan, Xun Zhen. The lower hexagram sequence of Silk Book is Qian Kun, Gen Dui, Kan Li, Zhen Xun. The direction is opposite. The lower hexagram sequence of Silk Book is four tetrahedral stars with four central axes viewed as diagonals of a cube. In theory, both ends of any central axis are yang pole and yin pole respectively and also the beginning and end points of the hexagram sequence. Taking a Tai Chi MKB as an example, theoretically any one hexagram can be used as the starting point for divination. Xia Lianshan's Yi Guigan started from Gen; Shang Guicang's Yi Kun started from Kun; Zhouyi’s Qian began only reflects three kinds among them. A Tai Chi MKB ball located at Yang Pole or North Pole or energy endpoint on its own spin axis represents the starting hexagram.
Therefore, in Silk Book upper trigram bagua sequence it goes: Qian Gen Kan Zhen Li Dui Xun Sun while in Yuanbao it should correspond to: Kun Dui Li Xun Qian Gen Kan Zhen according to their respective directions which are reversed when comparing each other’s sequences.
Based on previous analysis on Yuanbao's bagua sequence and JingfangWorld Soul analysis on Yuanbao we know that there exists a complete correspondence between Yuanbao 64 gua with Jingfang64 gua Cube Taiji MKB and pre-heavenly 64 gua Cube Taiji MKB in Silk Books."
In summary, Silk Book spins around the Qian Kun axis and is mirror-symmetric (MKB central axis with Qian above and Kun below), while Yuanbao has a central axis of Kun above and Qian below, which is opposite to that of the hexagram sequence in Silk Book. It can be seen that Yuanbao 64 gua retains the correspondence relationship with the 64 gua Cube Taiji MKB lost by the original Silk Book 64 gua (which reflects Zhouyi's 64 gua). If we multiply the upper trigram bagua sequence of Silk Books by itself, it will be completely mirror-symmetric to Jingfang's 64 gua.
Figure 3.36: The Relationship Diagram of Bo Xian, Jing Xian, and Yuan Bao's 64 Gua
The original silk book of the 64 gua unearthed reflects the Zhouyi gua sequence based on dividing cubes to determine yin and yang. If we use the logic of determining yin and yang based on tetrahedral star rotation (yin-yang tetrahedral mutual rotation) to obtain the pre-heavenly 64 gua sequence in silk books, then its relationship is as described above. The Yuanbao Classic's 64 gua corresponds completely to the geometric structure of the cube-based 64 gua described by Jing Fang's Eight Palaces' principles according to shi hun (world soul). This geometric structure is mirror-symmetric with that of pre-heavenly 64 guas in silk books. Therefore, Yuanbao's 64 Gua logically supplements what was missing from Silk Book Yi Guas' Pre-Heavenly 64 Gua (Bo Xian).
Silk Book Jing appeared around the first century BC while Yuanbao appeared in the sixth century AD. From a historical perspective, they should have been passed down earlier than Zhouyi system’s Shang Gui Cang or even earlier Xia Lianshan systems. According to Jing Fang’s own account, it can be traced back to Confucius; actually it should be even earlier than that or at least when Confucius saw Yi Jing which included both Zhouyi and Shang Gui Cang Yi Jings but Silk Books Bo Xian/Jing/Yuan Bao inherited only part of Shang Gui Cang.
Laozi also saw Gui Cang Yi which means that primitive "Yi" was a geometric model for macrocosm/microcosm and naturally served as a framework for human body-mind cultivation too. As Daoism says: Kongzi (Confucius) understood it through reason to establish the Zhouyi philosophical system, while Laozi explained it through qi to establish the alchemical practice framework. In terms of overall civilization development, this is yin-yang mutual aid; Dao is the essence and principle within which Qi operates. The operation mode of combining principle with energy is the manifestation of invisible Dao (the universe consciousness that has not yet manifested into visible universe consciousness). Gui Cang gradually became non-mainstream in Yi Xue during Han Dynasty and was excluded by mainstream academic circles so its traces were scattered or hidden in numerology. Mainstream academic circles did not discuss Yuanbao or even Jing Fang based on Gui Cang system, let alone Silk Book Yi Guas until recently when they were unearthed.
Wei Boyang's (魏伯陽)"Zhouyi Cantongqi" (周易參同契)during Han Dynasty used Zhouyi system as a framework for body-mind cultivation in alchemy, which can explain that there is a very close relationship between Yi gua and qi's operation structure of body-mind energy. This evolved into medical applications of Yi. Looking at Wei Yuansong’s background in Confucianism, Taoism and Buddhism allowed him to avoid being biased towards philosophy like Zhouyi but rather closer to the original face of Yi Gua itself. Those who do not cultivate themselves often feel puzzled about how qi follows changes because they do not understand its principles; this is science rather than just philosophy.
Yuan Bao points not only to King Wen from Zhou dynasty but also earlier times indicating that although Wei Yuansong imitated Yang Xiong's Tai Xuan style when creating Yuan Bao Classic he had his own source too - similar to Bo Xian/Jing pointing at least far back toward Shang Gui Cang (starting with Kun Gua), if not even earlier - thus reflecting the geometric structure of Yi gua.
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Note
Chapter 1 1-23, Chapter 2 24-66, Chapter 3 67-103, Chapter 4 104-116
Chapter 3 section 1 67-80
67. See Figure 2.2.
68. The water in the container is quantifiable. The number of containers is also countable, but because geometric containers come directly from the information of universal consciousness, for us the containers are countable but infinite. That is to say, geometry will inevitably contain what we consider to be infinite. The simplest example is that the ratio of the length and short sides of a rectangle equals the ratio of its perimeter to its long side, which forms an infinite golden ratio spiral and this is exactly the growth pattern that organisms tend towards according to Fibonacci sequence.
69. According to multiple universe theory, there may not be only one material universe with form and appearance.
70. Yin Yang fish Tai Chi diagram refers to the commonly used Tai Chi diagram. See Section One "Introduction" in Chapter Three.
71.See BC-related diagrams as well as clockwise and counterclockwise hearts.The result is that life can accelerate towards or away from center.
72.Tian Ren Di Bagua three Yao in sixty-four hexagrams six Yao are Liang Wu (6th line), Si San (4th line) , Er Chu (2nd line).
73.Sections One and Two mainly rely on speeches given at "The Chinese Society for Life Electromagnetic Science" annual meeting on April 15th ,2012 by author,and two articles titled "On Geometric Origins of I Ching"and "Continued Discussion on Cultural Positioning of I Ching",which were included in conference proceedings entitled “Body,Mind,Spirit Science - Proceedings Of The Nineteenth Academic Symposium(2012)”p8~27.This article has made extensive revisions and supplements based on these conference proceedings.
74.See Figure 2.5.
75.The four fundamental forces of physics are gravity, strong nuclear force, weak nuclear force and electromagnetic force. Gravity is the most basic force in the material world. It is the material aspect of cosmic inertial power and represents the state when T△ reaches its extreme during centrifugal stage of BC universe evolution.
76.Turtle and old ancient sounds are similar, turtle is a symbol of longevity in religion as it can live for a long time.Wang Chong's "Lun Heng" divination section records: "Zilu asked Confucius: Can we get auspicious signs from pig shoulders or sheep backs? Can we get numbers from wild grasses? Why do we need to use yarrow stalks or tortoise shells?" Confucius said: "No. We just take their names. Yarrow stalks represent age while turtles represent antiquity." Confucius' rational explanation illustrates that knowledge requires accumulation and inheritance over time.Jade Tablet containing Bagua represents the entire knowledge system while Jade Turtle represents accumulated time.
77.Cutting a regular tetrahedron means cutting along its star tetrahedron, which also means cutting along each side of the regular octahedron's eight trigrams.
78.According to scholar Wei Zhangbing's research on "Water Book" by ethnic minorities in Dushan County, Guizhou Province, China.
79.Nan Huaijin's "Miscellaneous Thoughts on I Ching": Fu Xi’s “Pre-Heaven Eight Trigrams” drawn on paper is flat and seems unreasonable.If there was an instrument that could make it three-dimensional,it would be easier to express its spirit.What is written on paper now is just a symbol.For example,the current Qian Gua (乾卦)is represented by three horizontal lines like this ☰,but it may not have been drawn like this in ancient times.Like the Ⅲ (three vertical lines) and ∴ we see in oracle bone inscriptions, they are also Qian Gua.Nan Huaijin's statement reveals the possibility of flat and three-dimensional hexagrams.
80.Wei Yuansong was born in the sixth century AD during the Northern and Southern Dynasties.He was proficient in yin-yang calendar calculation,and was once a monk.After returning to secular life, he wrote to Emperor Wu of Northern Zhou criticizing Buddhism and Taoism. Wei Yuansong imitated Yang Xiong's Tai Xuan Jing style from Western Han Dynasty to write "Yuan Bao Jing" with ten volumes.Because it is difficult to understand, it has rarely been noticed in the history of Yi learning.
