Acupuncture Treating Heart Disease Based on Eight Palaces or Eight Veins —Mathematical Reasoning of Treatment Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Medicine (IV)
Abstract: Theory of eight palaces (八宫) or eight veins (八脉) is useful in understanding the basic sick subsystems that may be to fall ills as the root-cause. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Medicine (TCM), this paper demonstrates the treatment principle: “Even if all changed, it is hard to change one’s nature” (江山易改, 本性难移). The eight palaces or eight veins can be used to diagnose basic sick subsystems that may be to fall ills as the root-cause. The first or second transfer law of human body energies of the eight palaces or eight veins according to the different blood pH values of a human body whether in the normal range or not, respectively, assuming that the range of blood pH value is divided into four parts from small to large. Both second and third are for a healthy human body. Both the root-cause and symptoms come from the first transfer law of human body energies. And both first and fourth are for an unhealthy human body. Both the root-cause and symptoms come from the second transfer law of human body energies. A disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, acupuncture is used to treat atrial premature beats as a congenital heart disease.

1. Introduction

Theory of eight palaces (八宫) or eight veins (八脉) is useful in determining the major or basic sick subsystems that may be to fall ills. Eight palaces is a general mathematical structure as the second physiological system of a steady multilateral system. It is to determine the major or basic sick subsystems that may be affected, based on the six indexes of comprehensive judgment. The six indexes are the energies of six subsystems wood ( $X$ ) = {liver, bravery}, xiang-fire ( ${X}_{S}^{x}$ ) = {pericardium, the triple energizer}, earth ( ${X}_{K}$ ) = {spleen, stomach}, metal ( ${K}_{X}$ ) = {lung, large intestine}, water ( ${S}_{X}$ ) = {kidney, bladder} and jun-fire ( ${X}_{S}^{j}$ ) = {heart, small intestine}, simple namely model of Jingluo or six hollow organs. The six indexes can be used to diagnose the major or basic sick subsystems that may be to fall ills.

The main purpose of observing the six energy indexes is in measuring all kinds of changes in energies for different subsystems of human body.

Let ${x}^{i}$ be one of the six indexes of the subsystem energies of the steady multilateral system for any $i\left(1\le i\le 6\right)$, denoted any one corresponding parameter of normal range (lower bound, upper bound, center) as follows respectively

$\left({a}^{i},{b}^{i},{t}_{0}^{i}\right)\text{,}i=1,2,3,4,5,6.$

Consider one of the six sign functions respectively

${f}_{i}=sign\left({x}^{i}-{t}_{0}^{i}\right)+\left({x}^{i}={t}_{0}^{i}\right),\text{}i=1,2,3,4,5,6.$

If ${f}_{i}=1$, the energy of the corresponding subsystem is Yang. Its state is intended to be real or real-normal.

If ${f}_{i}=-1$, the energy of the corresponding subsystem is Yin. Its state is intended to be virtual or virtual-normal.

The Hexagram-image of the eight palaces is as follows:

$f=\left({f}_{1},\text{}{f}_{2},\text{}{f}_{3},\text{}{f}_{4},\text{}{f}_{5},\text{}{f}_{6}\right)$.

There is a total of 64 Hexagram-images. There is also a total of eight palaces. Each of palaces has eight Hexagram-images.

There is a rule: for each of eight palaces, its all Hexagram-images have the same as nature, namely, “Even if all changed, it is hard to change one’s nature” (江山易改,本性难移).

By using the treatment principle, the way of judging what palace a hexagram image belongs to can be used to diagnose the major or basic subsystems that may be to fall ills.

The human body blood pH value of eight palaces or eight veins is a general parameter linking together the complexity of relations between organ pairs, the organ itself, the capabilities for intervention reaction and self-protection of the body and mind as a whole, related to the environment, food, health and personal history, air, water, earth, climate, season, etc. By using the human body blood pH value of eight palaces, the way can be to determine the human body whether healthy or unhealthy.

There is an important indicator for human health: the value of blood pH, which, under normal conditions, ranges from 7.35 to 7.45, and the center is 7.4. Outside this range (acid: Yin condition; alkaline: Yang condition), disease appears. Almost always, when there is disease, the condition of blood is a Yin condition, little is a Yang condition.

There are a lot of evidences (e.g., experimental identification for probability and real applications) to support this viewpoint, such as, Shirakabe et al. [1], Kaur et al. [2], Aly et al. [3], Intven et al. [4], Patel et al. [5], Handman et al. [6], Natalia et al. [7], Barfod et al. [8], Zhu et al. [9], Zhu et al. [10], Robert et al. [11], Mona et al. [12], Saritas et al. [13], Stevens et al. [14], and so on.

The body begins to activate the necessary mechanisms to restore this parameter to its appropriate range. If the body is unable to restore optimal pH levels, the disease may become chronic and lead to dire consequences.

Zhang et al. [15] - [24] have started a great interest and admired works for Traditional Chinese Medicine (TCM), where, through mathematical reasoning, they demonstrate the presence of incompatibility relations, which are predominant in daily life, yet absent in traditional Aristotelian Western true-false logic.

Many people as Western person are beyond all doubt that the Yin Yang Wu Xing theory is superior to the traditional true-false logic, which does not contemplate incompatibility relations, which Zhang and Shao [20] have expertly explained from a mathematical standpoint.

The work Zhang [15] [16] has started, allows many people like Western person to think of a true re-foundation of mathematical language, to make it a better suited tool for the needs of mankind and the environment. Even so, Zhang and Shao [20] also bring to light the difficulty of establishing the values of both the intervention reaction coefficients ${\rho }_{1},{\rho }_{2}$ and the self-protection coefficient ${\rho }_{3}$ as parameters with due accuracy.

In this paper, the introduction of six parameters such as the six indexes of subsystem energies of a human body will be suggested, in order to diagnose the major or basic subsystems that may be to fall ills. On the other hand, the introduction of a parameter such as a human body blood pH value will be suggested, in order to determine the human body whether healthy or unhealthy, by facilitating the understanding and the calculation of the values of both the intervention reaction coefficients ${\rho }_{1},{\rho }_{2}$ and the self-protection coefficient ${\rho }_{3}$. This paper ventures to suggest this with all due to respect, because it is believed that the path Zhang [15] [16] has started, in such an understandable way from the mathematical point of view, will be very useful for all mankind searching for tools to understand the mechanisms of human body system.

Latest works discovered the academic relationships between Leibnitz and Jesuit priest J. Bouvet, linking the deduction of the Trigrams to German binary system, situation that coincidentally appears in quoted paper. This will clearly realize the scientific-mathematical fundamentals of TCM (see Contributions).

There are some publications [25] - [30], devoted to demonstrating in Occident the exact basis of Chinese Medicine, i.e. as Chinese Five Elements find precise consistency with Euclid’s Five Regular Polyhedra, as well as the trigrammatic order of the I-Ching hexagrams.

The article proceeds as follows. Section 2 contains a parameter model and basic theorems, in order to explain both the intervention reaction coefficients ${\rho }_{1},{\rho }_{2}$ and the self-protection coefficient ${\rho }_{3}$ through the introduction of a parameter model to study the normal range of human body blood pH value, while the first or second transfer law of human body energies is demonstrated in Section 3, through the concept of both relation costs and a relationship analysis of the Hexagram-images of eight palaces. Furthermore, the major or basic subsystems that may be affected will be diagnosed with the Hexagram-image of the six indexes as eight palaces. If the range of the human body blood pH value is divided into four parts, for the human body in every part, the prevention or treatment method of human body diseases as the treatment principle of TCM is given in Section 4. As an application, acupuncture is used to treat atrial premature beats as congenital heart disease in Section 5 and conclusions are drawn in Section 6.

2. Parameter Model and Basic Theorems

The concepts and notations in Zhang [17] [18] are used start and still.

Let the note $\phi =\left(\sqrt{5}-1\right)/2=0.61803399$ be the gold number. Suppose that the note ${\rho }_{0}=0.5897545123$ is namely healthy number. It is because the healthy number ${\rho }_{0}$ can make the healthy balance conditions that ${\rho }_{1}={\rho }_{3}$, ${\rho }_{2}={\rho }_{1}{\rho }_{3}$ and $1-{\rho }_{2}{\rho }_{3}={\rho }_{1}+{\rho }_{2}{\rho }_{3}$ hold if ${\rho }_{1}={\rho }_{0},{\rho }_{2}={\rho }_{0}^{2}$ and ${\rho }_{3}={\rho }_{0}$. Assume that the note ${{\rho }^{\prime }}_{0}=0.68232780$ is namely unhealthy number. It is because under the poor self-protection ability, the unhealthy number ${{\rho }^{\prime }}_{0}$ can make the following unhealthy balance conditions hold:

$\begin{array}{l}{\rho }_{1}-{\rho }_{3}={\rho }_{3}={{\rho }^{\prime }}_{0}/2=0.34116390,\\ {\rho }_{2}-{\rho }_{1}{\rho }_{3}={\rho }_{1}{\rho }_{3}={\left({{\rho }^{\prime }}_{0}\right)}^{2}/2=0.23278561\\ 1-{\rho }_{2}{\rho }_{3}={\rho }_{1}+{\rho }_{2}{\rho }_{3}\end{array}$

if ${\rho }_{1}={{\rho }^{\prime }}_{0},{\rho }_{2}={\left({{\rho }^{\prime }}_{0}\right)}^{2}=0.46557123$ and ${\rho }_{3}={{\rho }^{\prime }}_{0}/2$. Thus ${\rho }_{0}<\phi <{{\rho }^{\prime }}_{0}$.

A parameter model of a human blood pH value in a mathematical sense based on Yin Yang Wu Xing Theory of TCM is reintroduced by using the functions $\lambda \left(x\right)$ and $\rho \left(x\right)$ of the human blood pH value x described as follows.

Let $x\in \left(7,7.8\right)$ be a human blood pH value, where the values 7 and 7.8 are the minimum and maximum acceptable the blood pH value. The center value 7.4 is the target as the expectation of the human blood pH value. Define a function $\lambda \left(x\right)$ of the blood pH value x in below:

$\begin{array}{c}\lambda \left(x\right)=\frac{|x-7.4|}{\left(7.8-x\right)\left(x-7\right)},\forall x\in \left(7,7.8\right)\\ =\left\{\begin{array}{cc}\frac{x-7.4}{\left(7.8-x\right)\left(x-7\right)},& 7.8>x\ge 7.4;\\ \frac{7.4-x}{\left(7.8-x\right)\left(x-7\right)},& 7 (1)

A parameter model is considered as

$\rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2},\forall x\in \left(7,7.8\right).$ (2)

Theorem 2.1. [23] Under model (2), the following statements hold.

1) The one that $0<\rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\le 1$ is equivalent to the other that $0\le \lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}<+\infty$, where $\lambda \left(x\right)$ is a monotone decreasing function of x if $x\in \left(7,7.4\right]$ or a monotone increasing function of x if $x\in \left[7.4,7.8\right)$ ; and $\rho \left(x\right)$ is a monotone decreasing function of $\lambda \left(x\right)$ if $\lambda \left(x\right)\in \left[0,+\infty \right)$ ; and $\lambda \left(x\right)$ is a monotone decreasing function of $\rho \left(x\right)$ if $\rho \left(x\right)\in \left(0,1\right]$.

2) If $1\ge \rho \left(x\right)\ge {\rho }_{0}$, then

$\lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \frac{1-{\rho }_{0}}{2{\rho }_{0}}={\rho }_{0}^{2}\le \rho {\left(x\right)}^{2}\le 1;$

$\frac{\lambda \left(x\right)}{\rho \left(x\right)}=\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{2}}\le \frac{1-{\rho }_{0}}{2{\rho }_{0}^{2}}={\rho }_{0}\le \rho \left(x\right)\le 1;$

and

$\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^{2}}=\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{3}}\le \frac{1-{\rho }_{0}}{2{\rho }_{0}^{3}}=1.$

3) If $0<\rho \left(x\right)<{\rho }_{0}$, then

$\lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}>\frac{1-{\rho }_{0}}{2{\rho }_{0}}={\rho }_{0}^{2}>\rho {\left(x\right)}^{2}>0;$

$\frac{\lambda \left(x\right)}{\rho \left(x\right)}=\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{2}}>\frac{1-{\rho }_{0}}{2{\rho }_{0}^{2}}={\rho }_{0}>\rho \left(x\right)>0;$

and

$\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^{2}}=\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{3}}>\frac{1-{\rho }_{0}}{2{\rho }_{0}^{3}}=1.$

4) Taking $0<{\rho }_{1}=\rho \left(x\right)<{\rho }_{0},{\rho }_{2}=\rho {\left(x\right)}^{2}$ and ${\rho }_{3}=c\rho \left(x\right)$ where $0\le c\le 1$, there are

${\rho }_{1}-{\rho }_{3}=\rho \left(x\right)\left(1-c\right)\ge 0,{\rho }_{2}-{\rho }_{1}{\rho }_{3}=\rho {\left(x\right)}^{2}\left(1-c\right)\ge 0$,

and $\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)=\rho \left(x\right)+c\rho {\left(x\right)}^{3}<1-{\rho }_{2}{\rho }_{3}=1-c\rho {\left(x\right)}^{3}$, where

$|\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)|>2\left(1-c\right){\rho }_{0}^{3}=\left(1-c\right)0.41024$.

5) Taking $1\ge {\rho }_{1}=\rho \left(x\right)\ge {\rho }_{0},{\rho }_{2}=\rho {\left(x\right)}^{2}$ and ${\rho }_{3}=c\rho \left(x\right)$ where $0\le c\le 1$, there are

Firstly, ${\rho }_{1}-{\rho }_{3}=\rho \left(x\right)\left(1-c\right)\ge 0,{\rho }_{2}-{\rho }_{1}{\rho }_{3}=\rho {\left(x\right)}^{2}\left(1-c\right)\ge 0$ and $\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)=\rho \left(x\right)+c\rho {\left(x\right)}^{3}\ge 1-{\rho }_{2}{\rho }_{3}=1-c\rho {\left(x\right)}^{3}$ if $1\ge c\ge \frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{3}}=\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^{2}}\ge 0$ ;

Secondly,

${\rho }_{1}-{\rho }_{3}=\rho \left(x\right)\left(1-c\right)>\rho \left(x\right)/2,{\rho }_{2}-{\rho }_{1}{\rho }_{3}=\rho {\left(x\right)}^{2}\left(1-c\right)>\rho {\left(x\right)}^{2}/2$

and

$\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)=\rho \left(x\right)+c\rho {\left(x\right)}^{3}<1-{\rho }_{2}{\rho }_{3}=1-c\rho {\left(x\right)}^{3}$

where $|\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)|\le {\left({{\rho }^{\prime }}_{0}\right)}^{3}=0.31767$ .

If $0\le c<\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{3}}=\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^{2}}\le \frac{1}{2}$ in which $1>\rho \left(x\right)\ge {{\rho }^{\prime }}_{0}$ ;

Thirdly,

${\rho }_{1}-{\rho }_{3}=\rho \left(x\right)\left(1-c\right)\ge \rho \left(x\right)/2,{\rho }_{2}-{\rho }_{1}{\rho }_{3}=\rho {\left(x\right)}^{2}\left(1-c\right)\ge \rho {\left(x\right)}^{2}/2$

and

$\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)=\rho \left(x\right)+c\rho {\left(x\right)}^{3}<1-{\rho }_{2}{\rho }_{3}=1-c\rho {\left(x\right)}^{3}$

where $|\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)|\le 2{\rho }_{0}^{3}=0.41024$.

If $0\le c\le \frac{1}{2}<\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^{3}}=\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^{2}}\le 1$ in which ${\rho }_{0}\le \rho \left(x\right)<{{\rho }^{\prime }}_{0}$ ;

Finally,

${\rho }_{1}-{\rho }_{3}=\rho \left(x\right)\left(1-c\right)<\rho \left(x\right)/2,{\rho }_{2}-{\rho }_{1}{\rho }_{3}=\rho {\left(x\right)}^{2}\left(1-c\right)<\rho {\left(x\right)}^{2}/2$

and

$\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)=\rho \left(x\right)+c\rho {\left(x\right)}^{3}<1-{\rho }_{2}{\rho }_{3}=1-c\rho {\left(x\right)}^{3}$

where $|\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)|<{\left({{\rho }^{\prime }}_{0}\right)}^{3}=0.31767$ .

If $\frac{1}{2} in which ${\rho }_{0}\le \rho \left(x\right)<{{\rho }^{\prime }}_{0}$.

In particular, when c is nearly to 1/2, there are

${\rho }_{1}-{\rho }_{3}=\rho \left(x\right)\left(1-c\right)\to \rho \left(x\right)/2,{\rho }_{2}-{\rho }_{1}{\rho }_{3}=\rho {\left(x\right)}^{2}\left(1-c\right)\to \rho {\left(x\right)}^{2}/2$

and the following statements hold.

a) The absolute value $|\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)|$ is nearly to 0 if $0 in which $1>\rho \left(x\right)\ge {{\rho }^{\prime }}_{0}$.

b) The value $\left[\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)\right]$ is included in the interval $\left[-{\rho }_{0}^{3}=-0.20512,0\right)$ if $0 in which ${\rho }_{0}\le \rho \left(x\right)<{{\rho }^{\prime }}_{0}$.

c) The value $\left[\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)-\left(1-{\rho }_{2}{\rho }_{3}\right)\right]$ is included in the interval $\left[-{\rho }_{0}^{3}=-0.20512,0\right)$ if $\frac{1}{2} in which ${\rho }_{0}\le \rho \left(x\right)<{{\rho }^{\prime }}_{0}$. #

Corollary 2.1. [23] Under model (2), the following statements hold.

1) For any $0, there is a unique solution $u\in \left(7,7.4\right)$ and there is also a unique solution $v\in \left(7.4,7.8\right)$, such that

$\lambda \left(7.4\right)=0\le \lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \lambda \left(u\right)=\lambda \left(v\right)=\left(1-d\right)/\left(2d\right),$

$\rho \left(u\right)=\rho \left(v\right)=d\le \rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\le 1=\rho \left(7.4\right).$

2) The condition $x\in \left[\text{7}\text{.35,7}\text{.45}\right]$ is equivalent to each of the following conditions:

$\lambda \left(7.4\right)=0\le \lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \lambda \left(7.35\right)=\lambda \left(7.45\right)=0.31743,$

$\rho \left(7.35\right)=\rho \left(7.45\right)=0.61167\le \rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\le 1=\rho \left(7.4\right).$

3) The condition $x\in \left[7.35129,7.44871\right]$ is equivalent to each of the following conditions:

$\lambda \left(7.4\right)=0\le \lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \lambda \left(7.35129\right)=\lambda \left(7.44871\right)=0.30902,$

$\rho \left(7.35129\right)=\rho \left(7.44871\right)=\phi \le \rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\le 1=\rho \left(7.4\right).$

4) The condition $x\in \left[7.34539,7.45461\right]$ is equivalent to each of the following conditions:

$\lambda \left(7.4\right)=0\le \lambda \left(x\right)\le \lambda \left(7.34539\right)=\lambda \left(7.45461\right)={\rho }_{0}^{2}=0.34781,$

$\rho \left(7.34539\right)=\rho \left(7.45461\right)={\rho }_{0}\le \rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\le 1=\rho \left(7.4\right).$

5) The condition $x\in \left[7.36307,7.43693\right]$ is equivalent to each of the following conditions:

$\lambda \left(7.4\right)=0\le \lambda \left(x\right)\le \lambda \left(\text{7}.\text{363}0\text{7}\right)=\lambda \left(\text{7}.\text{43693}\right)={\left({{\rho }^{\prime }}_{0}\right)}^{2}/2=\text{0}\text{.23279,}$

$\rho \left(7.36307\right)=\rho \left(7.43693\right)={{\rho }^{\prime }}_{0}\le \rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\le 1=\rho \left(7.4\right).$ #

In west, through experiment or through practice observation, many researchers [1] - [14] have obtained the normal range of human blood pH value as $x\in \left[7.35,7.45\right]$. But in TCM, from Yin Yang Wu Xing Theory, Zhang [17] has already determined: ${\rho }_{0}\le {\rho }_{1}\le 1$ for the normal range of a healthy body. Taking ${\rho }_{1}=\rho \left(x\right),{\rho }_{2}=\rho {\left(x\right)}^{2}$ and ${\rho }_{3}=c\rho \left(x\right)$ where $0\le c\le 1$ for a human body which has the capabilities of both intervention reaction and self-protection. From Corollary 2.1, the condition ${\rho }_{0}\le {\rho }_{1}=\rho \left(x\right)\le 1$ is equivalent to $x\in \left[7.34539,7.45461\right]$. In other words, in Theory of TCM, the normal range of human blood pH value is considered as $x\in \left[7.34539,7.45461\right]$, nearly to $x\in \left[7.35,7.45\right]$. Of course, little difference of the two intervals which makes the diagnosis of disease as a result, there may be no much difference as a suspect. In fact, TCM uses the rule ${\rho }_{0}\le {\rho }_{1}\le 1$ from the Yin Yang Wu Xing Theory instead of the normal range of human blood pH value. The equivalence of Corollary 2.1 shows that TCM is the scientific.

Zhang [17] has already determined: a body is said healthy when the intervention reaction coefficient ${\rho }_{1}$ satisfies $1\ge {\rho }_{1}\ge {\rho }_{0}$. In logic and practice, it’s reasonable that ${\rho }_{1}+{\rho }_{2}$ is near to 1 if the input and output in a human body is balanced, since an output organ is absolutely necessary other organs of all consumption. In case: ${\rho }_{1}+{\rho }_{2}=1$, all the energy for intervening organ can transmit to other organs which have neighboring relations or alternate relations with the intervening organ. The condition $1\ge {\rho }_{1}\ge {\rho }_{0}$ can be satisfied when ${\rho }_{2}={\rho }_{1}{\rho }_{3}$ and ${\rho }_{3}={\rho }_{1}$ for an organ since ${\rho }_{1}+{\rho }_{2}=1$ implies ${\rho }_{1}=\phi \approx 0.61803\ge {\rho }_{0}$. In this case, ${\rho }_{2}={\phi }^{2}\approx 0.38197$. If this assumption is set up, then the intervening principle: “Real disease with a healthy body is to rush down its son and virtual disease with a healthy body is to fill its mother” based on the Yin Yang Wu Xing theory in image mathematics by Zhang and Shao [20], is quite reasonable. But, in general, the ability of self-protection is often insufficient for a usual human body, i.e., ${\rho }_{3}$ is small. A common standard is ${\rho }_{3}=\left(1-{\rho }_{1}\right)/\left(2{\rho }_{2}\right)\approx 1/2$ which comes from the balance condition $\left(1-{\rho }_{2}{\rho }_{3}\right)=\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)$ of the loving relationship if ${\rho }_{1}+{\rho }_{2}\approx 1$. In other words, there is a principle which all losses are bear in a human body. Thus the general condition is often ${\rho }_{1}\approx 0.61803\ge {\rho }_{3}\approx 0.5\ge {\rho }_{2}\approx 0.38197$. Interestingly, they are all near to the golden numbers. It is the idea to consider the unhealthy number ${{\rho }^{\prime }}_{0}=0.68232780$ since the poor condition of self-protection ability ${\rho }_{3}={{\rho }^{\prime }}_{0}/2=0.34116390$ can make the unhealthy balance conditions hold

$\begin{array}{l}{\rho }_{1}-{\rho }_{3}={\rho }_{3}={{\rho }^{\prime }}_{0}/2=0.34116390,\\ {\rho }_{2}-{\rho }_{1}{\rho }_{3}={\rho }_{1}{\rho }_{3}={\left({{\rho }^{\prime }}_{0}\right)}^{2}/2=0.23278561\\ 1-{\rho }_{2}{\rho }_{3}={\rho }_{1}+{\rho }_{2}{\rho }_{3}\end{array}$

if ${\rho }_{1}={{\rho }^{\prime }}_{0}$ and ${\rho }_{2}={\left({{\rho }^{\prime }}_{0}\right)}^{2}=0.46557123$.

By Theorem 2.1 and Corollary 2.1, $x\in \left[7.35,7.45\right]$ implies $1\ge {\rho }_{1}=\rho \left(x\right)\ge 0.61167=\rho \left(7.35\right)=\rho \left(7.45\right)$.

And $x\in \left[7.35129,7.44871\right]$ implies

$1\ge {\rho }_{1}=\rho \left(x\right)\ge \phi =\rho \left(7.35129\right)=\rho \left(7.44871\right)$.

And $x\in \left[7.34539,7.45461\right]$ implies

$1\ge {\rho }_{1}=\rho \left(x\right)\ge {\rho }_{0}=\rho \left(7.34539\right)=\rho \left(7.45461\right),$

where $\lambda \left(7.34539\right)=\lambda \left(7.45461\right)=\frac{1-{\rho }_{0}}{2{\rho }_{0}}={\rho }_{0}^{2}$.

Since $\left(1-{\rho }_{0}^{3}\right)=\left({\rho }_{0}+{\rho }_{0}^{3}\right)$.

And $x\in \left[7.36307,7.43693\right]$ implies

$1\ge {\rho }_{1}=\rho \left(x\right)\ge {{\rho }^{\prime }}_{0}=\rho \left(7.36307\right)=\rho \left(7.43693\right),$

where $\lambda \left(7.36307\right)=\lambda \left(7.43693\right)=\frac{1-{{\rho }^{\prime }}_{0}}{2{{\rho }^{\prime }}_{0}}=\frac{{\left({{\rho }^{\prime }}_{0}\right)}^{2}}{2}$.

Since $\left(1-{{\rho }^{\prime }}_{0}\right)={\left({{\rho }^{\prime }}_{0}\right)}^{3}$.

The last one is the healthy interval in a person’s self-protection ability poor conditions. The interval range is relative to the normal human body’s health requirements too strict. Only the first three interval ranges are considered as a normal human body’s health. If keep two decimal places, then the first three intervals are the same as $x\in \left[7.35,7.45\right]$. This shows that range $x\in \left[7.35,7.45\right]$ is stable. The interval as the normal range of human blood pH value may be also appropriate. To conservative estimates, the interval of the largest length of the first three range intervals is used, i.e., $x\in \left[7.34539,7.45461\right]$, as the theoretical analysis of the normal range. In fact, the range $x\in \left[7.34539,7.45461\right]$ is better than the range $x\in \left[7.35,7.45\right]$. It is because the range $x\in \left[7.34539,7.45461\right]$ satisfies the healthy balance conditions ${\rho }_{1}={\rho }_{3},{\rho }_{2}={\rho }_{1}{\rho }_{3}$ and $\left(1-{\rho }_{2}{\rho }_{3}\right)\le \left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)$ if ${\rho }_{1}=\rho \left(x\right),{\rho }_{2}=\rho {\left(x\right)}^{2}$ and ${\rho }_{3}=c\rho \left(x\right)\to {\rho }_{1}$. In other words, the parameter ${\rho }_{1}=\rho \left(x\right)\ge {\rho }_{0}$ or the range $x\in \left[7.34539,7.45461\right]$ is the healthy running condition of both the killing relationship and the loving relation at the same time. But neither are the others. The human blood pH value must be precise calculation to keep at least 5 decimal places can ensure correct because of its sensitivity to the diagnosis of disease.

3. Relations of Steady Multilateral Systems

3.1. Energy Changes of a Steady Multilateral System

In order to apply the reasoning to other fields rather than the health of the human body complex system, Zhang [18] has started a steady multilateral system imitating a human body complex system. A most basic steady multilateral system is as follows.

Theorem 3.1. Zhang and Shao [20] For each element x in a steady multilateral system $V$ with two incompatibility relations, there exist five equivalence classes below:

$X=\left\{y\in V|y~x\right\},{X}_{S}=\left\{y\in V|x\to y\right\},{X}_{K}=\left\{y\in V|x⇒y\right\},$

${K}_{X}=\left\{y\in V|y⇒x\right\},{S}_{X}=\left\{y\in V|y\to x\right\},$

which the five equivalence classes have relations in Figure 1. #

The Yin Yang Wu Xing model can be written as follows: Define

${V}_{0}=X,{V}_{1}={X}_{S},{V}_{2}={X}_{K},{V}_{3}={K}_{X},{V}_{4}={S}_{X},$

Figure 1. Finding Yin Yang Wu Xing model.

corresponding to wood, fire, earth, metal, water, respectively, and assume $V={V}_{0}+{V}_{1}+{V}_{2}+{V}_{3}+{V}_{4}$ where ${V}_{i}\cap {V}_{j}=\varnothing ,\forall i\ne j$.

And take $\Re =\left\{{R}_{0},{R}_{1},\cdots ,{R}_{4}\right\}$ satisfying

${R}_{r}=\underset{i=0}{\overset{4}{\sum }}{V}_{i}×{V}_{mod\left(i+r,5\right)},\forall r\in \left\{0,1,\cdots ,4\right\},{R}_{i}*{R}_{j}\subseteq {R}_{mod\left(i+j,5\right)},$

where ${V}_{i}×{V}_{j}=\left\{\left(x,y\right):x\in {V}_{i},y\in {V}_{j}\right\}$ is the Descartesian product in set theory and the following note ${R}_{i}*{R}_{j}=\left\{\left(x,y\right):\exists u\in V\text{suchthat}\left(x,u\right)\in {R}_{i},\left(u,y\right)\in {R}_{j}\right\}$ is the relation multiplication operation. The relation multiplication of $*$ is isomorphic to the addition of module A. Then ${V}^{5}$ is a steady multilateral system with one equivalent relation ${R}_{0}$ and two incompatibility relations ${R}_{1}={R}_{4}^{-1}$ and ${R}_{2}={R}_{3}^{-1}$ where the note ${R}_{i}^{-1}=\left\{\left(x,y\right):\left(y,x\right)\in {R}_{i}\right\}$ is the relation inverse operation.

The Yin and Yang mean the two incompatibility relations and the Wu Xing means the collection of five disjoint classification of ${V}^{5}={V}_{0}^{5}+{V}_{1}^{5}+{V}_{2}^{5}+{V}_{3}^{5}+{V}_{4}^{5}$. The model is called Yin Yang Wu Xing model, denoted simply by ${V}^{5}=\left\{0,1,2,3,4\right\}$.

It can be proved that the steady multilateral system in Theorem 3.1 is the reasoning model of Yin Yang Wu Xing in TCM if there is an energy function $\phi \left(*\right)$ satisfying

$\begin{array}{l}\frac{\Delta \phi \left(X\right)}{\Delta }\to \frac{\text{d}\phi \left(X\right)}{\text{d}X}=\left(1-{\rho }_{2}{\rho }_{3}\right)=\left(1-c\rho {\left(x\right)}^{3}\right)>0;\\ \frac{\Delta \phi \left({X}_{S}\right)}{\Delta }\to \frac{\text{d}\phi \left({X}_{S}\right)}{\text{d}X}=\left({\rho }_{1}+{\rho }_{2}{\rho }_{3}\right)=\rho \left(x\right)\left(1+c\rho {\left(x\right)}^{2}\right)>0;\\ \frac{\Delta \phi \left({X}_{K}\right)}{\Delta }\to \frac{\text{d}\phi \left({X}_{K}\right)}{\text{d}X}=-\left({\rho }_{1}-{\rho }_{3}\right)=-\rho \left(x\right)\left(1-c\right)<0;\\ \frac{\Delta \phi \left({K}_{X}\right)}{\Delta }\to \frac{d\phi \left({K}_{X}\right)}{\text{d}X}=-\left({\rho }_{2}-{\rho }_{1}{\rho }_{3}\right)=-\rho {\left(x\right)}^{2}\left(1-c\right)<0;\\ \frac{\Delta \phi \left({S}_{X}\right)}{\Delta }\to \frac{\text{d}\phi \left({S}_{X}\right)}{\text{d}X}=\left({\rho }_{2}-{\rho }_{1}{\rho }_{3}\right)=\rho {\left(x\right)}^{2}\left(1-c\right)>0,\end{array}$

if increase the energy of $X$ ( $\forall \Delta \phi \left(X\right)=\Delta >0$ ),

where ${\rho }_{1}=\rho \left(x\right),{\rho }_{2}=\rho {\left(x\right)}^{2},{\rho }_{3}=c\rho \left(x\right),0<\rho \left(x\right)<1,0\le c\le 1$.

The parameter ${\rho }_{v}={\rho }_{1}+{\rho }_{2}{\rho }_{3}$ is called the coefficient of the vital or righteousness energy. The parameter ${\rho }_{e}=1-{\rho }_{2}{\rho }_{3}$ is called the coefficient of the evil energy. A Human Body complex system is called healthy if the vital or righteousness coefficient ${\rho }_{v}={\rho }_{1}+{\rho }_{2}{\rho }_{3}$ is greater than or equal to the evil coefficient ${\rho }_{e}=1-{\rho }_{2}{\rho }_{3}$. Otherwise, the Human Body complex system is called unhealthy. For a healthy Human Body complex system, the transfer law of the Yang vital or righteousness energy in the Yin Yang Wu Xing Model is

$\begin{array}{l}\text{Wood}\left(X\right)\to \text{Fire}\left({X}_{S}\right)\to \text{Earth}\left({X}_{K}\right)\to \text{Metal}\left({K}_{X}\right)\\ \to \text{Water}\left({S}_{X}\right)\to \text{Wood}\left(X\right)\to \cdots .\end{array}$

Figure 1 in Theorem 3.1 is the figure of Yin Yang Wu Xing theory in Ancient China. The steady multilateral system $V$ with two incompatibility relations is equivalent to the logic architecture of reasoning model of Yin Yang Wu Xing theory in Ancient China. What describes the general method of the steady multilateral system $V$ with two incompatibility relations can be used in the Human Body complex systems.

By non-authigenic logic of TCM, i.e., a logic which is similar to a group has nothing to do with the research object in Zhang and Shao [20], in order to ensure the reproducibility such that the analysis conclusion can be applicable to any complex system, a logical analysis model can be chosen which has nothing to do with the object of study. The Tao model of Yin and Yang is a generalized one which means that two is basic. But the Tao model of Yin Yang is simple in which there is not incompatibility relation. The analysis conclusion of Tao model of Yin Yang cannot be applied to an incompatibility relation model. Thus the Yin Yang Wu Xing model with two incompatibility relations of Theorem 3.1 will be selected as the logic analysis model in this paper.

On the other hand, the steady multilateral system $\left({V}^{2},{\Re }^{2}\right)=\left({V}_{0}^{2}+{V}_{1}^{2},\left\{{R}_{0}^{2},{R}_{1}^{2}\right\}\right)$ is called the Tao model, denoted simply by ${V}^{2}=\left\{0,1\right\}$, if it satisfies the following conditions:

$\begin{array}{l}{R}_{r}^{2}=\underset{i=0}{\overset{1}{\sum }}{V}_{i}^{2}×{V}_{mod\left(i+r,2\right)}^{2},\forall r\in \left\{0,1\right\},{R}_{i}^{2}*{R}_{j}^{2}={R}_{mod\left(i+j,2\right)}^{2},\\ {R}_{0}^{2}=\left\{\left(0,0\right),\left(1,1\right)\right\},{R}_{1}^{2}=\left\{\left(0,1\right),\left(1,0\right)\right\}.\end{array}$

The relation multiplication of $*$ is isomorphic to the addition of module 2. The element 1or 0 is called a Yang force or a Yin force respectively. For a healthy human body, the transfer law of the Tao force in the Tao model is from Yang to Yin.

In TCM, any material can be found, not Yang is Yin. No matter of Yin and Yang are unable to see, known as dark matter, or nonphysical. Therefore, the Tao force is often existing in the physical world. Any a steady multilateral system only force under the action of the Tao, may be to be perceived.

In TCM, it is believed that any a Yin Yang Wu Xing complex system is made up of three types of talent or material to combined changes. The three types come from the Yin energy in it’s a layer Yin Yang Wu Xing system. It is because a lot of complex systems can be seen as a Yin Yang Wu Xing system. However, any a Yin Yang Wu Xing system is a human body observation of the objective object in one logic level, it will be a layer of the Yin Yang Wu Xing system of restriction and generation. In the Yin Yang Wu Xing system, both wood and fire are Yang; three types including earth, metal and water are Yin. So any Yin Yang Wu Xing system is generated by the three talents (earth, gold and water) at the upper logical level. The three types are generated from an upper layer of the Yin Yang Wu Xing system. For example, an upper layer of controlling on the Yin Yang Wu Xing system of human body is the nature, Tao, heaven, earth and people system, so the formation of the human body three materials are heaven (1), earth (2) and people (3).

The three Tao model can combine forming a steady multilateral system

$\left({V}^{8},{\Re }^{8}\right)=\left({V}_{1}^{8}+\cdots +{V}_{8}^{8},\left\{{R}_{1}^{8},\cdots ,{R}_{8}^{8}\right\}\right)$

is called the Eight-Hexagram (八卦) model, denoted simply by

${V}^{8}=\left\{\left(1,1,1\right),\left(0,1,1\right),\left(1,0,1\right),\left(0,0,1\right),\left(1,1,0\right),\left(0,1,0\right),\left(1,0,0\right),\left(0,0,0\right)\right\}$

which satisfies the following conditions:

$\begin{array}{l}{R}_{r}^{8}=\underset{i=1}{\overset{8}{\sum }}{V}_{i}^{8}×{V}_{i*r}^{8},\forall r\in \left\{1,2,\cdots ,8\right\},\\ {R}_{i}^{8}*{R}_{j}^{8}={R}_{i*j}^{8},\forall i,j\in \left\{1,2,\cdots ,8\right\},\end{array}$

The number $1,2,3,4,5,6,7,8$ is called the Qian (乾), Dui (兑), Li (离), Zhen (震), Xun (巽), Kan (坎), Gen (艮), Kun (坤) respectively. The set of $\left\{1,2,3,4,5,6,7,8\right\}$ is called the Eight-Hexagram (八卦) system.

On the other hand, the three types heaven (1), earth (2) and people (3) to any change combine forming the Telluric effluvium model as follows:

$\left({V}^{6},{\Re }^{6}\right)=\left({V}_{1}^{6}+\cdots +{V}_{6}^{6},\left\{{R}_{1}^{6},\cdots ,{R}_{6}^{6}\right\}\right)$

is called the Telluric effluvium model, denoted simply by ${V}^{6}=\left\{e,\left(12\right),\left(13\right),\left(23\right),\left(123\right),\left(132\right)\right\}$, if it satisfies the following conditions:

$\begin{array}{l}{R}_{r}^{6}=\underset{i=1}{\overset{6}{\sum }}{V}_{i}^{6}×{V}_{i*r}^{6},\forall r\in \left\{1,2,\cdots ,6\right\},\\ {R}_{i}^{6}*{R}_{j}^{6}={R}_{i*j}^{6},\forall i,j\in \left\{1,2,\cdots ,6\right\},\end{array}$

$\begin{array}{ccccccc}i*r& 1=e& 2=\left(12\right)& 3=\left(13\right)& 4=\left(23\right)& 5=\left(123\right)& 6=\left(132\right)\\ 1=e& 1=e& 2=\left(12\right)& 3=\left(13\right)& 4=\left(23\right)& 5=\left(123\right)& 6=\left(132\right)\\ 2=\left(12\right)& 2=\left(12\right)& 1=e& 5=\left(123\right)& 6=\left(132\right)& 3=\left(13\right)& 4=\left(23\right)\\ 3=\left(13\right)& 3=\left(13\right)& 6=\left(132\right)& 1=e& 5=\left(123\right)& 4=\left(23\right)& 2=\left(12\right)\\ 4=\left(23\right)& 4=\left(23\right)& 5=\left(123\right)& 6=\left(132\right)& 1=e& 2=\left(12\right)& 3=\left(13\right)\\ 5=\left(123\right)& 5=\left(123\right)& 4=\left(23\right)& 2=\left(12\right)& 3=\left(13\right)& 6=\left(132\right)& 1=e\\ 6=\left(132\right)& 6=\left(132\right)& 3=\left(13\right)& 4=\left(23\right)& 2=\left(12\right)& 1=e& 5=\left( 123 \right)\end{array}$

The number 1 or 2 or 3 is called the tengen (天元), the earth material (地元), the people ability (人元), respectively. The set of {1, 2, 3} is called three types of talent or material. It is with elements, $e,\left(12\right),\left(13\right),\left(23\right),\left(123\right),\left(132\right)$ The each of elements, $e,\left(12\right),\left(13\right),\left(23\right),\left(123\right),\left(132\right)$ is called the primordial energy (元气), essence derived from food (谷气), defensive energy (卫气), essential substance circulating in the Meridians and blood Meridians (营气), genuine energy (真气), pectoral energy (宗气), respectively. Another name is respectively

$\begin{array}{l}\text{shaoyang}\left(e\right)\left(少阳\right),\text{yangming}\left(\left(12\right)\right)\left(阳明\right),\text{taiyang}\left(\left(13\right)\right)\left(太阳\right),\\ \text{jueyin}\left(\left(23\right)\right)\left(厥阴\right),\text{shaoyin}\left(\left(123\right)\right)\left(少阴\right),\text{taiyin}\left(\left(132\right)\right)\left(太阴\right).\end{array}$

Generally positive or Yang material, they are able to be perceived, but few can see the material itself, can only use signs. Therefore, the Yang energy symptoms of the set ${M}_{1}=\left\{e,\left(12\right),\left(13\right)\right\}$ is called the marrow energy (髓); The Yin energy of the set ${M}_{2}=\left\{\left(123\right)\right\}$ is called the blood energy (血); The Yin energy of the set ${M}_{3}=\left\{\left(132\right)\right\}$ is called the saliva energy (津); The Yin energy of the set ${M}_{4}=\left\{\left(23\right)\right\}$ is called the essence of water and grain (水谷精微).

Growth and conveyance in the six energies $e,\left(12\right),\left(13\right),\left(23\right),\left(123\right),\left(132\right)$ known as the six roots (根); As the fruit of these six energies $e,\left(12\right),\left(13\right),\left(23\right),\left(123\right),\left(132\right)$ known as the six fruits (结); Storage of these four energies ${M}_{1},{M}_{2},{M}_{3},{M}_{4}$ known as the four seas (四海); Energy exchange of the four kinds of ${M}_{1},{M}_{2},{M}_{3},{M}_{4}$ known as the four streets (四街). Of course, for a healthy human body, the transfer law of each of the six energies $e,\left(12\right),\left(13\right),\left(23\right),\left(123\right),\left(132\right)$ is from its root (root-causes) (根) to its fruit (symptoms) (结).

Western Medicine is different from TCM because the TCM has a concept of Chi or Qi () as a form of energy of steady multilateral systems. It is believed that this energy exists in all things of steady multilateral systems (living and non-living) including air, water, food and sunlight. Chi is said to be the unseen vital force that nourishes steady multilateral systems’ body and sustains the life of a steady multilateral system imitating the human body complex system. It is also believed that an individual is born with an original amount of Chi at the beginning of life of a steady multilateral system imitating the human body complex system and as a steady multilateral system grows and lives, the steady multilateral system acquires or attains Chi or energy from “eating” and “drinking”, from “breathing” the surrounding “air” and also from living in its environment. The steady multilateral system having an energy function is called the anatomy system or the first physiological system. And the first physiological system also affords Chi or energy for the steady multilateral system’s meridian system (Zangxiang (藏象) and Jingluo (经络)) which forms a parasitic system of the steady multilateral system, called the second physiological system of the steady multilateral system. The second physiological system of the steady multilateral system controls the first physiological system of the steady multilateral system. A steady multilateral system would become ill or dies if the Chi or energy in the steady multilateral system is imbalanced or exhausted, which means that ${\rho }_{1}=\rho \left(x\right)\to 0,{\rho }_{2}=\rho {\left(x\right)}^{2}\to 0$ and ${\rho }_{3}=c\rho \left(x\right)\to 0$.

For example, in TCM, a human body as the first physiological system of the steady multilateral system following the Yin Yang Wu Xing theory was classified into five equivalence classes as follows:

Wood ( $X$ ) = {liver, bravery, soul, ribs, sour, east, spring, birth};

Xiang-fire ( ${X}_{S}^{x}$ ) = {pericardium, the triple energizer, nerve, blood vessel, bitter taste, the south, summer, growth};

Earth ( ${X}_{K}$ ) = {spleen, stomach, willing, meat, sweetness, center, long summer, combined};

Metal ( ${K}_{X}$ ) = {lung, large intestine, boldness, fur, spicy, west, autumn, accept};

Water ( ${S}_{X}$ ) = {kidney, bladder, ambition, bone, salty, the north, winter, hiding};

Jun-fire ( ${X}_{S}^{j}$ ) = {heart, small intestine, nerve, making blood, bitter taste, whole body, whole direction, throughout the year, overall growth}.

Fire ( ${X}_{S}$ ) = xiang-fire ( ${X}_{S}^{x}$ ) $\cup$ jun-fire ( ${X}_{S}^{j}$ ).

The five equivalence classes also are called as five Zang-Organs or five subsystems of a steady complex system imitating a Human Body complex system. Each of five Zang-Organs is called as Liver Zang-organ as wood ( $X$ ), Heart Zang-organ as fire ( ${X}_{S}$ ), Spleen Zang-organ as earth ( ${X}_{K}$ ), Lung Zang-organ as metal ( ${K}_{X}$ ) and Kidney Zang-organ as water ( ${S}_{X}$ ), respectively. There is only one of both the loving relation and killing relation between every two classes or organs. General close is loving, alternate is killing.

Suppose that the class fire ( ${X}_{S}$ ) is divided into two classes xiang-fire ( ${X}_{S}^{x}$ ) and jun-fire ( ${X}_{S}^{j}$ ). These six equivalence classes are also called six fu-organs or six hollow organs. Each of six fu-organs is called as Liver Fu-organ as wood ( $X$ ), Pericardium Fu-organ or mutually Fu-organ or Xiang (相) Fu-organ as xiang-fire ( ${X}_{S}^{x}$ ), Spleen Fu-organ as earth ( ${X}_{K}$ ), Lung Fu-organ as metal ( ${K}_{X}$ ), Kidney Fu-organ as water ( ${S}_{X}$ ), and Heart Fu-organ or Js mammy Fu-organ or Jun (君) Fu-organ as jun-fire ( ${X}_{S}^{j}$ ), respectively.

Although the energy of Jun (君) Fu-organ as jun-fire ( ${X}_{S}^{j}$ ) is similar to or likes the energy of Xiang (相) Fu-organ as xiang-fire ( ${X}_{S}^{x}$ ) in logic, the energy of the six fu-organs can be observed, but the energy of the five zang-organs (especially the energy of the heart Zang-organ) cannot be observed, only can be inferred.

In every category of internal, think that they are with an equivalent relationship, between each two of their elements there is a force of similar material accumulation of each other. It is because their pursuit of the goal is the same, i.e., follows the same “Axiom system”. It can increase the energy of the class at low cost near to zero if they accumulate together. Any nature material activity follows the principle of maximizing so energy or minimizing the cost. In other woods, the same energy attracts each other (同气相招).

In general, the size of the force of similar material accumulation of each other is smaller than the size of the loving force or the killing force in a stable Human Body complex system. The stability of any a Human Body complex system first needs to maintain the equilibrium of the killing force and the loving force. The key is the killing force. For a stable Human Body complex system, if the killing force is large, i.e., the self-protection coefficient ${\rho }_{3}=c\rho \left(x\right)$ becomes larger, in which needs a positive exercise, then the loving force is also large such that the force of similar material accumulation of each other is also large. They can make the Human Body complex system more stable. If the killing force is small, i.e., the self-protection coefficient ${\rho }_{3}=c\rho \left(x\right)$ becomes smaller, which means little exercise, then the loving force is also small such that the force of similar material accumulation of each other is also small. They can make the Human Body complex system becoming unstable.

The Chi or energy is also called the food hereafter for simply. In order to get the food, by Attaining Rule below, the second physiologic system must make the first physiologic system done an intervention of it, namely exercise. It is because only by intervention on the first physiologic system, the second physiologic system can be to get food.

The second physiologic system of the steady multilateral system controls the first physiologic system of the steady multilateral system imitating a Human Body complex system, abiding by the following rule.

Intervention Rule: In the case of virtual disease, the treatment method of intervention is to increase the energy. If the treatment has been done on $X$, the energy increment (or, increase degree) $|\Delta \phi \left({X}_{S}\right)|$ of the son ${X}_{S}$ of $X$ is greater than the energy increment (or, increase degree) $|\Delta \phi \left({S}_{X}\right)|$ of the mother ${S}_{X}$ of $X$, i.e., the best benefit is the son ${X}_{S}$ of $X$. But the energy decrease degree $|\Delta \phi \left({X}_{K}\right)|$ of the prisoner ${X}_{K}$ of $X$ is greater than the energy decrease degree $|\Delta \phi \left({K}_{X}\right)|$ of the bane ${K}_{X}$ of $X$, i.e., the worst victim is the prisoner ${X}_{K}$ of $X$.

In the case of real disease, the treatment method of intervention is to decrease the energy. If the treatment has been done on $X$, the energy decrease degree $|\Delta \phi \left({S}_{X}\right)|$ of the mother ${S}_{X}$ of $X$ is greater than the energy decrease degree $|\Delta \phi \left({X}_{S}\right)|$ of the son ${X}_{S}$ of $X$ i.e., the best benefit is the mother ${S}_{X}$ of $X$. But the energy increment (or, increase degree) $|\Delta \phi \left({K}_{X}\right)|$ of the bane ${K}_{X}$ of $X$ is greater than the energy increment (or, increase degree) $|\Delta \phi \left({X}_{K}\right)|$ of the prisoner ${X}_{K}$ of $X$, i.e., the worst victim is the bane ${K}_{X}$ of $X$.

In mathematics, the changing laws are as follows.

1) If $\Delta \phi \left(X\right)=\Delta >0$, then $\Delta \phi \left({X}_{S}\right)={\rho }_{1}\Delta$, $\Delta \phi \left({X}_{S}\right)=-{\rho }_{1}\Delta$, $\Delta \phi \left({X}_{K}\right)=-{\rho }_{2}\Delta$, $\Delta \phi \left({S}_{X}\right)={\rho }_{2}\Delta$ ;

2) If $\Delta \phi \left(X\right)=-\Delta <0$, then $\Delta \phi \left({S}_{X}\right)=-{\rho }_{1}\Delta$, $\Delta \phi \left({K}_{X}\right)={\rho }_{1}\Delta$, $\Delta \phi \left({X}_{K}\right)={\rho }_{2}\Delta$, $\Delta \phi \left({X}_{S}\right)=-{\rho }_{2}\Delta$ ;

where $1\ge {\rho }_{1}\ge {\rho }_{2}\ge 0$.

Both ${\rho }_{1}$ and ${\rho }_{2}$ are called intervention reaction coefficients, which are used to represent the capability of intervention reaction. The larger the intervention reaction coefficient ${\rho }_{1}$ is, the better the capability of intervention reaction is. The state ${\rho }_{1}=1$ is the best state but the state ${\rho }_{1}=0$ is the worst state.

The Intervention rule can be explained as: In general, the intervention rule is similar to force and reaction in Physics. In other words, if a subsystem of a multilateral system V has been done an intervention of it, then the energy of subsystem which has a neighboring relation (or beneficiary) changes in the same direction of the force, and the energy of subsystem which has an alternate relation (or victim) changes in the opposite direction of the force. The size of the energy changed is equal, but the direction opposite.

Self-protection Rule: In the case of virtual disease, the treatment method of intervention is to increase the energy. If the treatment has been done on $X$, the worst victim is the prisoner ${X}_{K}$ of $X$. Thus, the treatment of self-protection is to restore the prisoner ${X}_{K}$ of $X$ and the restoring method of self-protection is to increase the energy $\phi \left({X}_{K}\right)$ of the prisoner ${X}_{K}$ of $X$ by using the intervention force on $X$ according to the intervention rule.

In the case of real disease, the treatment method of intervention is to decrease the energy. If the treatment has been done on $X$, the worst victim is the bane ${K}_{X}$ of $X$. Thus, the treatment of self-protection is to restore the bane ${K}_{X}$ of $X$ and the restoring method of self-protection is to decrease the energy $\phi \left({K}_{X}\right)$ of the bane ${K}_{X}$ of $X$ by using the same intervention force on $X$ according to the intervention rule.

In mathematics, the following self-protection laws hold.

1) If $\Delta \phi \left(X\right)=\Delta >0$, then the energy of subsystem ${X}_{K}$ will decrease the increment $\left(-{\rho }_{1}\Delta \right)$, which is the worst victim. So the capability of self-protection increases the energy of subsystem ${X}_{K}$ by increment $\left({\rho }_{3}\Delta \right)\left(0\le {\rho }_{3}\le {\rho }_{1}\right)$ in order to restore the worst victim ${X}_{K}$ by according to the intervention rule.

2) If $\Delta \phi \left(X\right)=-\Delta <0$, then the energy of subsystem ${K}_{X}$ will increase the increment $\left({\rho }_{1}\Delta \right)$, which is the worst victim. So the capability of self-protection decreases the energy $\phi \left({K}_{X}\right)$ of subsystem ${K}_{X}$ by increment $\left(-{\rho }_{3}\Delta \right)\left(0\le {\rho }_{3}\le {\rho }_{1}\right)$ in order to restore the worst victim ${K}_{X}$ by according to the intervention rule.

The self-protection rule can be explained as: the general principle of a self-protection subsystem is that the worst victim is protected firstly, the protection method is in the same way to the intervention force but any beneficiary should be not protected.

Attaining Rule: The second physiologic system of the steady multilateral system will work by using Attaining Rule, if the first physiologic system of the steady multilateral system runs normally. The work is in order to attain the Chi or energy from the first physiologic system of the steady multilateral system by mainly utilizing the balance of the loving relationship of the first physiologic system.

In mathematics, suppose that the steady multilateral system imitating the Human Body complex system of $X$ is healthy. If $X$ is done an intervention of it, then the second physiologic system will attain the Chi or energy from $X$ directly.

Suppose that the steady multilateral system imitating the Human Body complex system of $X$ is unhealthy. If $X$ is done an intervention of it, then the second physiologic system will attain the Chi or energy from $X$ indirectly. If virtual $X$ is done an intervention of it, it will attain the Chi or energy (Yang energy) from the son ${X}_{S}$ of $X$. If real $X$ is done an intervention of it, it will attain the Chi or energy (Yin energy) from the mother ${S}_{X}$ of $X$.

Affording Rule: The second physiologic system of the steady multilateral system will work by using Affording Rule, if the first physiologic system of the steady multilateral system runs hardly. The work is in order to afford the Chi or energy for the first physiologic system of the steady multilateral system, by mainly protecting or maintaining the balance of the killing relationship of the steady multilateral system, to drive the first physiologic systems will begin to run normally.

In mathematics, suppose that the steady multilateral system imitating the Human Body complex system of $X$ is healthy. The second physiologic system doesn’t afford any Chi or energy for the first physiologic system.

Suppose that the steady multilateral system imitating the Human Body complex system of $X$ is unhealthy and the capability of self-protection is lack, i.e., ${\rho }_{3}=c\rho \left(x\right)\ge 0$ and $0<{\rho }_{1}<{\rho }_{0}$. The second physiologic system will afford the Chi or energy for $X$ directly, at the same time, affording the Chi or energy for other subsystems, in order to protect or maintain the balance of the killing relationship, abiding by the intervening principle of “Strong inhibition of the same time, support the weak”, such that the capability of self-protection is restored, i.e., ${\rho }_{3}=c\rho \left(x\right)>0$ and $1\ge {\rho }_{1}=\rho \left(x\right)>{\rho }_{0}$, to drive the first physiologic system beginning to work. #

The Chi or energy is also called the food hereafter for simply. In order to get the food, by Attaining Rule, the second physiologic system must make the first physiologic system done an intervention of it, namely exercise. It is because only by intervention in the first physiologic system, the second physiologic system can be to get food.

In particular, the eight palaces system is defined in mathematically as follows:

Definition 3.1. (eight palaces or eight veins) Assume that the Eight-Hexagram model ${V}^{8}$ is implemented by the Eight-Hexagram force of the Eight-Hexagram model ${V}^{8}$ . Then the steady multilateral system ${V}^{8}×{V}^{8}=\left\{\left(i,j\right)|i\in {V}^{8},j\in {V}^{8}\right\}$ is called the model of eight palaces or eight veins of the steady multilateral system.

The model satisfies as follows:

$\begin{array}{l}{R}_{\left(r,{r}^{\prime }\right)}^{\left(8,8\right)}=\underset{\left(i,{i}^{\prime }\right)=\left(1,1\right)}{\overset{\left(8,8\right)}{\sum }}{V}_{\left(i,{i}^{\prime }\right)}^{\left(8,8\right)}×{V}_{\left(i*r,{i}^{\prime }*{r}^{\prime }\right)}^{\left(8,9\right)},\forall \left(r,{r}^{\prime }\right)\in {V}^{8}×{V}^{8},\\ {R}_{\left(i,{i}^{\prime }\right)}^{\left(8,8\right)}*{R}_{\left(j,{j}^{\prime }\right)}^{\left(8,8\right)}={R}_{\left(i*j,{i}^{\prime }*{j}^{\prime }\right)}^{\left(8,8\right)}.\end{array}$

Here, the multiplication operation * is that of the Eight-Hexagram Model.

Each of the elements,

$\begin{array}{l}\left(1,1\right),\left(1,5\right),\left(1,7\right),\left(1,8\right),\left(5,8\right),\left(7,8\right),\left(3,8\right),\left(3,1\right),\\ \left(2,2\right),\left(2,6\right),\left(2,8\right),\left(2,7\right),\left(6,7\right),\left(8,7\right),\left(4,7\right),\left(4,2\right),\\ \left(3,3\right),\left(3,7\right),\left(3,5\right),\left(3,6\right),\left(7,6\right),\left(5,6\right),\left(1,6\right),\left(1,3\right),\\ \left(4,4\right),\left(4,8\right),\left(4,6\right),\left(4,5\right),\left(8,5\right),\left(6,5\right),\left(2,5\right),\left(2,4\right),\end{array}$

$\begin{array}{l}\left(5,5\right),\left(5,1\right),\left(5,3\right),\left(5,4\right),\left(1,4\right),\left(3,4\right),\left(7,4\right),\left(7,5\right),\\ \left(6,6\right),\left(6,2\right),\left(6,4\right),\left(6,3\right),\left(2,3\right),\left(4,3\right),\left(8,3\right),\left(8,6\right),\\ \left(7,7\right),\left(7,3\right),\left(7,1\right),\left(7,2\right),\left(3,2\right),\left(1,2\right),\left(5,2\right),\left(5,7\right),\\ \left(8,8\right),\left(8,4\right),\left(8,2\right),\left(8,1\right),\left(4,1\right),\left(2,1\right),\left(6,1\right),\left(6,8\right),\end{array}$

is called respectively

$\begin{array}{l}Qian\left(1,1\right),Gou\left(1,5\right),Dun\left(1,7\right),Fou\left(1,8\right),Guan\left(5,8\right),Bo\left(7,8\right),\\ Jin\left(3,8\right),You\left(3,1\right);\\ Dui\left(2,2\right),Kun\left(2,6\right),Cui\left(2,8\right),Xian\left(2,7\right),Jian\left(6,7\right),Qian\left(8,7\right),\\ Xiao\left(4,7\right),Mei\left(4,2\right);\end{array}$

$\begin{array}{l}Li\left(3,3\right),Lv\left(3,7\right),Ding\left(3,5\right),Wei\left(3,6\right),Meng\left(7,6\right),Huan\left(5,6\right),\\ Song\left(1,6\right),Ren\left(1,3\right);\\ Zhen\left(4,4\right),Yu\left(4,8\right),Jie\left(4,6\right),Heng\left(4,5\right),Sheng\left(8,5\right),Jing\left(6,5\right),\\ Da\left(2,5\right),Sui\left(2,4\right);\end{array}$

$\begin{array}{l}Xun\left(5,5\right),Xu\left(5,1\right),Jia\left(5,3\right),Yi\left(5,4\right),Wang\left(1,4\right),He\left(3,4\right),\\ Yi\left(7,4\right),Gu\left(7,5\right);\\ Kan\left(6,6\right),Jie\left(6,2\right),Tun\left(6,4\right),Ji\left(6,3\right),Ge\left(2,3\right),Feng\left(4,3\right),\\ Ming\left(8,3\right),Shi\left(8,6\right);\end{array}$

$\begin{array}{l}Gen\left(7,7\right),Bi\left(7,3\right),Xu\left(7,1\right),Sun\left(7,2\right),Gui\left(3,2\right),Lv\left(1,2\right),\\ Fu\left(5,2\right),Jian\left(5,7\right);\\ Kun\left(8,8\right),Fu\left(8,4\right),Lin\left(8,2\right),Tai\left(8,1\right),Zhuang\left(4,1\right),Guai\left(2,1\right),\\ Xu\left(6,1\right),Bi\left(6,8\right);\end{array}$

corresponding to the Chinese words respectively:

Also corresponding to the notations in Theorem 3.1 respectively:

$\begin{array}{l}{K}_{X}^{+}\left(1,1\right),{K}_{X}^{+}\left(1,5\right),{K}_{X}^{+}\left(1,7\right),{K}_{X}^{+}\left(1,8\right),{K}_{X}^{+}\left(5,8\right),{K}_{X}^{+}\left(7,8\right),\\ {K}_{X}^{+}\left(3,8\right),{K}_{X}^{+}\left(3,1\right);\\ {K}_{X}^{-}\left(2,2\right),{K}_{X}^{-}\left(2,6\right),{K}_{X}^{-}\left(2,8\right),{K}_{X}^{-}\left(2,7\right),{K}_{X}^{-}\left(6,7\right),{K}_{X}^{-}\left(8,7\right),\\ {K}_{X}^{-}\left(4,7\right),{K}_{X}^{-}\left(4,2\right);\end{array}$

$\begin{array}{l}{X}_{S}^{-}\left(3,3\right),{X}_{S}^{-}\left(3,7\right),{X}_{S}^{-}\left(3,5\right),{X}_{S}^{-}\left(3,6\right),{X}_{S}^{-}\left(7,6\right),{X}_{S}^{-}\left(5,6\right),\\ {X}_{S}^{-}\left(1,6\right),{X}_{S}^{-}\left(1,3\right);\\ {X}^{+}\left(4,4\right),{X}^{+}\left(4,8\right),{X}^{+}\left(4,6\right),{X}^{+}\left(4,5\right),{X}^{+}\left(8,5\right),{X}^{+}\left(6,5\right),\\ {X}^{+}\left(2,5\right),{X}^{+}\left(2,4\right);\end{array}$

$\begin{array}{l}{X}^{-}\left(5,5\right),{X}^{-}\left(5,1\right),{X}^{-}\left(5,3\right),{X}^{-}\left(5,4\right),{X}^{-}\left(1,4\right),{X}^{-}\left(3,4\right),\\ {X}^{-}\left(7,4\right),{X}^{-}\left(7,5\right);\\ {S}_{X}^{+}\left(6,6\right),{S}_{X}^{+}\left(6,2\right),{S}_{X}^{+}\left(6,4\right),{S}_{X}^{+}\left(6,3\right),{S}_{X}^{+}\left(2,3\right),{S}_{X}^{+}\left(4,3\right),\\ {S}_{X}^{+}\left(8,3\right),{S}_{X}^{+}\left(8,6\right);\end{array}$

$\begin{array}{l}{X}_{K}^{+}\left(7,7\right),{X}_{K}^{+}\left(7,3\right),{X}_{K}^{+}\left(7,1\right),{X}_{K}^{+}\left(7,2\right),{X}_{K}^{+}\left(3,2\right),{X}_{K}^{+}\left(1,2\right),\\ {X}_{K}^{+}\left(5,2\right),{X}_{K}^{+}\left(5,7\right);\\ {X}_{K}^{-}\left(8,8\right),{X}_{K}^{-}\left(8,4\right),{X}_{K}^{-}\left(8,2\right),{X}_{K}^{-}\left(8,1\right),{X}_{K}^{-}\left(4,1\right),{X}_{K}^{-}\left(2,1\right),\\ {X}_{K}^{-}\left(6,1\right),{X}_{K}^{-}\left(6,8\right).\end{array}$

Here, each of the elements: $X,{X}_{S},{X}_{K},{K}_{X},{S}_{X}$ is called wood, fire, earth, metal, water, respectively, and this is ${*}^{+}$ Yang, ${*}^{-}$ is Yin. Each of sets:

${K}_{X}^{+}\left(\text{*,*}\right),{K}_{X}^{-}\left(\text{*,*}\right),{X}_{S}^{-}\left(\text{*,*}\right),{X}^{+}\left(\text{*,*}\right),{X}^{-}\left(\text{*,*}\right),{S}_{X}^{+}\left(\text{*,*}\right),{X}_{K}^{+}\left(\text{*,*}\right),{X}_{K}^{-}\left( *,* \right)$

is called Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫), respectively.

Each of elements:

${K}_{X}^{+}\left(\text{1,1}\right),{K}_{X}^{-}\left(\text{2,2}\right),{X}_{S}^{-}\left(\text{3,3}\right),{X}^{+}\left(\text{4,4}\right),{X}^{-}\left(5,5\right),{S}_{X}^{+}\left(6,6\right),{X}_{K}^{+}\left(7,7\right),{X}_{K}^{-}\left( 8,8 \right)$

is called the primordial spirit (元神) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫), respectively.

Each of elements:

${Κ}_{X}^{+}\left(\text{1,5}\right),{K}_{X}^{-}\left(\text{2,6}\right),{X}_{S}^{-}\left(\text{3,7}\right),{X}^{+}\left(\text{4,8}\right),{X}^{-}\left(5,1\right),{S}_{X}^{+}\left(6,2\right),{X}_{K}^{+}\left(7,3\right),{X}_{K}^{-}\left( 8,4 \right)$

is called the First generation (一世) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫), respectively.

Each of elements:

${K}_{X}^{+}\left(\text{1,7}\right),{K}_{X}^{-}\left(\text{2,8}\right),{X}_{S}^{-}\left(\text{3,5}\right),{X}^{+}\left(\text{4,6}\right),{X}^{-}\left(5,3\right),{S}_{X}^{+}\left(6,4\right),{X}_{K}^{+}\left(7,1\right),{X}_{K}^{-}\left( 8,2 \right)$

is called the Second generation (二世) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫), respectively.

Each of elements:

${K}_{X}^{+}\left(\text{1,8}\right),{K}_{X}^{-}\left(\text{2,7}\right),{X}_{S}^{-}\left(\text{3,6}\right),{X}^{+}\left(\text{4,5}\right),{X}^{-}\left(5,4\right),{S}_{X}^{+}\left(6,3\right),{X}_{K}^{+}\left(7,2\right),{X}_{K}^{-}\left( 8,1 \right)$

is called the Third generation (三世) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫), respectively.

Each of elements:

${K}_{X}^{+}\left(\text{5,8}\right),{K}_{X}^{-}\left(\text{6,7}\right),{X}_{S}^{-}\left(\text{7,6}\right),{X}^{+}\left(\text{8,5}\right),{X}^{-}\left(1,4\right),{S}_{X}^{+}\left(2,3\right),{X}_{K}^{+}\left(3,2\right),{X}_{K}^{-}\left( 4,1 \right)$

is called the Fourth generation (四世) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫), respectively.

Each of elements:

${K}_{X}^{+}\left(\text{7,8}\right),{K}_{X}^{-}\left(\text{8,7}\right),{X}_{S}^{-}\left(\text{5,6}\right),{X}^{+}\left(\text{6,5}\right),{X}^{-}\left(3,4\right),{S}_{X}^{+}\left(4,3\right),{X}_{K}^{+}\left(1,2\right),{X}_{K}^{-}\left( 2,1 \right)$

is respectively called the Fifth generation (五世) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫).

Each of elements:

${K}_{X}^{+}\left(\text{3,8}\right),{K}_{X}^{-}\left(\text{4,7}\right),{X}_{S}^{-}\left(\text{1,6}\right),{X}^{+}\left(\text{2,5}\right),{X}^{-}\left(7,4\right),{S}_{X}^{+}\left(8,3\right),{X}_{K}^{+}\left(5,2\right),{X}_{K}^{-}\left( 6,1 \right)$

is respectively called the Wandering soul (游魂) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫).

Each of elements:

${K}_{X}^{+}\left(\text{3,1}\right),{K}_{X}^{-}\left(\text{4,2}\right),{X}_{S}^{-}\left(\text{1,3}\right),{X}^{+}\left(\text{2,4}\right),{X}^{-}\left(7,5\right),{S}_{X}^{+}\left(8,6\right),{X}_{K}^{+}\left(5,7\right),{X}_{K}^{-}\left( 6,8 \right)$

is respectively called the Return of the soul (归魂) of Qian palace (乾宫), Dui palace (兑宫), Li palace (离宫), Zhen palace (震宫), Xun palace (巽宫), Kan palace (坎宫), Gen palace (艮宫), Kun palace (坤宫).

In the eight palaces or eight veins, Yang is respectively:

Qian palace (乾宫), Kan palace (坎宫), Gen palace (艮宫), Zhen palace (震宫).

Yin is respectively:

Xun palace (巽宫), Li palace (离宫), Kun palace (坤宫), Dui palace (兑宫).

Yin is in the inside (), Yang is in the outside (). The relationship between the inside and the outside is the symmetrical relationship.

The eight palaces are also corresponding to eight veins. Therefore, in eight palaces or eight veins, other names of them are corresponding to the human body organs respectively:

Belt vein (带脉) as Qian palace (乾宫) ${K}_{X}^{+}\left(*,*\right)$ corresponding to metal ( ${K}_{X}$ ) = {lung, large intestine}: For Yang meridians, It links the foot ShaoYang gallbladder meridian ${X}^{+}\left(0,e\right)$ (足少阳胆经) in DaiMai (带脉, GB26), WuQu (五枢, GB27), WeiDao (维道, GB28) and ZuLinQi (足临泣, GB41). It is the penetration of the Yang link vein (阳维脉) and the Yang cross vein (阳跷脉) through the foot ShaoYang gallbladder meridian ${X}^{+}\left(0,e\right)$ (足少阳胆经). Also links the governor vein (督脉) in YaMen (哑门, DU15) and FengFu (风府, DU16) through the Yang link vein (阳维脉).

For Yin meridians, it connects the ren vein (任脉) through the governor vein (督脉) in n HuiYin (会阴, RN1). It also connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉). The idea is that veins meet in TaiYuan (太渊, Lu9).

The idea is that ZuLinQi (足临泣, GB41) mainly manages the Belt vein (带脉) as Qian palace (乾宫) ${K}_{X}^{+}\left(*,*\right)$. It is mainly in order to absorb the energy of ${K}_{X}^{+}\left(*,*\right)$ belonging to metal ( ${K}_{X}$ ) = {lung, large intestine} and to maintain the security of $X$.

Yin link vein (阴维脉) as Dui palace (兑宫) ${K}_{X}^{-}\left(*,*\right)$ corresponding to {lower energizer} $\subset {X}_{S}^{x+}\left(1,e\right)$ (手少阳三焦经): For Yin meridians, it links the foot JueYin liver meridian ${X}^{-}\left(\text{0,}\left(\text{23}\right)\right)$ (足厥阴肝经) in QiMen (旗门, LR14), links the hand JueYin pericardium meridian ${X}_{S}^{x-}\left(1,\left(23\right)\right)$ (手厥阴心包经) in NeiGuan (内关, PC6), links the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经) in ZhuBin (筑宾, KI9), links the foot TaiYin spleen meridian ${X}_{K}^{-}\left(0,\left(132\right)\right)$ (足太阴脾经) in ChongMen (冲门, SP12), FuHui (府会, SP13), DaHeng (大横, SP15) and FuAi (腹哀, SP16).

Also it links the ren vein (任脉) in TianTu (天突, RN22) and LianQuan (廉泉, RN23). Connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉). The idea is that veins meet in TaiYuan (太渊, Lu9).

The idea is that NeiGuan (内关, PC6) mainly manages the Yin link vein (阴维脉) as Dui palace (兑宫) ${K}_{X}^{-}\left(*,*\right)$. It is mainly in order to absorb the energy of ${K}_{X}^{-}\left(*,*\right)$ corresponding to {lower energizer} $\subset {X}_{S}^{x+}\left(1,e\right)$ (手少阳三焦经) and to maintain the security of ${X}_{S}^{x}$.

Governor vein (督脉) as Li palace (离宫) ${X}_{S}^{-}\left(*,*\right)$ corresponding to fire ( ${X}_{S}^{j}$ ) = {heart, small intestine}: For Yang meridians, it links the foot ShaoYang Gallbladder meridian ${X}^{+}\left(0,e\right)$ (足少阳胆经) in ChangQiang (长强, DU1) and DaZhui (大锥, DU14) and BaiHui (百会, DU20), links the hand ShaoYang triple energizer meridian ${X}_{S}^{x+}\left(\text{1,}e\right)$ (手少阳三焦经) in DaZhui (大锥, DU14) and BaiHui (百会, DU20), links the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经) in DaZhui (大锥, DU14) and BaiHui (百会, DU20) and ShenTing (神庭, DU24) and ShuiGou (水沟, DU26), links the hand YangMing large intestine ${K}_{X}^{+}\left(\text{1,}\left(\text{12}\right)\right)$ (手阳明大肠经) in DaZhui (大锥, DU14) and BaiHui (百会, DU20) and ShuiGou (水沟, DU26), links the foot TaiYang bladder meridian ${S}_{X}^{+}\left(0,\left(13\right)\right)$ (足太阳膀胱经) in DaZhui (大锥, DU14), BaiHui (百会, DU20), NaoHu (脑户, DU17), ShenTing (神庭, DU24) and TaoDao (陶道, DU13). And links the hand TaiYang small intestine meridian ${X}_{S}^{j\text{+}}\left(\text{1,}\left(\text{13}\right)\right)$ (手太阳小肠经) in HouXi (后溪, SI3), DaZhui (大锥, DU14) and BaiHui (百会, DU20).

For Yin meridians, it links the foot JueYin liver meridian ${X}^{-}\left(\text{0,}\left(\text{23}\right)\right)$ (足厥阴肝经) in BaiHui (百会, DU20), links the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经) in ChangQiang (长强, DU1). Also links the ren vein (任脉) and the impact vein (冲脉) in HuiYin (会阴, RN1). Connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉) or directly contacting the hand YangMing large intestine ${K}_{X}^{+}\left(\text{1,}\left(\text{12}\right)\right)$ (手阳明大肠经). The idea is that veins meet in TaiYuan (太渊, Lu9).

The idea is that HouXi (后溪, SI3) mainly manages the Governor vein (督脉) as Li palace (离宫) ${X}_{S}^{-}\left(*,*\right)$. It is mainly in order to absorb the energy of ${X}_{S}^{-}\left(*,*\right)$ belonging to jun-fire ( ${X}_{S}^{j}$ ) = {heart, small intestine} and to maintain the security of ${K}_{X}$.

Yang cross vein (阳跷脉) as Zhen palace (震宫) ${X}^{+}\left(*,*\right)$ corresponding to wood ( $X$ ) = {liver, bravery}: For Yang meridians, it links the foot ShaoYang Gallbladder meridian ${X}^{+}\left(0,e\right)$ (足少阳胆经) in JuLiao (居髎, GB29), links the hand ShaoYang triple energizer meridian ${X}_{S}^{x+}\left(1,e\right)$ (手少阳三焦经) in TianLiao (天髎, SJ15), links the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经) in ChengQi (承泣, ST1) and JuLiao (巨髎, ST3) and DiCang (地仓, ST4), links the hand YangMing large intestine meridian ${K}_{X}^{+}\left(\text{1,}\left(\text{12}\right)\right)$ (手阳明大肠经) in JianYu (肩髃, LI15), JuGu (巨骨, LI16) and DiCang (地仓, ST4), links the foot TaiYang bladder meridian ${S}_{X}^{+}\left(0,\left(13\right)\right)$ (足太阳膀胱经) in ShenMai (申脉, BL62) and PuCan (仆参, BL61) and PuYang (跗阳, BL59) and QngMing (晴明, BL1), and link the hand TaiYang small intestine meridian ${X}_{S}^{j\text{+}}\left(\text{1,}\left(\text{13}\right)\right)$ (手太阳小肠经) in NaoShu (臑俞, SI10).

For Yin meridians, it also contacts the ren vein (任脉) in ChengQi (承泣, ST1) of the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经), and connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉) or directly contacting the hand YangMing large intestine meridian ${K}_{X}^{+}\left(\text{1,}\left(\text{12}\right)\right)$ (手阳明大肠经). The idea is that veins meet in TaiYuan (太渊, Lu9).

The idea is that ShenMai (申脉, BL62) mainly manages the Yang cross vein (阳跷脉) as Zhen palace (震宫) ${X}^{+}\left(*,*\right)$. It is mainly in order to absorb the energy of ${X}^{+}\left(*,*\right)$ belonging to wood ( $X$ ) = {liver, bravery} and to maintain the security of ${K}_{X}$.

Yin cross Vein (阴跷脉) as Xun palace (巽宫) ${X}^{-}\left(*,*\right)$ corresponding to {liver, middle energizer} $\subset X\cup {X}_{S}^{x+}\left(1,e\right)$ : For Yin meridians, it links the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经) in Zhaohai (照海, K16) and JiaoXin (交信, K18).

Also it contacts the well point YongQuan (涌泉, K11) through the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经). The upper part of the well point YongQuan (涌泉, K11) runs through the liver diaphragm corresponding to the foot JueYin liver meridian ${X}^{-}\left(\text{0,}\left(\text{23}\right)\right)$ (足厥阴肝经).

And it is also in the penetration of the impact vein (冲脉) through the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经) in JiaoXin (交信, KI8) and ZhuBin (筑宾, KI9) which are chieh or Qie dens. And also contacts the ren vein (任脉) through the impact vein (冲脉) in HuiYin (会阴, RN1). And also connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉). The idea is that veins meet in TaiYuan (太渊, Lu9).

For Yang meridians, it links the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经) in QingMing (晴明, BL1), links the foot TaiYang bladder meridian ${S}_{X}^{+}\left(0,\left(13\right)\right)$ (足太阳膀胱经) in QingMing (晴明, BL1), and links the hand TaiYang small intestine meridian ${X}_{S}^{j\text{+}}\left(\text{1,}\left(\text{13}\right)\right)$ (手太阳小肠经) in QingMing (晴明, BL1). Also links the Yang cross vein (阳跷脉) in QingMing (晴明, BL1). And contacts the foot ShaoYang Gallbladder meridian ${X}^{+}\left(0,e\right)$ (足少阳胆经) in JuLiao (居髎, GB29) through the Yang cross Vein (阳跷脉).

The idea is that ZhaoHai mainly manages the Yin cross vein (阴跷脉) as Xun palace (巽宫) ${X}^{-}\left(*,*\right)$. It is mainly in order to absorb the energy of ${X}^{-}\left(*,*\right)$ corresponding to {liver, middle energizer} $\subset X\cup {X}_{S}^{x+}\left(1,e\right)$ and to maintain the security of ${K}_{X}$.

Ren vein (任脉) as Kan palace (坎宫) ${S}_{X}^{+}\left(*,*\right)$ corresponding to water ( ${S}_{X}$ ) = {kidney, bladder}: For Yin meridians, it links the foot JueYin liver meridian ${X}^{-}\left(\text{0,}\left(\text{23}\right)\right)$ (足厥阴肝经) in QuGu (曲骨, RN2) and ZhongJi (中极, RN3) and GuanYuan (关元, RN4), links the foot TaiYin spleen meridian ${X}_{K}^{-}\left(0,\left(132\right)\right)$ (足太阴脾经) in XiaWang (下脘, RN10), ZhongJi (中极, RN3) and GuanYuan (关元, RN4), links the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经) in ZhongJi (中极, RN3) and GuanYuan (关元, RN4).

And it connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9). The idea is that veins meet in TaiYuan (太渊, Lu9).

For Yang meridians, it links the hand ShaoYang triple energizer meridian ${X}_{\text{S}}^{x+}\left(1,e\right)$ (手少阳三焦经) in ZhongWan (中脘, RN12), links the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经) in ZhongWan (中脘, RN12) and ShangWan (上脘, RN13), and links the hand TaiYang small intestine meridian ${X}_{S}^{j\text{+}}\left(\text{1,}\left(\text{13}\right)\right)$ (手太阳小肠经) in ZhongWan (中脘, RN12) and ShangWan (上脘, RN13).

The idea is that LieQue mainly manages the Ren vein (任脉) as Kan palace (坎宫) ${S}_{X}^{+}\left(*,*\right)$. It is mainly in order to absorb the energy of ${S}_{X}^{+}\left(*,*\right)$ belonging to water ( ${S}_{X}$ ) = {kidney, bladder} and to maintain the security of ${X}_{K}$.

Yang link Veins (阳维脉) as Gen palace (艮宫) ${X}_{K}^{+}\left(*,*\right)$ corresponding to {upper energizer} $\subset {X}_{S}^{x+}\left(1,e\right)$ (手少阳三焦经): For Yang meridians, it links the foot ShaoYang Gallbladder meridian ${X}^{+}\left(0,e\right)$ (足少阳胆经) in YangJiao (阳交, GB35) and JianBing (肩并, GB21), links the hand ShaoYang triple energizer meridian ${X}_{S}^{x+}\left(1,e\right)$ (手少阳三焦经) in TianLiao (天髎, SJ15) and WaiGuan (外关, SJ5), links the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经) in TouWei (头维, ST8), links the foot TaiYang bladder meridian ${S}_{X}^{+}\left(0,\left(13\right)\right)$ (足太阳膀胱经) in JinMen (金门, BL63) and links the hand TaiYang small intestine meridian ${X}_{S}^{j\text{+}}\left(\text{1,}\left(\text{13}\right)\right)$ (手太阳小肠经) in NaoShu (臑俞, SI10). Also links the governor vein (督脉) in YaMen (哑门, DU15) and FengFu (风府, DU16).

For Yin meridians, it connects the ren vein (任脉) through the governor vein (督脉) in HuiYin (会阴, RN1). It also connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉). The idea is that veins meet in TaiYuan (太渊, Lu9).

The idea is that WaiGuan (外关, SJ5) mainly manages the Yang link vein (阳维脉) as Gen palace (艮宫) ${X}_{K}^{+}\left(*,*\right)$. It is mainly in order to absorb the energy of ${X}_{K}^{+}\left(*,*\right)$ corresponding to {upper energizer} and to maintain the security of ${X}_{S}^{j}$.

Impact vein (冲脉) as Kun palace (坤宫) ${X}_{K}^{-}\left(*,*\right)$ corresponding to earth ( ${X}_{K}$ ) = {spleen, stomach}: For Yin meridians, it links the foot TaiYin spleen meridian ${X}_{K}^{-}\left(0,\left(132\right)\right)$ (足太阴脾经) in GongSun (公孙, SP4), and contacts the foot ShaoYin kidney meridian ${S}_{X}^{-}\left(0,\left(123\right)\right)$ (足少阴肾经) in HengGu (横骨, KI11), DaHe (大赫, KI12), QiXue (气穴, KI13), SiMan (四满, Ki14), ZhongZhu (中注, KI15), HuangShu (肓俞, KI16), ShangQu (商曲, KI17), ShiGuan (石关, KI18), YinDu (阴都, KI19), FuTongGu (腹通谷, KI20) and YouMen (幽门, KI21). Also links the ren vein (任脉) in YinJiao (阴交, RN7) and HuiYin (会阴, RN1). It also connects the hand TaiYin lung meridian ${K}_{X}^{-}\left(1,\left(132\right)\right)$ (手太阴肺经) in LieQue (列缺, Lu7) and TaiYuan (太渊, Lu9) through the ren vein (任脉). The idea is that veins meet in TaiYuan (太渊, Lu9).

For Yang meridians, links the foot YangMing stomach meridian ${X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)$ (足阳明胃经) in QiChong (气冲, ST30). Also links the governor vein (督脉) in HuiYin (会阴, RN1).

The idea is that GongSun (公孙, SP4) mainly manages the impact vein (冲脉) as Kun palace (坤宫) ${X}_{K}^{-}\left(*,*\right)$. The impact vein (冲脉) is a sea of blood and a sea of twelve meridians. It is mainly in order to absorb the energy of ${X}_{K}^{-}\left(*,*\right)$ belonging to earth ( ${X}_{K}$ ) = {spleen, stomach} and to maintain the security of ${S}_{X}$.

The laws of Five Zang-organs, Six fu-organs, Ten heavenly stems hidden behind Twelve earthly branches, Ten heavenly stems and Twelve earthly branches hidden behind eight palaces or eight veins are summarized in Figures 2-5. #

Figure 2. Relations of ten heavenly stems.

Figure 3. Relations of twelve earthly branches.

Figure 4. Ten heavenly stems hidden behind twelve earthly branches.

Figure 5. Relations between eight palaces and six fu-organs.

In TCM, the model of eight palaces or eight veins is not only the anatomy systems as the first physiological system corresponding to their steady multilateral systems, but also it is the human body logic model as the second physiological system corresponding to their steady multilateral systems. If there is the Eight-Hexagram model ${V}^{8}$, then the model of eight palaces or eight veins ${V}^{8}×{V}^{8}$ must be existed in logic. So they form a parasitic system of the Yin Yang Wu Xing system ${V}^{5}$, namely the second physiological system ${V}^{8}×{V}^{8}$ of the steady multilateral systems.

In TCM, in spite of the Zangxiang model cannot be observed, but the model of Jingluo or six hollow organs can. Thus it can be reasoned according to the system reasoning of eight palaces or eight veins ${V}^{8}×{V}^{8}$. So the system logic relation of both the ten heavenly stems ${V}^{2}×{V}^{5}$, the twelve earthly branches ${V}^{2}×{V}^{6}$ and eight palaces or eight veins ${V}^{8}×{V}^{8}$ must be known.

Definition 3.2. (Logic relation between ten heavenly stems, twelve earthly branches and eight palaces) All logic relations of that both ten heavenly stems and twelve earthly branches are hidden behind the eight palaces must follow the relationship between the symmetry of the eight palaces.

All logic relations of that both ten heavenly stems and twelve earthly branches are hidden behind the Eight-Palaces are summarized in Table 1.

Watch Table 1, all pure Yang: Ren-Jia, Wu, Bing, Geng of Ten Heavenly Stems are hidden behind all pure Yang: Qian, Kan, Gen, Zhen of the eight palaces; all pure Yin: Gui-Yi, Ji, Ding, Xin of Ten Heavenly Stems are hidden behind clockwise all pure Yin: Qun, Li, Dui, Xun of the eight palaces.

All pure Yang: Wu-Zi, Xu-Chen, Shen-Yin, Wu-Zi of twelve earthly branches are hidden behind all pure Yang: Qian, Kan, Gen, Zhen of the eight palaces; all pure Yin: Chou-Wei, Hai-Si, You-Mao, Wei-Chou of twelve earthly branches are hidden behind counterclockwise all pure Yin: Qun, Li, Dui, Xun of the eight palaces. #

Example 2.1. The name of the primordial spirit of Qian Palace is

$\begin{array}{l}{K}_{X}^{+}\left(1,1\right)={K}_{X}^{+}\left(\text{Outside of Qian},\text{Inside of Qian}\right)\\ =\left(\text{Qian Ren Xu,Qian Ren Shen,Qian Ren Wu;}\\ \text{}\text{QianJiaChen,QianJiaYin,QianJiaZi}\right).\end{array}$

The name of the two generations of Dui Palace is

$\begin{array}{l}{K}_{X}^{-}\left(2,8\right)={K}_{X}^{-}\left(\text{Outside of Dui},\text{Inside of Qun}\right)\\ =\left(\text{Dui Ding Si,Dui Ding Wei,Dui Ding You;}\\ \text{}\text{Qun Yi Mao,Qun Yi Si,Qun Yi Wei}\right).\end{array}$

All eight palace elements for naming can use the following formula:

$\text{Eight-Hexagram}+\text{Ten Stems}+\text{Twelve Branches}.$ #

Definition 3.3. (Energy of eight palaces or eight veins) Suppose that the each Hexagram-image of eight palaces is represented as a six-dimensional vector:

$f=\left({f}_{1},\text{}{f}_{2},\text{}{f}_{3},\text{}{f}_{4},\text{}{f}_{5},\text{}{f}_{6}\right),\text{}{f}_{i}\in \left\{1,-1\right\},\text{}i=1,2,3,4,5,6.$

Then the following number is called the energy of the Hexagram-image.

$\begin{array}{l}{e}_{f}=\left(\left(|{f}_{1}|+{f}_{1}\right)/2\right){2}^{5}+\left(\left(|{f}_{2}|+{f}_{2}\right)/2\right){2}^{4}+\left(\left(|{f}_{3}|+{f}_{3}\right)/2\right){2}^{3}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left(\left(|{f}_{4}|+{f}_{4}\right)/2\right){2}^{2}+\left(\left(|{f}_{5}|+{f}_{5}\right)/2\right){2}^{1}+\left(\left(|{f}_{6}|+{f}_{6}\right)/2\right),\\ \text{}{f}_{i}\in \left\{1,-1\right\},\text{}i=1,2,3,4,5,6.\end{array}$ #

Property 3.1. (Energy Distribution of eight palaces or Eight Veins)

Table 1. Ten heavenly stems and twelve earthly branches hidden behind eight palaces for making names.

The energy of every Hexagram-image in every Palace, or its average value in every palace, or its standard deviation in every palace is as follows respectively.

1) Qian () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ 1& 1& 1& 1& 1& 1& 63& 0& 1\\ 1& 1& 1& 1& 1& -1& 62& 1& 1\\ 1& 1& 1& 1& -1& -1& 60& 2& 1\\ 1& 1& 1& -1& -1& -1& 56& 3& 1\\ 1& 1& -1& -1& -1& -1& 48& 4& 1\\ 1& -1& -1& -1& -1& -1& 32& 5& 1\\ 1& -1& 1& -1& -1& -1& 40& 6& 1\\ 1& -1& 1& 1& 1& 1& 47& 7& 1\end{array}$

The average energy is equal to 51.0 and the standard deviation of energy is equal to11.20.

2) Dui () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ -1& 1& 1& -1& 1& 1& 27& 0& 2\\ -1& 1& 1& -1& 1& -1& 26& 1& 2\\ -1& 1& 1& -1& -1& -1& 24& 2& 2\\ -1& 1& 1& 1& -1& -1& 28& 3& 2\\ -1& 1& -1& 1& -1& -1& 20& 4& 2\\ -1& -1& -1& 1& -1& -1& 4& 5& 2\\ -1& -1& 1& 1& -1& -1& 12& 6& 2\\ -1& -1& 1& -1& 1& 1& 11& 7& 2\end{array}$

The average energy is equal to 19.0 and the standard deviation of energy is equal to 8.93.

3) Li () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ 1& -1& 1& 1& -1& 1& 45& 0& 3\\ 1& -1& 1& 1& -1& -1& 44& 1& 3\\ 1& -1& 1& 1& 1& -1& 46& 2& 3\\ 1& -1& 1& -1& 1& -1& 42& 3& 3\\ 1& -1& -1& -1& 1& -1& 34& 4& 3\\ 1& 1& -1& -1& 1& -1& 50& 5& 3\\ 1& 1& 1& -1& 1& -1& 58& 6& 3\\ 1& 1& 1& 1& -1& 1& 61& 7& 3\end{array}$

The average energy is equal to 47.5 and the standard deviation of energy is equal to 8.72.

4) Zhen () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ -1& -1& 1& -1& -1& 1& 9& 0& 4\\ -1& -1& 1& -1& -1& -1& 8& 1& 4\\ -1& -1& 1& -1& 1& -1& 10& 2& 4\\ -1& -1& 1& 1& 1& -1& 14& 3& 4\\ -1& -1& -1& 1& 1& -1& 6& 4& 4\\ -1& 1& -1& 1& 1& -1& 22& 5& 4\\ -1& 1& 1& 1& 1& -1& 30& 6& 4\\ -1& 1& 1& -1& -1& 1& 25& 7& 4\end{array}$

The average energy is equal to 15.5 and the standard deviation of energy is equal to 8.98.

5) Xun () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ 1& 1& -1& 1& 1& -1& 54& 0& 5\\ 1& 1& -1& 1& 1& 1& 55& 1& 5\\ 1& 1& -1& 1& -1& 1& 53& 2& 5\\ 1& 1& -1& -1& -1& 1& 49& 3& 5\\ 1& 1& 1& -1& -1& 1& 57& 4& 5\\ 1& -1& 1& -1& -1& 1& 41& 5& 5\\ 1& -1& -1& -1& -1& 1& 33& 6& 5\\ 1& -1& -1& 1& 1& -1& 38& 7& 5\end{array}$

The average energy is equal to 47.5 and the standard deviation of energy is equal to 8.98.

6) Kan () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ -1& 1& -1& -1& 1& -1& 18& 0& 6\\ -1& 1& -1& -1& 1& 1& 19& 1& 6\\ -1& 1& -1& -1& -1& 1& 17& 2& 6\\ -1& 1& -1& 1& -1& 1& 21& 3& 6\\ -1& 1& 1& 1& -1& 1& 29& 4& 6\\ -1& -1& 1& 1& -1& 1& 13& 5& 6\\ -1& -1& -1& 1& -1& 1& 5& 6& 6\\ -1& -1& -1& -1& 1& -1& 2& 7& 6\end{array}$

The average energy is equal to 15.5 and the standard deviation of energy is equal to 8.72.

7) Gen () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ 1& -1& -1& 1& -1& -1& 36& 0& 7\\ 1& -1& -1& 1& -1& 1& 37& 1& 7\\ 1& -1& -1& 1& 1& 1& 39& 2& 7\\ 1& -1& -1& -1& 1& 1& 35& 3& 7\\ 1& -1& 1& -1& 1& 1& 43& 4& 7\\ 1& 1& 1& -1& 1& 1& 59& 5& 7\\ 1& 1& -1& -1& 1& 1& 51& 6& 7\\ 1& 1& -1& 1& -1& -1& 52& 7& 7\end{array}$

The average energy is equal to 44.0 and the standard deviation of energy is equal to 8.93.

8) Kun () =

$\begin{array}{ccccccccc}{f}_{1}& {f}_{2}& {f}_{3}& {f}_{4}& {f}_{5}& {f}_{6}& \text{energy}& \text{image}& \text{palace}\\ -1& -1& -1& -1& -1& -1& 0& 0& 8\\ -1& -1& -1& -1& -1& 1& 1& 1& 8\\ -1& -1& -1& -1& 1& 1& 3& 2& 8\\ -1& -1& -1& 1& 1& 1& 7& 3& 8\\ -1& -1& 1& 1& 1& 1& 15& 4& 8\\ -1& 1& 1& 1& 1& 1& 31& 5& 8\\ -1& 1& -1& 1& 1& 1& 23& 6& 8\\ -1& 1& -1& -1& -1& -1& 16& 7& 8\end{array}$

The average energy is equal to 12.0 and the standard deviation of energy is equal to 11.20.

9) The energy of all eight palaces total average and total standard deviation is as follows respectively. Meet with “The same energy attracting each other” rule.

$\begin{array}{cccccc}palace& average& deviation& palace& average& deviation\\ Qian& 51.00& 11.20& Kun& 12.00& 11.20\\ Kan& 15.50& 8.72& Li& 47.50& 8.72\\ Gen& 44.00& 8.93& Dui& 19.00& 8.93\\ Zhen& 15.50& 8.98& Xun& 47.50& 8.98\end{array}$

The energy balance

$\left(11.20=11.20,8.72=8.72,8.93=8.93,8.98=8.98\right)$

between the standard deviation of all symmetrical palaces shows that the distribution of the energy is reasonable.

The energy difference

$\begin{array}{l}\left(11.2=\mathrm{max}\left(11.2,8.72,8.73,8.93\right)\\ <12.0=\mathrm{min}\left(51.00,12.00,15.50,47.50,44.00,19.00\right)\right)\end{array}$

between the standard deviation and the average of all palaces shows that the classification of the energy is reasonable.

10) The energy of all eight palaces total average is equal to 31.5 and the energy of all Eight palaces total standard deviation is equal to 18.62.

The energy of first four hexagrams of all palaces total average is equal to 31.5 and the energy of first four hexagrams of all palaces total standard deviation is equal to 17.93.

The energy of last four hexagrams of all palaces total average energy is equal to 31.5 and the energy of last four hexagrams of all palaces total standard deviation is equal to 19.58.

The energy balance $\left(31.5=31.5=31.5\right)$ of total average between all palaces, the first four hexagrams of all palaces and the last four hexagrams energy of all palaces shows that the distribution of energy is reasonable.

The energy difference

$\left(19.58=\mathrm{max}\left(18.62,17.35,19.58\right)<31.5\right)$

of total standard deviation and total average between all palaces, the first four hexagrams of all palaces and the last four hexagrams energy of all palaces shows that the classification of the energy is reasonable.

11) The energy of every outsider and insider in every palace total average or the energy of every outsider and insider in every palace total standard deviation is in Table 2, respectively. Meet with “The same energy attracting each other” rule.

The energy balance

$\begin{array}{l}\left(7.41=7.41,12.10=12.10,6.55=6.55,10.37=10.37;\\ 3.10=3.10,1.71=1.71,1.71=1.71,2.63=2.63\right)\end{array}$

Table 2. Eight palaces energy distribution.

between the standard deviation of all symmetrical outsider and insider palaces shows that the distribution of the energy is reasonable.

The energy difference

$\begin{array}{l}\left(12.10=\mathrm{max}\left(7.41,12.10,6.55,10.37\right)\\ \approx 11.75=\mathrm{min}\left(41.75,21.25,12.25,50.75,36.75,11.75,20.75,42.25\right);\\ 3.10=\mathrm{max}\left(\text{3}\text{.10,1}\text{.71,1}\text{.71,2}\text{.63}\right)\\ \approx 2.75=\mathrm{min}\left(60.25,2.75,18.75,44.25,51.25,26.25,10.25,52.75\right)\right)\end{array}$

between the standard deviation and the average of all symmetrical outsider or insider palaces shows that the classification of the energy is reasonable.

12) Eight palace disposition (八宫秉性):

Qian palace (Yang metal, father): Gou (), Dun (), Fou (), Guan (), Bo (), Jin (), You ().

Dui palace (Yin metal, girl): Kun (), Cui (), Xian (), Jian (), Qian (), Xiao (), Mei ().

Li palace (Yin fire, female): Lv (), Ding (), Wei (), Meng (), Huan (), Song (), Ren ().

Zhen palace (Yang fire, old male): Yu (), Jie (), Heng (), Sheng (), Jing (), Da (), Sui ().

Xun palace (Yin wood, old female): Xv (), Jia (), Yi (), Wang (), He (), Yi (), Gu ().

Kan palace (Yang water, male): Jie (), Dun (), Ji (), Ge (), Feng (), Ming (), Shi ().

Gen palace (Yang earth, boys): Bi (), Xu (), Sun (), Gui (), Lv (), Fu (), Jian ().

Kun palace (Yin earth, mother): Fu (), Lin (), Tai (), Zhuang (), Guai (), Xv (), Bi (). #

Energy concept is an important concept in Physics. Zhang [17] [18] introduces this concept to the human body. And image mathematics in Zhang and Shao [20] uses these concepts to deal with the human body diseases. By eight palaces or eight veins ${V}^{8}×{V}^{8}$, it can be used to determine the major or basic subsystems that may be affected by using the six indexes of comprehensive judgment as the Eight palaces.

In mathematics, a human body is said to have Energy (or Dynamic) if there is a non-negative function $\phi \left(*\right)$ which makes every organ or subsystem meaningful of the human body.

Suppose that $V$ is a human body having an energy function, then $V$ in the human body during a normal operation, its energy function for any organ or subsystem of the human body has an average (or expected value in Statistics), this state is called as normal when the energy function is nearly to the average. Normal state is the better state.

That an organ of the human body is not running properly (or disease, abnormal) is that the energy deviation from the average of the subsystems is too large, the high (real disease) or the low (virtual disease).

In addition to study these real or virtual diseases, TCM is often not only considered the energy change (Attaining or Affording in Zhang [23] ) of each element in the corresponding group ${V}^{8}×{V}^{8}$, but also studied a kind of relation costs in group ${V}^{8}×{V}^{8}$.

There are three kinds of relationship between each of two elements of eight palaces or eight veins ${V}^{8}×{V}^{8}$, namely the merged, synthesized and combined.

The merged relationship between two energy elements x and y is the joining operation in the corresponding group system ${V}^{8}×{V}^{8}$, i.e., $\left\{x\right\}\cup \left\{y\right\}=\left\{z\right\}$. The element z is the result of two energy elements x and y merging. The purpose of merging is in order to get the large result energy of element z through inputting two energy elements x and y.

The synthesized relationship between two elements x and y is the multiply operation in the corresponding group system ${V}^{8}×{V}^{8}$ with a multiplication *, i.e., $x*y=z$. The element z is the result of two elements x and y synthesized. The purpose of synthesized is in order to get the result energy of element z through inputting two elements x and y.

The combined relationship between two elements x and y is the division operation in the corresponding group system ${V}^{8}×{V}^{8}$ with a multiplication *, i.e., ${x}^{-1}*y=z$ The element z is the cost of two elements x and y combined. The purpose of combined is in order to maintain or strengthen the relation between x and y through inputting the cost element z.

But in eight palaces or eight veins ${V}^{8}×{V}^{8}$, the synthesized and combined operations are the same since ${x}^{-1}=x$.

In general, a relationship cost is low if the cost element in the corresponding group is easy to get. A relationship cost is high, on the other hand, if the cost element in the corresponding is hard to come by.

Denoted the human body blood pH value x of the normal range (lower bound, upper bound, center) as follows

$\left(a=7.34539,b=7.45461,{t}_{0}=7.4\right).$

In this case, in general, the human body blood pH value $x\in \left[a,b\right]$ which means ${\rho }_{0}\le {\rho }_{1}=\rho \left(x\right)\le 1$. This relation cost is low because this relation cost element is easy to get. The low relation cost can make the intervention increasing the sizes of both the intervention reaction coefficients ${\rho }_{1},{\rho }_{2}$ and the self-protection coefficient ${\rho }_{3}$.

If a human body belongs to a palace, then Hexagram-image change of he/she is in the same palace. For insider of every palaces: Qian, Dui. Li, Zhen, Xun, Kan, Gen, and Zhen, the difference is small. The adjacent relationship between insider elements of palace is with low costs.

But in general, the human body blood pH value $x\notin \left[a,b\right]$ which means $0<{\rho }_{1}=\rho \left(x\right)<{\rho }_{0}$. This relation cost is high because the relation cost element is hard to come by. The high relation cost can make the sizes of both the intervention reaction coefficients ${\rho }_{1},{\rho }_{2}$ and the self-protection coefficient ${\rho }_{3}$ decreasing response to intervention.

If a human body belongs to a palace, then Hexagram-image change of he/she is in the same palace. But for symmetrical palaces: Qian and Kun, Dui and Gen, Li and Kan, Zhen and Xun, the difference is big. All relationship of symmetrical palaces is with high costs.

The purpose of intervention is to make the human body return to normal state. The method of intervention is to increase or decrease the energy of an organ.

What kind of intervening should follow the principle to treat it? Western medicine emphasizes directly human body treatments on a sick organ after the sick of organ has occurred, but the indirect intervening of oriental medicine is required before the sick of organ will occur. Which is more reasonable?

Based on this idea, many issues are worth further discussion. For example, if an intervening has been implemented to a sick organ before the sick of organ will occur, what Hexagram-image relation will be low cost which does not need to be done an intervention of it? what Hexagram-image relation will be high cost which needs to be done an intervention of it?

3.2. Kinds of Relationship Costs of Steady Multilateral Systems

For a steady multilateral system $V$ with two incompatibility relations, suppose that the subsystems $X,{X}_{S},{X}_{K},{K}_{X},{S}_{X}$ are the same as those defined in Theorem 3.1. Then the relation diseases can be decomposed into the following classes:

Definition 3.4. (merged (合并), synthesized (合化或者合成) and combined (化合)) Suppose that both x and y are two elements of system of eight palaces or Eight Extra Meridians or Eight Veins ${V}^{8}×{V}^{8}$.

The merged relationship between two energy elements x and y is the joining operation in the corresponding group system ${V}^{8}×{V}^{8}$, i.e., $\left\{x\right\}\cup \left\{y\right\}=\left\{z\right\}$ The element z is the result of two same energy elements x and y merging. The purpose of merging is in order to get the large result energy of element z through inputting two energy elements x and y.

The synthesized relationship between two elements x and y is the multiply operation in the corresponding group system ${V}^{8}×{V}^{8}$ with a multiplication *, i.e., $x*y=z$. The element z is the result of two elements x and y synthesized. The purpose of synthesized is in order to get the result energy of element z through inputting two elements x and y.

The combined relationship between two elements x and y is the division operation in the corresponding group system ${V}^{8}×{V}^{8}$ with a multiplication *, i.e., ${x}^{-1}*y=z$ The element z is the cost of two elements x and y combined. The purpose of combined is in order to maintain or strengthen the relation between x and y through inputting the cost element z.

The synthesized and combined operations in system of the eight palaces or eight veins ${V}^{8}×{V}^{8}$ are the same since ${x}^{-1}=x$ . #

Property 3.2. Suppose that both x and y are two elements of eight palaces or eight veins ${V}^{8}×{V}^{8}$. Then the following statements are true.

1) The synthesized and combined relationships of eight palaces or eight veins ${V}^{8}×{V}^{8}$ at low costs is as follows:

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Qian palace nature}\text{.}\\ \text{Qian}\left(\text{1,1}\right)\text{,Gou}\left(\text{1,5}\right)\text{,Dun}\left(\text{1,7}\right)\text{,Fou}\left(\text{1,8}\right)\text{,Guan}\left(\text{5,8}\right)\text{,Bo}\left(\text{7,8}\right)\text{,}\\ \text{Jin}\left(\text{3,8}\right)\text{,You}\left(\text{3,1}\right)\text{;}\end{array}$

$\begin{array}{l}\text{Qian}{\left(\text{1,1}\right)}^{±\text{1}}\text{*Gou}\left(\text{1,5}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(8,4\right)\text{as the energy 1}\text{.}\\ \text{Gou}{\left(\text{1,5}\right)}^{±\text{1}}\text{*Dun}\left(\text{1,7}\right)=\text{Shi}\left(8,\text{6}\right)={S}_{X}^{+}\left(8,\text{6}\right)\text{as the energy 2}\text{.}\\ \text{Dun}{\left(\text{1,7}\right)}^{±\text{1}}\text{*Fou}\left(\text{1,8}\right)=\text{Qian}\left(8,7\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Fou}{\left(\text{1,8}\right)}^{±\text{1}}\text{*Guan}\left(\text{5,8}\right)=\text{Yu}\left(\text{4},\text{8}\right)={X}^{+}\left(\text{4},\text{8}\right)\text{as the energy 8}\text{.}\end{array}$

$\begin{array}{l}\text{Guan}{\left(\text{5,8}\right)}^{±\text{1}}\text{*Bo}\left(\text{7,8}\right)=\text{Bi}\left(6,8\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}\text{.}\\ \text{Bo}{\left(\text{7,8}\right)}^{±\text{1}}\text{*Jin}\left(\text{3,8}\right)=\text{Yu}\left(\text{4},\text{8}\right)={X}^{+}\left(\text{4},\text{8}\right)\text{as the energy 8}.\\ \text{Jin}{\left(\text{3,8}\right)}^{±\text{1}}\text{*You}\left(\text{3,1}\right)=\text{Tai}\left(8,1\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{You}{\left(\text{3,1}\right)}^{±\text{1}}\text{*Qian}\left(\text{1,1}\right)=\text{Bi}\left(6,8\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

One’s Qian Palace nature is Gou () (1, 5), Dun () (1, 7), Fu () (1, 8), Guan () (5, 8), Bo () (7, 8), Jin () (3, 8), You () (3, 1). They mean: This father saw the beauty to hide away of Gou () (1, 5), to stop hiding behind anything of Dun () (1, 7), and to other people’s advice to veto ability of Fu () (1, 8). Strong ability to observe things around of Guan () (5, 8), seizes the chance to have exploited actively of Bo () (7, 8), and creates life by leaps and bounds promotion of Jin () (3, 8). Finally will achieve great wealth of You () (3, 1).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Dui palace nature}\text{.}\\ \text{Dui}\left(\text{2,2}\right)\text{,Kun}\left(\text{2,6}\right)\text{,Cui}\left(\text{2,8}\right)\text{,Xian}\left(\text{2,7}\right)\text{,Jian}\left(\text{6,7}\right)\text{,Qian}\left(\text{8,7}\right)\text{,}\\ \text{Xiao}\left(\text{4,7}\right)\text{,Mei}\left(\text{4,2}\right)\text{;}\end{array}$

$\begin{array}{l}\text{Dui}{\left(\text{2,2}\right)}^{±\text{1}}\text{*Kun}\left(\text{2,6}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(8,4\right)\text{as the energy 1}\text{.}\\ \text{Kun}{\left(\text{2,6}\right)}^{±\text{1}}\text{*Cui}\left(\text{2,8}\right)=\text{Shi}\left(8,\text{6}\right)={S}_{X}^{+}\left(8,\text{6}\right)\text{as the energy 2}\text{.}\\ \text{Cui}{\left(\text{2,8}\right)}^{±\text{1}}\text{*Xian}\left(\text{2,7}\right)=\text{Qian}\left(8,7\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Xian}{\left(\text{2,7}\right)}^{±\text{1}}\text{*Jian}\left(\text{6,7}\right)=\text{Yu}\left(\text{4},\text{8}\right)={X}^{+}\left(\text{4},\text{8}\right)\text{as the energy 8}\text{.}\end{array}$

$\begin{array}{l}\text{Jian}{\left(\text{6,7}\right)}^{±\text{1}}\text{*Qian}\left(\text{8,7}\right)=\text{Bi}\left(6,8\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{Qian}{\left(\text{8,7}\right)}^{±\text{1}}\text{*Xiao}\left(\text{4,7}\right)=\text{Yu}\left(\text{4},\text{8}\right)={X}^{+}\left(\text{4},\text{8}\right)\text{as the energy 8}.\\ \text{Xiao}{\left(\text{4,7}\right)}^{±\text{1}}\text{*Mei}\left(\text{4,2}\right)=\text{Tai}\left(8,1\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{Mei}{\left(\text{4,2}\right)}^{±\text{1}}\text{*Dui}\left(\text{2,2}\right)=\text{Bi}\left(6,8\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

One’s Dui Palace nature is Kun () (2, 6), Cui () (2, 8), Xian () (2, 7), Jian () (6, 7), Qian () (8, 7), Xiao () (4, 7), Mei () (4, 2). They mean: The young daughter life is difficult of Kun () (2, 6), but her thinking to excel of Cui () (2, 8), and to help know gratitude of Xian () (2, 7). Because things are difficult of Jian () (6, 7), to deal with things more modest low-key of Qian () (8, 7), and cause life is too small clearance into small chance of Xiao () (4, 7). Finally its best chance is to find a good husband get married of Mei () (4, 2).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Li palace nature}\text{.}\\ \text{Li}\left(\text{3,3}\right)\text{,Lv}\left(\text{3,7}\right)\text{,Ding}\left(\text{3,5}\right)\text{,Wei}\left(\text{3,6}\right)\text{,Meng}\left(\text{7,6}\right)\text{,Huan}\left(\text{5,6}\right)\text{,}\\ \text{Song}\left(\text{1,6}\right)\text{,Ren}\left(\text{1,3}\right)\text{;}\end{array}$

$\begin{array}{l}\text{Li}{\left(\text{3,3}\right)}^{\text{±1}}\text{*Lv}\left(\text{3,7}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(8,4\right)\text{as the energy}1.\\ \text{Lv}{\left(\text{3,7}\right)}^{\text{±1}}\text{*Ding}\left(\text{3,5}\right)=\text{Shi}\left(\text{8,6}\right)={S}_{X}^{+}\left(8,6\right)\text{as the energy}2.\\ \text{Ding}{\left(\text{3,5}\right)}^{\text{±1}}\text{*Wei}\left(\text{3,6}\right)=\text{Qian}\left(\text{8,7}\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Wei}{\left(\text{3,6}\right)}^{\text{±1}}\text{*Meng}\left(\text{7,6}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\end{array}$

$\begin{array}{l}\text{Meng}{\left(\text{7,6}\right)}^{\text{±1}}\text{*Huan}\left(\text{5,6}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{Huan}{\left(\text{5,6}\right)}^{\text{±1}}\text{*Song}\left(\text{1,6}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\\ \text{Song}{\left(\text{1,6}\right)}^{\text{±1}}\text{*Ren}\left(\text{1,3}\right)=\text{Tai}\left(\text{8,1}\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{Ren}{\left(\text{1,3}\right)}^{\text{±1}}\text{*Li}\left(\text{3,3}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

Ones Li Palace nature is Lv () (3, 7), Ding () (3, 5), Wei () (3, 6), Huan () (7, 6), Huan () (5, 6), Song () (1, 6), Ren () (1, 3). They mean: The middle-aged daughter good nature tourism of Lv () (3, 7), but parents are loyal to leadership of Ding () (3, 5), work like dont like quiet of Wei () (3, 6). Because like illuminating new things of Huan () (7, 6), do things distractions to focus on one thing for a long time of Huan () (5, 6), and a natural but argue action ability of the brain of Song () (1, 6). Finally her excellent interpersonal relationship of Ren () (1, 3).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Zhen palace nature}\text{.}\\ \text{Zhen}\left(\text{4,4}\right)\text{,Yu}\left(\text{4,8}\right)\text{,Jie}\left(\text{4,6}\right)\text{,Heng}\left(\text{4,5}\right)\text{,Sheng}\left(\text{8,5}\right)\text{,Jing}\left(\text{6,5}\right)\text{,}\\ \text{Da}\left(\text{2,5}\right)\text{,Sui}\left(\text{2,4}\right)\text{;}\end{array}$

$\begin{array}{l}\text{Zhen}{\left(\text{4,4}\right)}^{\text{±1}}\text{*Yu}\left(\text{4,8}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(\text{8,4}\right)\text{as the energy}1.\\ \text{Yu}{\left(\text{4,8}\right)}^{\text{±1}}\text{*Jie}\left(\text{4,6}\right)=\text{Shi}\left(\text{8,6}\right)={S}_{X}^{+}\left(8,6\right)\text{as the energy}2.\\ \text{Jie}{\left(\text{4,6}\right)}^{\text{±1}}\text{*Heng}\left(\text{4,5}\right)=\text{Qian}\left(\text{8,7}\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Heng}{\left(\text{4,5}\right)}^{\text{±1}}\text{*Sheng}\left(\text{8,5}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(\text{4,8}\right)\text{as the energy 8}.\end{array}$

$\begin{array}{l}\text{Sheng}{\left(\text{8,5}\right)}^{\text{±1}}\text{*Jing}\left(\text{6,5}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{Jing}{\left(\text{6,5}\right)}^{\text{±1}}\text{*Da}\left(\text{2,5}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(\text{4,8}\right)\text{as the energy 8}.\\ \text{Da}{\left(\text{2,5}\right)}^{\text{±1}}\text{*Sui}\left(\text{2,4}\right)=\text{Tai}\left(\text{8,1}\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{Sui}{\left(\text{2,4}\right)}^{\text{±1}}\text{*Zhen}\left(\text{4,4}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

Ones Zhen Palace nature is Yu () (4, 8), Jie () (4, 6), Heng () (4, 5), Sheng () (8, 5), Jing () (6, 5), Da () (2, 5), Sui () (2, 4). They mean: The older son has nature feeling ability of Yu () (4, 8), to put their own interpretation did not solve the problem like and view of, Jie () (4, 6), but to do things with perseverance of Heng () (4, 5). Life opportunities under normal rising of Sheng () (8, 5), handles affairs in order of Jing () (6, 5), and causes the life with the mark of luck of Da () (2, 5). Finally it is the excellent random strain capacity of Sui () (2, 4).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Xun palace nature}\text{.}\\ Xun\left(5,5\right),Xu\left(5,1\right),Jia\left(5,3\right),Yi\left(5,4\right),Wang\left(1,4\right),He\left(3,4\right),\\ Yi\left(7,4\right),Gu\left(7,5\right);\end{array}$

$\begin{array}{l}\text{Xun}{\left(5,5\right)}^{\text{±1}}\text{*Xu}\left(5,1\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(8,4\right)\text{as the energy}1.\\ \text{Xu}{\left(5,1\right)}^{\text{±1}}\text{*Jia}\left(5,3\right)=\text{Shi}\left(\text{8,6}\right)={S}_{X}^{+}\left(8,6\right)\text{as the energy}2.\\ \text{Jia}{\left(5,3\right)}^{\text{±1}}\text{*Yi}\left(5,4\right)=\text{Qian}\left(\text{8,7}\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Yi}{\left(5,4\right)}^{\text{±1}}\text{*Wang}\left(1,4\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(\text{4,8}\right)\text{as the energy 8}.\end{array}$

$\begin{array}{l}\text{Wang}{\left(1,4\right)}^{\text{±1}}\text{*He}\left(3,4\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{He}{\left(3,4\right)}^{\text{±1}}\text{*Yi}\left(7,4\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(\text{4,8}\right)\text{as the energy 8}.\\ \text{Yi}{\left(7,4\right)}^{\text{±1}}\text{*Gu}\left(7,5\right)=\text{Tai}\left(\text{8,1}\right)={X}_{K}^{-}\left(\text{8,1}\right)\text{as the energy 7}.\\ \text{Gu}{\left(7,5\right)}^{\text{±1}}\text{*Xun}\left(5,5\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(\text{6,8}\right)\text{as the energy 16}.\end{array}$

One’s Xun Palace nature is Xu () (5, 1), Jia () (5, 3), Yi () (5, 4), Wang () (1, 4), He () (3, 4), Yi () (7, 4), Gu () (7, 5). They mean: The older daughter likes a small amount of saving money of Xu () (5, 1), more attention to a family of Jia () (5, 3), and friends can get income from her of Yi () (5, 4). But her own delusion has a greater chance of making a fortune of Wang () (1, 4), doing thing hesitant of He () (3, 4), if a delusion of convergence, then she will inspire the live of Yi () (7, 4). Final convergence delusion if not, then she can often be loved ones under the method of deception of Gu () (7, 5).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Kan palace nature}\text{.}\\ \text{Kan}\left(\text{6,6}\right)\text{,Jie}\left(\text{6,2}\right)\text{,Tun}\left(\text{6,4}\right)\text{,Ji}\left(\text{6,3}\right)\text{,Ge}\left(\text{2,3}\right)\text{,Feng}\left(\text{4,3}\right)\text{,}\\ \text{Ming}\left(\text{8,3}\right)\text{,Shi}\left(\text{8,6}\right)\text{;}\end{array}$

$\begin{array}{l}\text{Kan}{\left(\text{6,6}\right)}^{\text{±1}}\text{*Jie}\left(\text{6,2}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(\text{8,4}\right)\text{as the energy}1.\\ \text{Jie}{\left(\text{6,2}\right)}^{\text{±1}}\text{*Tun}\left(\text{6,4}\right)=\text{Shi}\left(\text{8,6}\right)={S}_{X}^{+}\left(8,6\right)\text{as the energy}2.\\ \text{Tun}{\left(\text{6,4}\right)}^{\text{±1}}\text{*Ji}\left(\text{6,3}\right)=\text{Qian}\left(\text{8,7}\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Ji}{\left(\text{6,3}\right)}^{\text{±1}}\text{*Ge}\left(\text{2,3}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\end{array}$

$\begin{array}{l}\text{Ge}{\left(\text{2,3}\right)}^{\text{±1}}\text{*Feng}\left(\text{4,3}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{Feng}{\left(\text{4,3}\right)}^{\text{±1}}\text{*Ming}\left(\text{8,3}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\\ \text{Ming}{\left(\text{8,3}\right)}^{\text{±1}}\text{*Shi}\left(\text{8,6}\right)=\text{Tai}\left(\text{8,1}\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{Shi}{\left(\text{8,6}\right)}^{\text{±1}}\text{*Kan}\left(\text{6,6}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

One’s Kan Palace nature is Jie () (6, 2), Tun () (6, 4), Ji () (6, 3), Ge () (2, 3), Feng () (4, 3), Ming () (8, 3), Shi () (8, 6). They mean: The middle-aged son loves to save of Jie () (6, 2), and be good at hoarding supplies of Tun () (6, 4), and doing things according to the established things of Ji () (6, 3). But he changes the ability strong of Ge () (2, 3), change can also get a harvest of Feng () (4, 3), and can see to understand a lot of things of Ming () (8, 3). Finally the person good at word and willing to teachers of Shi () (8, 6).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Gen palace nature}\text{.}\\ \text{Gen}\left(\text{7,7}\right)\text{,Bi}\left(\text{7,3}\right)\text{,Xu}\left(\text{7,1}\right)\text{,Sun}\left(\text{7,2}\right)\text{,Gui}\left(\text{3,2}\right)\text{,Lv}\left(\text{1,2}\right)\text{,}\\ \text{Fu}\left(\text{5,2}\right)\text{,Jian}\left(\text{5,7}\right)\text{;}\end{array}$

$\begin{array}{l}\text{Gen}{\left(\text{7,7}\right)}^{\text{±1}}\text{*Bi}\left(\text{7,3}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(8,4\right)\text{as the energy}1.\\ \text{Bi}{\left(\text{7,3}\right)}^{\text{±1}}\text{*Xu}\left(\text{7,1}\right)=\text{Shi}\left(\text{8,6}\right)={S}_{X}^{+}\left(8,6\right)\text{as the energy}2.\\ \text{Xu}{\left(\text{7,1}\right)}^{\text{±1}}\text{*Sun}\left(\text{7,2}\right)=\text{Qian}\left(\text{8,7}\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Sun}{\left(\text{7,2}\right)}^{\text{±1}}\text{*Gui}\left(\text{3,2}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\end{array}$

$\begin{array}{l}\text{Gui}{\left(\text{3,2}\right)}^{\text{±1}}\text{*Lv}\left(\text{1,2}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{Lv}{\left(\text{1,2}\right)}^{\text{±1}}\text{*Fu}\left(\text{5,2}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\\ \text{Fu}{\left(\text{5,2}\right)}^{\text{±1}}\text{*Jian}\left(\text{5,7}\right)=\text{Tai}\left(\text{8,1}\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{Jian}{\left(\text{5,7}\right)}^{\text{±1}}\text{*Gen}\left(\text{7,7}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

One’s Gen Palace nature is Bi () (7, 3), Xu () (7, 1), Sun () (7, 2), Gui () (3, 2), Lv () (1, 2), Fu () (5, 2), Jian () (5, 7). They mean: The young son works hard and likes to do all the things by the recognition of Bi () (7, 3), and is good at saving a lot of money of Xu () (7, 1), and do things get damaged income also not care of Sun () (7, 2). But he is difficult to get the respect they deserve of Gui () (3, 2), to be honest to fulfill a commitment of Lv () (1, 2), and life the pursuit of a smooth transition of Fu () (5, 2). Finally the status of the growth of life often is gradually rising slowly of Jian () (5, 7).

$\begin{array}{l}\text{Even if all changed, it is hard to change one's Kun palace nature}\text{.}\\ Kun\left(8,8\right),Fu\left(8,4\right),Lin\left(8,2\right),Tai\left(8,1\right),Zhuang\left(4,1\right),Guai\left(2,1\right),\\ Xu\left(6,1\right),Bi\left(6,8\right);\end{array}$

$\begin{array}{l}\text{Kun}{\left(\text{8,8}\right)}^{\text{±1}}\text{*Fu}\left(\text{8,4}\right)=\text{Fu}\left(\text{8,4}\right)={X}_{K}^{-}\left(8,4\right)\text{as the energy}1.\\ \text{Fu}{\left(\text{8,4}\right)}^{\text{±1}}\text{*Lin}\left(\text{8,2}\right)=\text{Shi}\left(\text{8,6}\right)={S}_{X}^{+}\left(8,6\right)\text{as the energy}2.\\ \text{Lin}{\left(\text{8,2}\right)}^{\text{±1}}\text{*Tai}\left(\text{8,1}\right)=\text{Qian}\left(\text{8,7}\right)={K}_{X}^{-}\left(8,7\right)\text{as the energy 4}.\\ \text{Tai}{\left(\text{8,1}\right)}^{\text{±1}}\text{*Zhuang}\left(\text{4,1}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\end{array}$

$\begin{array}{l}\text{Zhuang}{\left(\text{4,1}\right)}^{\text{±1}}\text{*Guai}\left(\text{2,1}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\\ \text{Guai}{\left(\text{2,1}\right)}^{\text{±1}}\text{*Xu}\left(\text{6,1}\right)=\text{Yu}\left(\text{4,8}\right)={X}^{+}\left(4,8\right)\text{as the energy 8}.\\ \text{Xu}{\left(\text{6,1}\right)}^{\text{±1}}\text{*Bi}\left(\text{6,8}\right)=\text{Tai}\left(\text{8,1}\right)={X}_{K}^{-}\left(8,1\right)\text{as the energy 7}.\\ \text{Bi}{\left(\text{6,8}\right)}^{\text{±1}}\text{*Kun}\left(\text{8,8}\right)=\text{Bi}\left(\text{6,8}\right)={X}_{K}^{-}\left(6,8\right)\text{as the energy 16}.\end{array}$

One’s Kun Palace nature is Fu () (8, 4), Lin () (8, 2), Tai () (8, 1), Zhuang () (4, 1), Guai () (2, 1), Xu () (6, 1), Bi () (6, 8). They mean: The mother likes doing repeating things over and over again of Fu () (8, 4), to visit a lot of things of Lin () (8, 2), and contax happiness life of Tai () (8, 1). In health body in middle age of Zhuang () (4, 1), things are not good at decision making of Guai () (2, 1), and a social demand is very big of Xu () (6, 1). Finally the person is good at and people with envy-envy-hate psychology of Bi () (6, 8).

2) The synthesized and combined relationships of eight palaces or eight veins ${V}^{8}×{V}^{8}$ at high costs are as follows:

$\begin{array}{l}\text{Symmetrial palaces of Qian}\left(\text{*,*}\right)\text{and Kun}\left(\text{*,*}\right)\text{are combined at high costs}\text{.}\\ Qian\left(1,1\right),Gou\left(1,5\right),Dun\left(1,7\right),Fou\left(1,8\right),Guan\left(5,8\right),Bo\left(7,8\right),\\ Jin\left(3,8\right),You\left(3,1\right);\\ Kun\left(8,8\right),Fu\left(8,4\right),Lin\left(8,2\right),Tai\left(8,1\right),Zhuang\left(4,1\right),Guai\left(2,1\right),\\ Xu\left(6,1\right),Bi\left(6,8\right).\end{array}$

$\begin{array}{l}\text{Qian}{\left(\text{1,1}\right)}^{\text{±1}}\text{*Kun}\left(\text{8,8}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Gou}{\left(\text{1,5}\right)}^{\text{±1}}\text{*Fu}\left(\text{8,4}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Dun}{\left(\text{1,7}\right)}^{\text{±1}}\text{*Lin}\left(\text{8,2}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Fou}{\left(\text{1,8}\right)}^{\text{±1}}\text{*Tai}\left(\text{8,1}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Guan}{\left(\text{5,8}\right)}^{\text{±1}}\text{*Zhuang}\left(\text{4,1}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Bo}{\left(\text{7,8}\right)}^{\text{±1}}\text{*Guai}\left(\text{2,1}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Jin}{\left(\text{3,8}\right)}^{\text{±1}}\text{*Xu}\left(\text{6,1}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Youi}{\left(\text{3,1}\right)}^{\text{±1}}\text{*Bi}\left(\text{6,8}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Symmetrial palaces of Dui}\left(\text{*,*}\right)\text{and Gen}\left(\text{*,*}\right)\text{are combined at high costs}\text{.}\\ Dui\left(2,2\right),Kun\left(2,6\right),Cui\left(2,8\right),Xian\left(2,7\right),Jian\left(6,7\right),Qian\left(8,7\right),\\ Xiao\left(4,7\right),Mei\left(4,2\right).\\ Gen\left(7,7\right),Bi\left(7,3\right),Xu\left(7,1\right),Sun\left(7,2\right),Gui\left(3,2\right),Lv\left(1,2\right),\\ Fu\left(5,2\right),Jian\left(5,7\right).\end{array}$

$\begin{array}{l}\text{Dui}{\left(\text{2,2}\right)}^{\text{±1}}\text{*Gen}\left(\text{7,7}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Kun}{\left(\text{2,6}\right)}^{\text{±1}}\text{*Bi}\left(\text{7,3}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Cui}{\left(\text{2,8}\right)}^{\text{±1}}\text{*Xu}\left(\text{7,1}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Xian}{\left(\text{2,7}\right)}^{\text{±1}}\text{*Sun}\left(\text{7,2}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Jian}{\left(\text{6,7}\right)}^{\text{±1}}\text{*Gui}\left(\text{3,2}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Qian}{\left(\text{8,7}\right)}^{\text{±1}}\text{*Lv}\left(\text{1,2}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Xiao}{\left(\text{4,7}\right)}^{\text{±1}}\text{*Fu}\left(\text{5,2}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\\ \text{Mei}{\left(\text{4,2}\right)}^{\text{±1}}\text{*Jian}\left(\text{5,7}\right)=\text{Qian}\left(\text{1,1}\right)={K}_{X}^{+}\left(\text{1,1}\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Symmetrial palaces of Li}\left(\text{*,*}\right)\text{andKan}\left(\text{*,*}\right)\text{arecombinedathighcosts}\text{.}\\ Li\left(3,3\right),Lv\left(3,7\right),Ding\left(3,5\right),Wei\left(3,6\right),Meng\left(7,6\right),Huan\left(5,6\right),\\ Song\left(1,6\right),Ren\left(1,3\right),\\ Kan\left(6,6\right),Jie\left(6,2\right),Tun\left(6,4\right),Ji\left(6,3\right),Ge\left(2,3\right),Feng\left(4,3\right),\\ Ming\left(8,3\right),Shi\left(8,6\right).\end{array}$

$\begin{array}{l}\text{Li}{\left(\text{3,3}\right)}^{\text{±1}}\text{*Kan}\left(\text{6,6}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Lv}{\left(\text{3,7}\right)}^{\text{±1}}\text{*Jie}\left(\text{6,2}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Ding}{\left(\text{3,5}\right)}^{\text{±1}}\text{*Tun}\left(\text{6,4}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Wei}{\left(\text{3,6}\right)}^{\text{±1}}\text{*Ji}\left(\text{6,3}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Meng}{\left(\text{7,6}\right)}^{\text{±1}}\text{*Ge}\left(\text{2,3}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Huan}{\left(\text{5,6}\right)}^{\text{±1}}\text{*Feng}\left(\text{4,3}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Song}{\left(\text{1,6}\right)}^{\text{±1}}\text{*Ming}\left(\text{8,3}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Ren}{\left(\text{1,3}\right)}^{\text{±1}}\text{*Shi}\left(\text{8,6}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Symmetrial palaces of Zhen}\left(\text{*,*}\right)\text{andXun}\left(\text{*,*}\right)\text{arecombinedathighcosts}\text{.}\\ Zhen\left(4,4\right),Yu\left(4,8\right),Jie\left(4,6\right),Heng\left(4,5\right),Sheng\left(8,5\right),Jing\left(6,5\right),\\ Da\left(2,5\right),Sui\left(2,4\right).\\ Xun\left(5,5\right),Xu\left(5,1\right),Jia\left(5,3\right),Yi\left(5,4\right),Wang\left(1,4\right),He\left(3,4\right),\\ Yi\left(7,4\right),Gu\left(7,5\right).\end{array}$

$\begin{array}{l}\text{Zhen}{\left(\text{4,4}\right)}^{\text{±1}}\text{*Xun}\left(\text{5,5}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Yu}{\left(\text{4,8}\right)}^{\text{±1}}\text{*Xu}\left(\text{5,1}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Jie}{\left(\text{4,6}\right)}^{\text{±1}}\text{*Jia}\left(\text{5,3}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Heng}{\left(\text{4,5}\right)}^{\text{±1}}\text{*Yi}\left(\text{5,4}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\end{array}$

$\begin{array}{l}\text{Sheng}{\left(\text{8,5}\right)}^{\text{±1}}\text{*Wang}\left(\text{1,4}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Jing}{\left(\text{6,5}\right)}^{\text{±1}}\text{*He}\left(\text{3,4}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Da}{\left(\text{2,5}\right)}^{\text{±1}}\text{*Yi}\left(\text{7,4}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\\ \text{Sui}{\left(\text{2,4}\right)}^{\text{±1}}\text{*Gu}\left(\text{7,5}\right)=\text{Qian}\left(1,1\right)={K}_{X}^{+}\left(1,1\right)\text{as the energy 63}.\end{array}$

All relation laws of eight palaces or eight veins are summarized in Figure 5.

It means that the Your palm in Figure 5, the adjacent relationship between insider elements of palace is with low costs but the relationship of symmetrical palaces is with high costs. #

Property 3.3. The energy of the eight palaces synthesized is summarized in Table 3, respectively.

Table 3. Energy synthesized of eight palaces.

Each of the eight palaces is corresponding to each of the eight veins in Table 3.

The energy of each of the eight palaces synthesized is the sum of energy of each element of ten heavenly stems for the corresponding palace in Table 3.

The boldface in Table 3 is the largest energy of ten heavenly stems for the corresponding palace.#

3.3. First Transfer Laws of a Human Body’s Energies of Steady Multilateral Systems with a Healthy Body

Theorem 3.2. (The first transfer law of the ten Heavenly Stems with a healthy body) [23] Suppose that a human body is healthy. Let the human blood pH value $x\in \left[7.34539,7.45461\right]$ which is equivalent to the conditions ${\rho }_{0}\le {\rho }_{1}=\rho \left(x\right)\le 1$ and $0.

The transfer law of each of the 10 kinds of energy in the Zangxiang system or the ten Heavenly Stems model is from its root-causes to its symptoms.

Furthermore, for the healthy body, the first transfer law of the Yang vital or righteousness energies of the ten heavenly stems is transferring along the loving or liking order of the ten heavenly stems as follows:

$\begin{array}{l}\stackrel{less}{\to }\text{realJia}\left(\text{1,0}\right){X}^{+}\stackrel{less}{↔}\text{realYi}\left(\text{0,0}\right){X}^{-}\\ \stackrel{less}{\to }\text{realBing}\left(\text{1,1}\right){X}_{S}^{+}\stackrel{less}{↔}\text{realDing}\left(\text{0,1}\right){X}_{S}^{-}\\ \stackrel{rare}{\to }\text{virtual Wu}\left(\text{1,2}\right){X}_{K}^{+}\stackrel{less}{↔}\text{virtual Ji}\left(\text{0,2}\right){X}_{K}^{-}\\ \stackrel{more}{\to }\text{virtual Geng}\left(\text{1,3}\right){K}_{X}^{+}\stackrel{less}{↔}\text{virtual Xin}\left(\text{0,3}\right){K}_{X}^{-}\\ \stackrel{rare}{\to }\text{realRen}\left(\text{1,4}\right){S}_{X}^{+}\stackrel{less}{↔}\text{realGui}\left(\text{0,4}\right){S}_{X}^{-}\\ \stackrel{less}{\to }\text{realJia}\left(\text{1,0}\right){X}^{+}\stackrel{less}{↔}\text{realYi}\left(\text{0,0}\right){X}^{-}\stackrel{less}{\to }\cdots .\end{array}$

And the first transfer law of the Yin vital or righteousness energies of the ten heavenly stems is transferring against the loving or liking order of the ten heavenly stems as follows:

$\begin{array}{l}\cdots \stackrel{less}{←}\text{virtual Yi}\left(\text{0,0}\right){X}^{-}\stackrel{less}{↔}\text{virtual Jia}\left(\text{1,0}\right){X}^{+}\\ \stackrel{less}{←}\text{virtual Gui}\left(\text{0,4}\right){S}_{X}^{-}\stackrel{less}{↔}\text{virtual Ren}\left(\text{1,4}\right){S}_{X}^{+}\\ \stackrel{rare}{←}\text{realXin}\left(\text{0,3}\right){K}_{X}^{-}\stackrel{less}{↔}\text{realGeng}\left(\text{1,3}\right){K}_{X}^{+}\\ \stackrel{more}{←}\text{realJi}\left(\text{0,2}\right){X}_{K}^{-}\stackrel{less}{↔}\text{real Wu}\left(\text{1,2}\right){X}_{K}^{+}\\ \stackrel{rare}{←}\text{virtual Ding}\left(\text{0,1}\right){X}_{S}^{-}\stackrel{less}{↔}\text{virtual Bing}\left(\text{1,1}\right){X}_{S}^{+}\\ \stackrel{less}{←}\text{virtual Yi}\left(\text{0,0}\right){X}^{-}\stackrel{less}{↔}\text{virtual Jia}\left(\text{1,0}\right){X}^{+}\stackrel{less}{←}\cdots .\end{array}$

All transfer laws of the Zangxiang system or the ten Heavenly Stems model for a healthy body are summarized in Figure 2.

It means that only both the liking relation and the loving relation have the first transfer law of the Yang or Yin vital or righteousness energies of the ten heavenly stems. Yang is transferring along the loving or liking order of the ten heavenly stems. Yin is transferring against the loving or liking order of the ten heavenly stems. #

Theorem 3.3. (The first transfer law of the twelve earthly branches with a healthy body) [23] Suppose that a human body is healthy. Let the human blood pH value $x\in \left[7.34539,7.45461\right]$ which is equivalent to the conditions ${\rho }_{0}\le {\rho }_{1}=\rho \left(x\right)\le 1$ and $0.

The transfer law of each of the 12 kinds of energy in the Jingluo system or the twelve earthly branches model is from its root-causes to its symptoms.

Furthermore, for the healthy body, the first transfer law of the Yang vital energies of the twelve earthly branches is transferring along the loving or liking order of the twelve earthly branches as follows:

$\begin{array}{l}\text{real Chou}{X}^{-}\left(\text{0,}\left(\text{23}\right)\right)\stackrel{less}{↔}\text{real Zi}{X}^{+}\left(0,e\right)\\ \stackrel{less}{\to }\text{real Hai}{X}_{S}^{x+}\left(1,e\right)\stackrel{less}{↔}\text{real Xu}{X}_{S}^{x-}\left(\text{1,}\left(\text{23}\right)\right)\\ \stackrel{rare}{⇐}\text{real You}{S}_{X}^{-}\left(\text{0,}\left(\text{123}\right)\right)\stackrel{less}{↔}\text{real Shen}{S}_{X}^{+}\left(\text{0,}\left(\text{13}\right)\right)\\ \stackrel{rare}{⇒}\text{real Wei}{X}_{S}^{j+}\left(\text{1,}\left(\text{13}\right)\right)\stackrel{less}{↔}\text{real Wu}{X}_{S}^{j-}\left(\text{1,}\left(\text{123}\right)\right)\\ \stackrel{rare}{\to }\text{virtual Si}{X}_{K}^{-}\left(\text{0,}\left(\text{132}\right)\right)\stackrel{less}{↔}\text{virtual Chen}{X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)\\ \stackrel{less}{\to }\text{virtual Mao}{K}_{X}^{+}\left(\text{1,}\left(\text{12}\right)\right)\stackrel{less}{↔}\text{virtual Yin}{K}_{X}^{-}\left(\text{1,}\left(\text{132}\right)\right)\text{.}\end{array}$

The first transfer law of the Yin vital energies of the twelve earthly branches is transferring against the loving or liking order of the ten heavenly stems as follows:

$\begin{array}{l}\stackrel{less}{←}\text{realYin}{K}_{X}^{-}\left(\text{1,}\left(\text{132}\right)\right)\stackrel{less}{↔}\text{realMao}{K}_{X}^{+}\left(\text{1,}\left(\text{12}\right)\right)\\ \stackrel{more}{←}\text{realChen}{X}_{K}^{+}\left(\text{0,}\left(\text{12}\right)\right)\stackrel{less}{↔}\text{realSi}{X}_{K}^{-}\left(\text{0,}\left(\text{132}\right)\right)\\ \stackrel{rare}{←}\text{virtual Wu}{X}_{S}^{j-}\left(\text{1,}\left(\text{123}\right)\right)\stackrel{less}{↔}\text{virtual Wei}{X}_{S}^{j+}\left(\text{1,}\left(\text{13}\right)\right)\\ \stackrel{rare}{⇐}\text{virtual Shen}{S}_{X}^{+}\left(\text{0,}\left(\text{13}\right)\right)\stackrel{less}{↔}\text{virtual You}{S}_{X}^{-}\left(\text{0,}\left(\text{123}\right)\right)\\ \stackrel{rare}{⇒}\text{virtual Xu}{X}_{S}^{x-}\left(\text{1,}\left(\text{23}\right)\right)\stackrel{less}{↔}\text{virtual Hai}{X}_{S}^{x+}\left(1,e\right)\\ \stackrel{less}{←}\text{virtual Zi}{X}^{+}\left(0,e\right)\stackrel{less}{↔}\text{virtual Chou}{X}^{-}\left(\text{0,}\left(\text{23}\right)\right)\text{.}\end{array}$

All first transfer laws of the Jingluo system or the twelve earthly branches model for a healthy body are summarized in Figure 3.

It means that only both the liking relation and the adjacent relation have the first transfer law of the Yang or Yin vital or righteousness energies of the twelve earthly branches. Yang is transferring along the loving or liking order of the twelve earthly branches. Yin is transferring against the loving or liking order of the twelve earthly branches. #

For a healthy body falling a real disease, the relation note $\text{real Xu}{X}_{S}^{x-}\stackrel{less}{↔}\text{real Hai}{X}_{S}^{x+}$ can be considered as the mother of the relation note $\text{real Wu}{X}_{S}^{j-}\stackrel{less}{↔}\text{real Wei}{X}_{S}^{j+}$. It is because the relationship note

$\begin{array}{l}\text{real Hai}{X}_{}^{}\end{array}$