Three Paintings of Fuxi and five lines of gossip.

Just draw a number axis representing the degree of yin and yang, the minimum value is-10 and the maximum value is 10. It is stipulated that the yin-yang degree of the soil in the five elements is 0, the yin-yang degree of the zero point of the river map is -5, and the yin-yang degree of the zero point of Luoshu number is-10, thus integrating the orientation theories of the five elements, the river map, Luoshu and Bagua into a logical system. Divide the five elements in the two-dimensional direction into two directions of "combination" inside and outside, and you can draw a three-dimensional river map; Based on the interaction of three-dimensional direction of river map, eight diagrams can be drawn; Shuo Gua recorded six methods of mutual movement and transformation among the eight trigrams, namely, the six sons of Luo Shu-inverse, innate gossip, acquired eight trigrams, Shen Ye, Luo Shu-shun and Gan Kun, among which Luo Shu-inverse, innate gossip and acquired eight trigrams are inverse numbers, and Shen Ye, Luo Shu-shun and Gan Kun are ordinal numbers.

Key words: Yin and Yang, Taixu, Luoshu transformation, innate gossip transformation.

Five elements, river map, Luo Shu and Eight Diagrams are the basic concepts and important components of the Book of Changes. They can study independently, and they have a close relationship. Through these logical structures, the ancestors vividly recorded the standard of dividing the universe by two-dimensional and three-dimensional concepts in the Book of Changes (the language of the Book of Changes should be two camps and three camps), and the law of interaction, mutual movement and mutual transformation of the universe divided by this standard. However, since ancient times, these concepts have been deified, and few scholars can understand this standard, further understand the logical relationship between these concepts, and grasp the true basic meaning of these concepts.

Next, I will briefly demonstrate this standard and the relationship between these logical structures.

When we try to divide the object to be studied into five sub-objects and further study the relationship between these five sub-objects, we enter the ancient five-element theory. So, what criteria are used to distinguish and divide these five sub-objects? Using the different aggregation and dispersion of five common substances: gold, wood, earth, water and fire, our ancestors vividly reminded us to distinguish and divide them according to their sizes and similarities. The river map and Luo Shu reveal to us more directly in the form of numbers: in the Book of Changes, we should classify all the objects to be studied according to different standards of yin and yang, as shown in figure 1 (the ∞ of the absolute size concept is 10 units).

1,-10 to 10 in the figure indicate the degree of yin and yang of the research object, where positive numbers are positive and negative numbers are negative. This number axis should actually be a closed crankshaft, and 10 is a point and connected. Here, for the convenience of drawing, it is drawn as a straight axis. One to ten represents the number of black and white points on the river map, and one' to nine' represents the number of black and white points on Luoshu. The number axis represents the total object, and the five elements, the river chart number, the Luo Shu number and the Eight Diagrams represent the sub-objects, and their yin and yang degrees are the same as those of the corresponding points on the number axis.

Next, I will take soil as an example to introduce three ways of understanding and expressing the size of Yin and Yang: Taiji, Taixu and Taiyi.

The way of Tai Chi: Tai, which means abundance, Tai Chi means extreme tai, abundance and abundance (such as the abundance in the Preface). Soil is composed of all the objects whose yin and yang degrees are expressed by the size of points between -2 and 2 on the number axis. Those greater than 0 are positive soil and those less than 0 are negative soil. Represented by line segment -2-2.

Taixu Road: The average size of Tai Chi is too empty, so the size of Tai Chi is the size represented by the midpoint of the line segment representing Tai Chi. The way of representing soil with 0 is too empty.

One-way: if the size of a research object changes repeatedly between -2 and 2, then this object is a one-way expression of soil, represented by -2. 2.

Tai Chi has nothing to do with Tai Xu. There is something inside, nothing inside and nothing outside. Taiyi is too empty in motion, and the relationship between Taiji and Taixu is the relationship between motion and static. There is stillness in movement, and there is movement in silence. In order to save space, this article uses the expression of too empty, hoping that readers can further interpret this article with the ideas of Tai Chi and Tai Yi, which will not only make readers have a newer and deeper understanding of the content of this article, but also be of great benefit to understanding the whole Yi-ology.

The orientation theory of five elements is an important part of the theory of five elements. In the five-element orientation theory, wood, fire, earth, gold and water respectively represent five orientations, namely east, south, middle, west and north, as shown in Figure 2. Figure 2 is an astronomical map of five elements, up, down, north, left, west, right and east. Numbers represent the size of these five directions. The orientation of the five elements is a two-dimensional spatial orientation.

Make the two river map numbers corresponding to these five directions not duplicate, and make the size of yin and yang in these five directions equal to the sum of yin and yang of the corresponding two river map numbers, which is called "coincidence" in connection.

Obviously, 1. -3 coincides with 6. 7, that is, Beishui. 4(-3+7=4), 2.- 1 coincides with 7. The 9th, that is, Huo Nan. 8(- 1+9=8), 3.30000.000000105 Through this "combination" transformation, the five orientations represented by the five elements are divided into two orientations, namely, the inner orientation and the outer orientation, so that one to five represent the inner orientation and six to ten represent the outer orientation. In this way, the five directions represented by the five elements are transformed into inner north. 1 -3, outer north. 6.7, Nenan. 2.- 1, inner south.

According to the number of river maps, we can draw a river map from Figure 3( 1), as shown in Figure 3(2). The orientation of the river map is a three-dimensional spatial orientation. It can be seen that the previous understanding of the five elements of the river map is wrong, but the interpretation of oriental wood and western gold is reversed. The river map is also an astronomical map, with the head south and the foot north, the left west and the right east, and the inside (sky) and the outside (ground).

Divide the three dimensions of the river map into yin and yang, that is, inside and outside, north and south, east and west, and you can draw three maps. The standard to distinguish yin and yang is "heaven" and "earth" in the number of heaven and earth in the copula. The "number of heaven and earth" is the number of the river map, with odd numbers as "days" and even numbers as "ground". Let the odd-numbered "days" be Yang (represented by 1) and the even-numbered "ground" be Yin (represented by-). Draw the first picture according to Figure 3( 1), with five "days" in the inner and outer dimensions as Yang and ten "grounds" as Yin; Draw the second picture with "heaven"-"heaven" seven is yang, "earth" two and "earth" six are yin; Draw the third hexagram with three days and nine days in the East-West dimension as the Yang and four or eight days in the Earth as the Yin, and you can draw eight hexagrams of Kun, Gen, Kan, Xun, Gan, Hui, Li and Zhen, representing the outer northwest, outer Manchuria, outer southwest, outer southeast and outer southeast respectively.

So, how do you get the yin and yang of this gossip?

As can be seen from Figure 3( 1), the first connection with the second phase can produce an inner north-south dimension with a yin-yang degree of -2, the sixth connection with the seventh phase can produce an outer north-south dimension with a yin-yang degree of 8, the third connection with the fourth phase can produce an inner east-west dimension with a yin-yang degree of 2, and the eighth connection with the ninth phase can produce an outer east-west dimension with a yin-yang degree of -8. Cohesion Biography calls this relationship "mutual gain", and "gain" means virtue, which means closeness.

If we also understand five and ten (1) in Figure 3 as the direction dimension generated by phase gain, then the phase gains of seven' .4 and eight' .6 are five and two'. -Six and three. -Four is ten. Jean 1. -Number three and number two. In fig. 3,-1( 1) and 7', 4 and 8', 6.7 and 7.9 with a phase of 5.5 degrees coincide with 2' respectively. -6 and 3' with phases of10. -5. In this way, we can get that the sum of Yin and Yang of Kun San in the outer northwest [(-6)+7+(-9) = (-8)] is (-8), which is equivalent to the Yin and Yang of Luoshu No.1; The sum of Yin and Yang in the three roots of outer Manchuria [(-6)+7+(-7) = (-6)] is -6, which is equivalent to the number two of Luo Shu. The sum of yin and yang of the three temples in the outer southwest [(-4)+9+(-9) = (-4)] is -4, which is equivalent to the number of yin and yang in Luoshu. The sum of yin and yang of the three temples in the outer southeast [(-4)+9+(-7) = (-2)] is -2, which is equivalent to the four' yin and yang in Luoshu. The sum of yin and yang of the three national trunk lines in the west and north [4+(-3)+ 1 = 2] is 2, which is equivalent to the yin and yang of the number six in Luoshu; The sum of yin and yang of beginning of winter-Northeast Dui San Gua [4+(-3)+3 = 4] is 4, which is equivalent to the yin and yang of Luoshu number seven; The sum of yin and yang of Li Xi Nan Li Sanyao [6+(- 1)+ 1 = 6] is 6, which is equivalent to the yin and yang of Luoshu number eight; The sum of yin and yang [6+(- 1)+3 = 8] of the three earthquakes in Lidongnan is 8, which is different from the yin and yang of Luoshu No.9, as shown in Figure 4. Like the Eight Diagrams, the Luo numbers 1', 2', 3', 4', 6', 7', 8' and 9' all represent eight directions: outer northwest, outer Manchuria, outer southwest, outer southeast, inner northwest, inner northeast, inner southwest and inner southeast. Gossip focuses on the interaction between the three dimensions that make up these eight directions, while Luoshu figures focus on the yin and yang in these eight directions. In Zhouyi, these eight directions move and transform with each other, and in the process of their movement transformation, they are transformed from eight three-dimensional directions in the three-dimensional space of astronomy to eight plane directions in the two-dimensional space of geography, as shown in Figure 6, and the law of their movement transformation is mainly recorded in Zhuan Gua Zhuan.

Suppose a particle is constantly moving between the eight diagrams (eight Luo Shu numbers) shown in Figure 4, and the yin and yang of this particle is equal to the yin and yang of which hexagram it moves to. For the convenience of observation, let's now look down at Figure 4. First, let's assume that this particle starts from Gen 2' and rotates counterclockwise. From the second generation of Outer Manchuria, we passed the Northeast Team. " Seven', Li, Gan.' 6', northwest of Waikun. I', and rotate up to the position of the outer southeast Xun. Number four. Then, this particle is influenced by the number five' in Luoshu (here, the position of five' is in China, which is used to cross two hexagrams, that is, the position in two directions). The trajectory of this particle's rotation and the sequence of its yin and yang changes are equivalent to the trajectory of a particle's clockwise rotation from southwest to eight directions and the sequence of its yin and yang changes shown in Figure 6. The eight diagrams shown in Figure 4 are transformed from eight three-dimensional directions in three-dimensional space to eight plane directions in two-dimensional space shown in Figure 7 (1).

According to the number of Luo Shu, we can draw Luo Shu Figure 7(2) from Figure 7( 1). We can imagine the process of transforming gossip representing three-dimensional space into gossip representing two-dimensional space as the rotation of a particle, which is called Luo Shu transformation. According to the definition in Shuo Gua Zhuan, for the azimuth observer, the counterclockwise rotation in Figure 6 represents the past (azimuth), which can be called Luo Shushun transformation; Clockwise rotation represents "knowing who is coming"-the future (orientation), which can be called the inverse transformation of Luoshu. The rotation transformation mentioned above, which let us finally draw Figure 7(2) of Luoshu, is the inverse transformation of Luoshu.

If the original azimuth observer, with his head facing south and his feet facing north, left, right, north, east, back and west, observes the orientation of the eastern (sky) river map, he stands on his head and observes Kun. 1', Foreign Manchuria Chuang2', Foreign Southwest Journal. 3', outside Southeast Xun. 4', Leahy Began. 6' and Li Dongdui. Moreover, this azimuth observer still defines the direction of head south foot north, left west right east and back outside according to his current posture. This azimuth observer will draw another set of gossip 1, earthquake 1, ridge 1, distance 1, gen 1, dui 65438 with another yin and yang standard. Another set of eight Luo Shu numbers of Yin and Yang standard, four 1, nine 1, three 1, eight 1, two 1, seven 1, six. When this observer takes Gen 1.2 1, Dui 1.7 1, Gan 1.6 1, Kun1. In the sequence of earthquake 1.9 1, when the orientation map of Luoshu is drawn according to the above-mentioned inverse transformation formula of Luoshu (1) (see Figure 8 (2)), in fact, the eight diagrams corresponding to it one by one are drawn, that is, dry, shaking, detachment, loss, ridge, Kun and root, that is,

In the Book of Changes, the basic transformation of gossip is not only the transformation of Luo Shu mentioned above, but also a transformation of innate gossip. Innate gossip transform is in the order of Luo Shu number, from decimal to large, which is innate gossip cis-transform, and from large to small, which is innate gossip inverse transform. Fig. 9 is a congenital eight diagrams diagram, with particles rotating clockwise from the northeast earthquake. 9' and pass through. Eight feet drunk driving. 7' and gan. 6', and then the particle receives the Luo Shu number 5' (five' is Chinese, and the function is to cross two hexagrams), and continues through Xun. Four feet, the canal. 3' and Gen .. stick to the day, stop with words, act with monarch, and hide with Kun ",while" those who know what is coming "implies the order of gossip movement and mutual transformation.

It can be understood from Figure 4 that the inverse transformation of innate gossip is a particle working between the eight diagrams in Figure 4. Formed by the shape movement, the particle started from the earthquake, moved westward, then moved downward and eastward to the right, and then moved westward and eastward to the trunk. It should have moved outward and eastward to Gen, but crossed Gen and Kun, directly moved to Xun, then moved westward to Kan, then moved downward and eastward to Gen, and finally moved westward to Kun, thus completing the movement of this particle between the eight diagrams. We can further extend the definition of innate gossip transform to the following form: Do particles do work between the eight three-dimensional directions represented by the eight diagrams in Figure 4? Shape movement, thus transformed into eight two-dimensional directions as shown in figure 6, which is innate gossip's cis-variant formula; Instead, do what? Deformation is the inverse transformation of innate gossip.

In figure 1, the Yin and Yang degrees of the four hexagrams of Kun, Gen, Kan and Xun are all negative, which are Yin hexagrams; The degrees of yin and yang of the four hexagrams of Gan, Dui, Li and Zhen are all positive numbers, which are positive. In the Book of Changes, in addition to this way of dividing gossip into yin and yang, there is also a common saying that the four hexagrams of Kun, Xun, Li and Dui are yin, and the four hexagrams of Gan, Zhen, Kan and Gen are yang. Therefore, Cohesion Biography said: "Yang Yi is more yin, and Yin Yi is more yang ... Yang Yi is odd, and Yin Yi is even ... Yang is a gentleman, but two people are gentlemen. Yin Erjun is alone, and the way of villains is also. " In order to make the four hexagrams of Gan, Zhen, Kan and Gen positive and the four hexagrams of Kun, Xun, Li and Quan negative, it is necessary to rotate the four hexagrams of Gan, Quan, Zhen and Quan clockwise by 90 degrees, which is called "Eight Diagrams Wrong", and Figure 4 is in the form of figure 10. The stem, earthquake, ridge and root of Siyang hexagrams are on the ABGH plane, and the hexagrams on the ABGH plane are Yang hexagrams. The four Yin hexagrams of Kun, Xun, Li and Hui are on the plane, and the hexagrams on the plane are Yin hexagrams.

The formula for transforming the eight three-dimensional directions represented by the Eight Diagrams in Figure 10 into the eight two-dimensional directions shown in Figure 6 is as follows: four yang-shaped bodies change from dry to ridge and root to earthquake, and then, under the action of Luo's number five' (five' is the Chinese side, which is used to transform Luo's inverse transformation into innate gossip transformation), four yin-shaped bodies are transformed into self-bifurcation. So as to complete the transformation from eight three-dimensional directions to eight two-dimensional directions represented by the eight diagrams, and the order of mutual movement and mutual transformation between the eight diagrams thus transformed is the acquired gossip order, as shown in figure 1 1, which means "Emperor's shock, loss of qi, separation from service." Everything is out of shock, shock, east; Qi is almost the same as Xun, Xun, Southeast, and Qi, and everything is clean and neat; People who leave are also bright, and everything meets. The same is true of divination in the south. Saints listen to the world from the south and cover these people from the Meiji world. Kun is also, the land is also, and everything is raised, so it is to serve Kun; Oppose, it is autumn, say everything, so say against; War is dry, dry, and the northwest is also thin; Kanzhe, water is also, the north is also, and the labor is also, everything belongs to it, so it is said that labor is on the Kanshang; Alas, divination in the northeast is also the beginning of everything, so it is embarrassing. "The mutual movement and transformation order of gossip mentioned in this passage.

10, the formula of the eight three-dimensional directions represented by the Eight Diagrams to the eight two-dimensional directions shown in Figure 6 is as follows: Four Yin hexagrams are transformed from Kun to Kun, and then into the formula of Luoshu, and then transformed into innate gossip's formula by Luoshu number five' () and Siyang hexagrams from self-drying to vibration, ridge and root, thus completing the Eight Diagrams. The order of mutual movement and mutual transformation between the eight trigrams transformed in this way can be called the order of the six sons of Gankun. Therefore, "Shuo Gua Chuan" said: "Dry, heaven is also, so it is called father; Kun, the land is also, so it is called mother; One person is killed by an earthquake, so it is called a long person; Xun got a daughter after a while, so she was called the eldest daughter; Kan has a man, so he is called a middleman; Get another woman from the telegram, that's called a woman; It is called a young man because you have a three-stringed man and a three-stringed girl. "

Kun, Dui, Li, Xun, Gan, Zhen, Kan and Gen in figure 10 correspond to Kun, Gan, Zhen, Xun, Li, Dui, Kan and Gen in figure 4, representing northwest, northwest, southeast, southeast and southwest respectively. Therefore, if the Eight Diagrams in Figure 4 are also transformed according to the above transformation formula, the mutual movement and transformation sequence between the Eight Diagrams will be as shown in Figure 13 (the earthquake is defined as East). We can call this order God and order. Therefore, The Biography of Divination says: "God is also a man who speaks wonderful words. He who moves everything does not worry about thunder; Catch people who don't care about anything; People who do everything are nothing more than fire; People who say everything don't say anything; Those who moisten everything are not moistened by water; In the end, everything is difficult at the beginning, and if it is not prosperous, it will be ... (ellipsis stands for Gan Kun) ",which is related to Luo Shushun's transformation formula. "So fire and water catch each other, thunder and wind are not contradictory, the mountains are ventilated ... (ellipsis stands for Gan Kun) and then it can change, that is, everything has changed."

To sum up, there is a close logical connection between the concepts of Five Elements, River Map, Luoshu and Bagua. According to the theory of five elements, we can draw a river map, and according to the river map, we can draw eight diagrams and calculate the number of Luoshu. The Zhuan Gua Zhuan records the laws of mutual movement and mutual transformation of six kinds of gossip, among which Luo Shu's inverse, innate gossip's and acquired gossip are inverse numbers, and Shen Ye, Luo Shu Shun and Gan Kun's six sons are ordinal numbers.

Some clauses in this paper seem very casual. For example, when drawing Luotu, the inside is the center position, and ten is the center position outside, but when calculating Luoshu number, five is divided into seven' and eight' parts, and ten is two' and three' parts, and other river maps are not separated; For another example, in the transformation of the eight diagrams and the six sons of Gan Kun the day after tomorrow, the four hexagrams of Gan, Hui, Li and Zhen in the river map should be rotated 90 degrees clockwise, but not in other transformations. These seemingly arbitrary rules actually contain other Yi-ology principles, and I intend to write another article to discuss these aspects. In the Book of Changes, you can draw the orientation of the five elements from a two-dimensional perspective, the river map and the three-line gossip from a three-dimensional perspective, and the sixty-four hexagrams in the Book of Changes from a four-dimensional perspective. For this method of "four camps changing" ("copula uploading"), please refer to my book "Yi Fa Yi Shu Jie".