ABSTRACT

GDP (Gross Domestic Product) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE), this paper demonstrates that for the GDP inflation rate of economic society, the normal range of theory is [5.8114%, 16.359%] nearly to [6%, 16%], and center is 10.208% nearly to 10%. The first or second transfer law of economic diseases changes according to the different GDP inflation rate whether in the normal range or not. The treatment principle: “Don’t have economic disease cure cure non-ill” (不治已病治未病) is abiding by the first or second transfer law of economic diseases. Assume that the range of the GDP inflation rate is divided into four parts from small to large. Both second and third are for a healthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law. And both first and fourth are for an unhealthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, the Chinese GDP inflation rate is used for the water system of steady multilateral system.

Keywords:

Traditional Chinese Economics (TCE), Yin Yang Wu Xing Theory, Steady Multilateral Systems, Incompatibility Relations, Side Effects, Economic Intervention Resistance Problem

1. Introduction

GDP (Gross Domestic Product) is useful in understanding economic disease. GDP is refers to in a certain period (a quarter or a year), the economy of a country or region to produce the value of all final goods and services, is often recognized as the best indicators of national economy. It not only can reflect a country’s economic performance, also can reflect a country’s national power and wealth.

Through the growth rate of price index to calculate the rate of inflation, prices can be respectively by the consumer price index (CPI), the producer price index (PPI), the retail price index (RPI), the gross domestic product (GDP), and the gross national product (GNP) as conversion price index. In order to examine a country’s national power and wealth, general use of GDP, its formula is as follows:

$x<a=\text{5}\text{.8114\%}$ (1)

where the type of digital and $a=\text{5}\text{.8114\%}\le x<t_0=\text{10}\text{.208\%}$ is the number in the subscript, $t_0=\text{10}\text{.208\%}\le x\le b=\text{16}\text{.359\%}$ in $x>b=\text{16}\text{.359\%}$ on behalf of the production of all kinds of the final product, $\min =-0.11,\max =0.81,t_0=10.208\%$ in $\rho \left(x\right)=\frac{1/2}{\lambda \left(x\right)+1/2}\iff \frac{\rho \left(x\right)}{1-\rho \left(x\right)}=\frac{1/2}{\lambda \left(x\right)}\iff \lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}$ on behalf of all kinds of the price of the final product.

Both the rate of GDP inflation and the GDP are two different concepts. Calculation method of the rate of GDP inflation through the calculation of the GDP changes:

$x\to \min$ (2)

where the price rise level from low to high, to base the level of prices for base. One of the base period is selected one price level as a reference, so that you can put the other periods of price level with a comparison between base level to measure the current level of inflation.

Note on the type, the GDP inflation rate is not a price index, which is not a price rise, but the GDP price index to rise. In fact, what is said above is just one of the five methods (CPI, PPI, RPI, GDP, GNP) of measuring inflation index reduced living consumption laws, but it is the most commonly used for studying a country’s national power and wealth, in addition to the gross national product (GNP), the consumer price index (CPI), the producer price index (PPI) and the retail price index (RPI) conversion method.

The GDP is the government measure of a country’s national power and wealth inflation one of the data. Popular speaking, the GDP inflation rate is the value of all final goods and services on the market growth percentage. As an important indicator, observe the level of a country’s national power and wealth inflation in China, much attention has been paid to also for such an important indicator, as a new era of youth, more objective view should be observed. First of all, let us meet the GDP. The GDP is to reflect a country’s national power and wealth, related to all final goods and services calculated price, usually observed inflation as an important indicator.

Ahmed & Suliman (2011) have found that the direction of causation between real GDP and prices is uni-directional from real GDP to CPI without any feedback. The GDP plays a key role in the CPI. So the central bank can minimize the inflation by taking certain predictive measures to keep the input prices under control. Because of the causation relation between the GDP and the CPI, the normal range of the GDP inflation rate can be obtained from the normal range of the CPI inflation rate. It is found that the normal range of the CPI inflation rate is from 2% to 5%. There are a lot of evidences (e.g., experimental identification for probability and real applications) to support this viewpoint, such as, Crone et al. (2010), Pauhofova & Qineti (2002), Funke et al. (2015), Formica & Kingston (2015), Fan et al. (2009), Adams (2014), Hausman (1999), Nahm (2015), Moosa (1997), Zhao (2013), Daniel (2012), Anonymous (1999a, 1999b), and so on.

It is believed that the normal range of the GDP inflation rate is from 6% to 16%. It is because the GDP is more sensitive than the CPI, so changes in the wider range. Thus the economic social system identifies an important indicator for an economic social system health: the value of GDP inflation rate, which, under normal conditions, ranges from 6% to 16%. Outside this range (low: Yin condition; high: Yang condition), economic disease appears. Almost always, when there is economic disease, the condition of inflation rate is a Yin condition, little is a Yang condition.

In this paper, the rate of GDP inflation is considered as the wealth level rises rather than the currency quantity rises from the basic concept of GDP. It is because the GDP is the direct reflection of living standards, although the wealth level increase is difficult to be controlled directly.

The GDP is a general parameter linking together the complexity of relations between subsystem pairs of economic social system, economic social system itself, the capabilities for intervention reaction and self-protection of the economic social system as an economy and mind as a whole, related to the environment, food, health and personal history, air, water, earth, climate, season, etc. GDP is as useful in understanding economic disease as the average is in statistics, or as the expected value is in probability calculation.

The economic social system as an economy begins to activate the necessary mechanisms to restore this parameter to its appropriate range. If the economic social system as an economy is unable to restore optimal GDP levels, the economic disease may become chronic and lead to dire consequences.

Zhang (1993, 2007, 2011a, 2011b, 2012, 2013, 2020) have started a great interest and admired works for Traditional Chinese Economics (TCE), where, through mathematical reasoning, they demonstrate the presence of incompatibility relations, which are predominant in daily life, yet absent in traditional Aristotelian Western logic.

Many people as Western persons are beyond all doubt the Yin Yang Wu Xing theory is superior to the traditional true-false logic, which does not contemplate incompatibility relations, which Zhang & Zhang (2013) have expertly explained from a mathematical standpoint.

The work Zhang (1993, 2007) 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 economic social system and the environment. Even so, Zhang & Zhang (2013) also bring to light the difficulty of establishing the values of both the intervention reaction coefficients ρ₁, ρ₂ and the self-protection coefficient ρ₃ as parameters with due accuracy.

In this paper, the introduction of a parameter such as a GDP inflation rate will be suggested, in order to facilitate the understanding and the calculation of the values of both the intervention reaction coefficients ρ₁, ρ₂ and the self-protection coefficient ρ₃. This paper ventures to suggest this with all due to respect, because it is believed that the path Zhang & Zhang (2013) have 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 economic social system.

The article proceeds as follows. Section 2 contains a parameter model and basic theorems, in order to explain both the intervention reaction coefficients ρ₁, ρ₂ and the self-protection coefficient ρ₃ through the introduction of a parameter model to study the normal range of a GDP inflation rate, while the first or second transfer law of economic diseases is demonstrated in Section 3, proved through the concept of both relation diseases and a relationship analysis of steady multilateral systems. Furthermore, if the range of GDP inflation rate is divided into four parts, for the economy in every part, the prevention or treatment method of economic diseases as treatment principle of TCE is given in Section 4. As an application, the Chinese GDP inflation rate is used for the water system of steady multilateral system in Section 5 and conclusions are drawn in Section 6.

2. Parameter Model and Basic Theorems

The concepts and notations in Zhang & Zhang (2013) are used still and start.

Let $x\to \max$ be the gold number. Denoted $\lambda \left(x\right)\to +\infty$, namely healthy number. It is because the healthy number $\rho \left(x\right)\to 0$ can make the healthy balance conditions $x=t_0$,$\lambda \left(x\right)=0$ and $\rho \left(x\right)=1$ hold if $0<\rho \left(x\right)\le 1$,$0\le \lambda \left(x\right)<+\infty$ and $\lambda \left(x\right)$. Assume that $x\in \left(\min ,t_0\right]$, namely balance number. It is because under a poor self-protection ability, the balance number $x\in \left[t_0,\max \right)$ can make the poor healthy balance conditions:

$\rho (\; x\; )$

and $\lambda \left(x\right)$ hold if $\lambda \left(x\right)\in \left[0,+\infty \right)$,$\lambda \left(x\right)$ and $\rho \left(x\right)$. Thus $\rho \left(x\right)\in \left(0,1\right]$.

A parameter model of a GDP inflation rate in a mathematical sense based on Yin Yang Wu Xing Theory of TCE is reintroduced by using the functions $\lambda \left(x\right)$ and $x\in \left(\min ,t_0\right]$ of the GDP inflation rate $\begin{array}{c}\frac{\text{d}\lambda \left(x\right)}{\text{d}x}=\frac{-\left(x-\min \right)\left(\max -x\right)-\left(t_0-x\right)\left[\left(\max -x\right)-\left(x-\min \right)\right]}{{\left[\left(x-\min \right)\left(\max -x\right)\right]}^2}\\ =-\frac{\left(x-\min \right)\left(\max -x\right)+\left(t_0-x\right)\left[\left(\max -x\right)-\left(x-\min \right)\right]}{{\left[\left(x-\min \right)\left(\max -x\right)\right]}^2}\\ =-\frac{\left[\left(x-\min \right)\left(\max -t_0\right)+\left(t_0-x\right)\left(\max -x\right)\right]}{{\left[\left(x-\min \right)\left(\max -x\right)\right]}^2}<0.\end{array}$ described as follows.

Let $\lambda \left(x\right)$ be a GDP inflation rate, where the values −0.11 and 0.81 are the minimum and maximum acceptable the GDP inflation rate. Denoted the value 0.10208 is the target as the expectation of the GDP inflation rate. Define a function $x\in \left[t_0,\max \right)$ of the GDP inflation rate $\begin{array}{c}\frac{\text{d}\lambda \left(x\right)}{\text{d}x}=\frac{\left(x-\min \right)\left(\max -x\right)-\left(x-t_0\right)\left[\left(\max -x\right)-\left(x-\min \right)\right]}{{\left[\left(x-\min \right)\left(\max -x\right)\right]}^2}\\ =\frac{\left(x-\min \right)\left(\max -x\right)-\left(x-t_0\right)\left[\left(\max -x\right)-\left(x-\min \right)\right]}{{\left[\left(x-\min \right)\left(\max -x\right)\right]}^2}\\ =\frac{\left[\left(\max -x\right)\left(t_0-\min \right)+\left(x-t_0\right)\left(x-\min \right)\right]}{{\left[\left(x-\min \right)\left(\max -x\right)\right]}^2}>0.\end{array}$ in below:

$\rho \left(x\right)$ (3)

A parameter model is considered as

$\lambda \left(x\right)$ (4)

Theorem 2.1 Under model (4), the following statements hold.

1) The one that $\lambda \left(x\right)\in \left[0,+\infty \right)$ is equivalent to the other that

$\frac{\text{d}\rho \left(x\right)}{\text{d}\lambda \left(x\right)}=\frac{-\left(1/2\right)\left[1\right]}{{\left[\lambda \left(x\right)+1/2\right]}^2}=\frac{-1}{2{\left[\lambda \left(x\right)+1/2\right]}^2}<0.$

where $\lambda \left(x\right)$ is a monotone decreasing function of $\rho \left(x\right)$ if $\rho \left(x\right)\in \left(0,1\right]$ or a monotone increasing function of $\frac{\text{d}\lambda \left(x\right)}{\text{d}\rho \left(x\right)}=\frac{1}{2}\left(\frac{\left(-1\right)\rho \left(x\right)-\left(1-\rho \left(x\right)\right)\left[1\right]}{\rho {\left(x\right)}^2}\right)=\frac{-1}{2\rho {\left(x\right)}^2}<0.$ if $f\left(u\right)=\left(u+u^3\right)-\left(1-u^3\right),u\in \left(0,1\right]$ ; and $f\left(u\right)$ is a monotone decreasing function of $f{\left(u\right)}^{\prime }=1+6u^2>0$ if $f\left({\rho }_0\right)=\left({\rho }_0+{\rho }_0^3\right)-\left(1-{\rho }_0^3\right)=0$ ; and $\rho \left(x\right)\ge {\rho }_0$ is a monotone decreasing function of $f\left(\rho \left(x\right)\right)=\left(\rho \left(x\right)+\rho {\left(x\right)}^3\right)-\left(1-\rho {\left(x\right)}^3\right)\ge f\left({\rho }_0\right)=0$ if $\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \rho {\left(x\right)}^2$ .

2) If $\lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \frac{1-{\rho }_0}{2{\rho }_0}={\rho }_0^2\le \rho {\left(x\right)}^2$ , then $\lambda \left(x\right)$ ; $\rho \left(x\right)$; and $0<{\rho }_0\le \rho \left(x\right)$ .

3) If $\frac{\lambda \left(x\right)}{\rho \left(x\right)}=\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^2}\le \frac{1-{\rho }_0}{2{\rho }_0^2}={\rho }_0\le \rho \left(x\right)$ , then $h\left(\rho \left(x\right)\right)=\frac{\lambda \left(x\right)}{\rho \left(x\right)}$ ; $\rho \left(x\right)$; and $0<{\rho }_0\le \rho \left(x\right)$ .

4) Taking $h\left(\rho \left(x\right)\right)=\frac{\lambda \left(x\right)}{\rho \left(x\right)}$ and $\frac{\text{d}h\left(\rho \left(x\right)\right)}{\text{d}\rho \left(x\right)}=\frac{1}{2}\left(\frac{\left(-1\right)\rho {\left(x\right)}^2-\left(1-\rho \left(x\right)\right)\left[2\rho \left(x\right)\right]}{\rho {\left(x\right)}^4}\right)=\frac{\rho \left(x\right)-2}{2\rho {\left(x\right)}^3}<0$ where $\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^2}=\frac{1-\rho \left(x\right)}{2\rho {\left(x\right)}^3}\le \frac{1-{\rho }_0}{2{\rho }_0^3}=1$ , there are $h\left(\rho \left(x\right)\right)=\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^2}$ , $\rho \left(x\right)$, and

$0<{\rho }_0\le \rho \left(x\right)$,

where $h\left(\rho \left(x\right)\right)=\frac{\lambda \left(x\right)}{\rho {\left(x\right)}^2}$ .

5) Taking $\frac{\text{d}h\left(\rho \left(x\right)\right)}{\text{d}\rho \left(x\right)}=\frac{1}{2}\left(\frac{\left(-1\right)\rho {\left(x\right)}^3-\left(1-\rho \left(x\right)\right)\left[3\rho {\left(x\right)}^2\right]}{\rho {\left(x\right)}^6}\right)=\frac{2\rho \left(x\right)-3}{2\rho {\left(x\right)}^4}<0$ , $g\left(u\right)=\left(u+c{u}^3\right)-\left(1-c{u}^3\right),u,c\in \left(0,1\right]$ and $g\left(u\right)$ where $g{\left(u\right)}^{\prime }=1+6c{u}^2>0$ , there are

Firstly, $0<c\le 1$ , $g\left(u\right)=2\left(c-1\right)u^3+f\left(u\right)$ and $f\left(u\right)=\left(u+u^3\right)-\left(1-u^3\right),u\in \left(0,1\right]$ if

$\rho \left(x\right)<{\rho }_0$;

Secondly, $g\left(\rho \left(x\right)\right)<0$ , $\left|g\left(\rho \left(x\right)\right)\right|>2\left(1-c\right){\rho }_0^3$ and $g\left(\rho \left(x\right)\right)<g\left({\rho }_0\right)=2\left(c-1\right){\rho }_0^3+f\left({\rho }_0\right)=2\left(c-1\right){\rho }_0^3\le 0$ where

$g\left(\rho \left(x\right)\right)<0$ if $\left({\rho }_1+{\rho }_2{\rho }_3\right)=\rho \left(x\right)+c\rho {\left(x\right)}^3<1-c\rho {\left(x\right)}^3=1-{\rho }_2{\rho }_3.$ in which $g\left(u\right)=2c{u}^3-\left(1-u\right)$ ;

Thirdly, $g\left(u\right)=0$ , $c=\frac{1-u}{2u^3}$ and $\frac{1-u}{2u^3}$ where

$c\left(u\right)$ if $c\left(u\right)=\frac{1-u}{2u^3}$ in which $u\in \left(0,1\right]$ ;

Finally, $c{\left(u\right)}^{\prime }=\frac{1}{2}\left(-3u^{-4}+2u^{-3}\right)=\frac{1}{2u^4}\left(-3+2u\right)<0,\forall ,u\in \left(0,1\right].$ , $c\ge c\left(u\right)$ and $c\ge \frac{1-u}{2u^3}$ where

$g\left(u\right)=2u^3\left(c-\frac{1-u}{2u^3}\right)\ge 0$ if $\left(u+c{u}^3\right)\ge \left(1-c{u}^3\right)$ in which $0\le c<c\left(u\right)$ .

In particular, when c is nearly to 1/2, there are $0\le c<\frac{1-u}{2u^3}$ , $g\left(u\right)=2u^3\left(c-\frac{1-u}{2u^3}\right)<0$ and the following statements hold.

a) The absolute value $\left(u+c{u}^3\right)<\left(1-c{u}^3\right)$ is nearly to 0 if

$\frac{1-u}{2u^3}=\frac{1}{2}$ in which $u={{\rho }^{\prime }}_0$ .

b) The value $c\left(u\right)=\frac{1-u}{2u^3}$ is included in the interval

$u\in \left({\rho }_0,1\right]$ if $u\in \left[{\rho }_0,{{\rho }^{\prime }}_0\right)\iff 1\ge \frac{1-u}{2u^3}>\frac{1}{2}$ in which $u\in \left[{{\rho }^{\prime }}_0,1\right)\iff 0<\frac{1-u}{2u^3}\le \frac{1}{2}$ .

c) The value $\left|g\left(u\right)\right|=\left|2c{u}^3+u-1\right|\le {\left({{\rho }^{\prime }}_0\right)}^3=0.31767,\forall u\in \left[{{\rho }^{\prime }}_0,1\right)$ is included in the interval

$0\le c<\frac{1-u}{2u^3}\le \frac{1}{2}$ if $\left|g\left(u\right)\right|=2u^3\left(\frac{1-u}{2u^3}-c\right)<2u^3\left(\frac{1-u}{2u^3}\right)=1-u\le 1-{{\rho }^{\prime }}_0={\left({{\rho }^{\prime }}_0\right)}^3=\mathrm{0.31767.}$ in which $\left|g\left(u\right)\right|=\left|2c{u}^3+u-1\right|\le 2{\rho }_0^3=0.41024,\forall u\in \left[{\rho }_0,{{\rho }^{\prime }}_0\right)$ . #

Corollary 2.1 Under model (2.2), the following statements hold.

1) For any $0\le c\le \frac{1}{2}<\frac{1-u}{2u^3}\le 1$ , there is an unique solution $\left|g\left(u\right)\right|=2u^3\left(\frac{1-u}{2u^3}-c\right)<2u^3\left(\frac{1-u}{2u^3}\right)=1-u\le 1-{\rho }_0=2{\rho }_0^3=\mathrm{0.41024.}$ and there is also an unique solution $\left|g\left(u\right)\right|=\left|2c{u}^3+u-1\right|\le 0.31767,\forall u\in \left[{\rho }_0,{{\rho }^{\prime }}_0\right)$ , such that

$\frac{1}{2}<c<\frac{1-u}{2u^3}\le 1$

$\left|g\left(u\right)\right|=\left|2u^3\left(c-\frac{1-u}{2u^3}\right)\right|\le 2u^3\cdot \frac{1}{2}=u^3\le {\left({{\rho }^{\prime }}_0\right)}^3=\mathrm{0.31767.}$

2) The condition $g\left(u\right)=2u^3\left(c-\frac{1-u}{2u^3}\right)$ is equivalent to each of the following conditions:

$u\in \left(0,1\right]$

${\rho }_1-{\rho }_3=\rho \left(x\right)\left(1-c\right)\to \rho \left(x\right)/2$

3) The condition ${\rho }_2-{\rho }_1{\rho }_3=\rho {\left(x\right)}^2\left(1-c\right)\to \rho {\left(x\right)}^2/2$ is equivalent to each of the following conditions:

$g\left({{\rho }^{\prime }}_0\right)=-\left(1-2c\right){\left({{\rho }^{\prime }}_0\right)}^3$

$g\left(u\right)=2u^3\left(c-\frac{1-u}{2u^3}\right)$

4) The condition $0<c<\frac{1-u}{2u^3}\le \frac{1}{2}$ is equivalent to each of the following conditions:

$u\in \left[{{\rho }^{\prime }}_0,1\right)$

$g\left({\rho }_0\right)=-2\left(1-c\right){\rho }_0^3$

5) The condition $g\left({{\rho }^{\prime }}_0\right)=-\left(1-2c\right){\left({{\rho }^{\prime }}_0\right)}^3$ is equivalent to each of the following conditions:

$-{\rho }_0^3=-0.20512,0$

$0<c\le \frac{1}{2}<\frac{1-u}{2u^3}\le 1$ #

Remark 1. In west, through experiment or through practice observation, by using the Granger causality relation between the GDP and the CPI, many researchers can obtain the normal range of the GDP inflation rate as $u\in \left[{\rho }_0,{{\rho }^{\prime }}_0\right)$ from the normal range of the CPI as $g\left({\rho }_0\right)=-2\left(1-c\right){\rho }_0^3$. But in TCE, from Yin Yang Wu Xing Theory, Zhang & Zhang (2013) have already determined: $g\left({{\rho }^{\prime }}_0\right)=-\left(1-2c\right){\left({{\rho }^{\prime }}_0\right)}^3$ for the normal range of a healthy economy. Assume that $-{\rho }_0^3=-0.20512,0$,$\frac{1}{2}<c<\frac{1-u}{2u^3}\le 1$ and $u\in \left[{\rho }_0,{{\rho }^{\prime }}_0\right)$ where $u=\rho \left(x\right)$ for an economic society which has the capabilities of both intervention reaction and self-protection. From Corollary 2.1, the condition ρ₀ ≤ ρ₁ ≤ 1 is equivalent to that $0<d<1$. In other words, in Theory of TCE, the normal range of the GDP inflation rate is considered as $u\in \left(-0.11,\text{10}\text{.208\%}\right]$, nearly to $v\in \left(\text{10}\text{.208\%},0.81\right)$, and center is 10.208 % nearly to 10%. 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, TCE uses the rule $\lambda \left(0.027047\right)=0\le \lambda \left(x\right)=\frac{1-\rho \left(x\right)}{2\rho \left(x\right)}\le \lambda \left(u\right)=\lambda \left(v\right)=\left(1-d\right)/\left(2d\right),$ from Yin Yang Wu Xing Theory instead of the normal range of a GDP inflation rate. The equivalence of Corollary 2.1 shows that TCE is The scientific which is from TCM (Traditional Chinese Medicine).

Zhang & Zhang (2013) have already determined: an economy is said a healthy mathematical complex system when the intervention reaction coefficient $\lambda \left(x\right)$ satisfies $x\in \left(-0.11,\text{10}\text{.208\%}\right]$. In logic and practice, it's reasonable that $x\in \left[\text{10}\text{.208\%},0.81\right)$ is near to 1 if the input and output in a complex system is balanced, since a mathematical output subsystem is absolutely necessary other subsystems of all consumption. In case: $0\le \left(1-d\right)/\left(2d\right)<+\infty$, all the energy for intervening mathematical complex subsystem can transmit to other mathematical complex subsystems which have neighboring relations or alternate relations with the intervening mathematical complex subsystem. The condition $\lambda \left(u\right)=\lambda \left(v\right)=\left(1-d\right)/\left(2d\right)$ can be satisfied when $\rho \left(u\right)=\frac{1/2}{\lambda \left(u\right)+1/2}=d=\frac{1/2}{\lambda \left(v\right)+1/2}=\rho \left(v\right)$ and $d={\rho }_0$ for a mathematical complex system since $\lambda \left(u\right)=\lambda \left(v\right)=\left(1-{\rho }_0\right)/\left(2{\rho }_0\right)={\rho }_0^2$ implies $\left({\rho }_0+{\rho }_0^3\right)=\left(1-{\rho }_0^3\right)$. In this case, $d={{\rho }^{\prime }}_0$. If this assumptions is set up, then the intervening principle: “Real disease with a healthy economy is to rush down his son and virtual disease with a healthy economy is to fill his mother” based on “Yin Yang Wu Xing” theory in image mathematics by Zhang & Shao (2012), is quite reasonable. But, in general, the ability of self-protection often is insufficient for an usual mathematical complex system,

i.e., $\lambda \left(u\right)=\lambda \left(v\right)=\left(1-{{\rho }^{\prime }}_0\right)/\left(2{{\rho }^{\prime }}_0\right)={\left({{\rho }^{\prime }}_0\right)}^2/2$ is small. A common standard is ${\left({{\rho }^{\prime }}_0\right)}^3=1-{{\rho }^{\prime }}_0$ which comes from the

balance condition $a=\text{5}\text{.8114\%},b=\text{16}\text{.359\%},t_0=\text{10}\text{.208\%}$ of the loving relationship if ${\downarrow }^0$. In other words, there is a principle which all losses are bear in mathematical complex system. Thus the general condition is often $\phi \left(X\right)$. Interestingly, they are all near to the golden numbers. It is the idea to consider the unhealthy balance number $\Delta \phi \left(X\right)=-\Delta <0$ since the poor condition of self-protection ability $\Delta \phi \left(S_X\right)=-{\rho }_1\Delta <0$ can make that the unhealthy balance conditions hold: ${\downarrow }^{+}$,$\Delta \phi \left(X_S\right)=-{\rho }_2\Delta <0$, and ${\downarrow }^{-}$ of the loving relationship if $\Delta \phi \left(K_X\right)={\rho }_1\Delta >0$ and ${\uparrow }^{+}$.

By Theorem 2.1 and Corollary 2.1, the interval $\Delta \phi \left(X_K\right)={\rho }_2\Delta >0$ implies the following condition

${\uparrow }^{-}$;

and the interval $\Delta \phi \left(K_X\right)={\rho }_1\Delta >0$ implies the following condition

$x\in \left[a,b\right]$;

and the interval $1\ge {\rho }_1=\rho \left(x\right)\ge {\rho }_0$ implies the following condition

${\rho }_1+{\rho }_2{\rho }_3=\rho \left(x\right)+c\rho {\left(x\right)}^3\ge 1-{\rho }_2{\rho }_3=1-c\rho {\left(x\right)}^3$,

where $1\ge c\ge \left[1-\rho \left(x\right)\right]/\left(2\rho {\left(x\right)}^3\right)>0,\forall x\ne t_0$ since $c>0$; and the interval $\Delta \phi {\left(K_X\right)}_1=-{\rho }_3\Delta <0$ implies the following condition

${\Downarrow }^0$,

where $\Delta \phi {\left(X_K\right)}_1=-{\rho }_1{\rho }_3\Delta <0$ since ${\Downarrow }^{+}$.

The last one is the healthy interval in an economic society’s self-protection ability poor conditions. The interval range than the normal economic society health requirements is too strict, only the first three interval ranges are considered as a normal economic society health ranges. If keep two decimal places, then first three intervals are the same as $\Delta \phi {\left(S_X\right)}_1=-{\rho }_2{\rho }_3\Delta <0$. This shows that range ${\Downarrow }^{-}$ is stable. The interval as the normal range of a GDP inflation rate may be also appropriate. To conservative estimates, the length of the largest of the first three interval ranges, i.e., $\Delta \phi {\left(X_S\right)}_1={\rho }_1{\rho }_3\Delta >0$, is used as our theoretical analysis of the normal range. In fact, the range ${\Uparrow }^{+}$ is better than the range $\Delta \phi {\left(X\right)}_1={\rho }_2{\rho }_3\Delta >0$ because both

${\Uparrow }^{-}$ and ${\rho }_3={\rho }_1=\rho (\; x\; )$

satisfy the healthy balance conditions: $c=1$,$\begin{array}{l}\Delta \phi {\left(X\right)}_2=\Delta \phi {\left(X\right)}_1+\Delta \phi \left(X\right)=-\left(1-{\rho }_2{\rho }_3\right)\Delta =-\left(1-c\rho {\left(x\right)}^3\right)\\ \to -\left(1-\rho {\left(x\right)}^3\right)<0,\end{array}$ and $\begin{array}{l}\Delta \phi {\left(S_X\right)}_2=\Delta \phi {\left(S_X\right)}_1+\Delta \phi \left(S_X\right)=-\left({\rho }_1+{\rho }_2{\rho }_3\right)\Delta =-\left(\rho \left(x\right)+c\rho {\left(x\right)}^3\right)\Delta \\ \to -\left(\rho \left(x\right)+\rho {\left(x\right)}^3\right)\Delta <0,\end{array}$ at the same time if $\Delta \phi {\left(K_X\right)}_2=\Delta \phi {\left(K_X\right)}_1+\Delta \phi \left(K_X\right)=\left({\rho }_1-{\rho }_3\right)\Delta =\rho \left(x\right)\left(1-c\right)\Delta \to 0+,$,$\Delta \phi {\left(X_K\right)}_2=\Delta \phi {\left(X_K\right)}_1+\Delta \phi \left(X_K\right)=\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =\rho {\left(x\right)}^2\left(1-c\right)\Delta \to 0+,$ and $\Delta \phi {\left(X_S\right)}_2=\Delta \phi {\left(X_S\right)}_1+\Delta \phi \left(X_S\right)=-\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =-\rho {\left(x\right)}^2\left(1-c\right)\Delta \to 0-.$ where $\Delta \phi {\left(X\right)}_2=-\left(1-{\rho }_2{\rho }_3\right)\Delta =\left(1-c\rho {\left(x\right)}^3\right)\Delta <0$. In other words, the parameter $x\in \left[a,b\right]$ or the range $1\ge \rho \left(x\right)\ge {\rho }_0$ is the healthy condition of both the killing relationship and the loving relation at the same time. But neither are the others. The GDP inflation rate must be precise calculation to keep at least 6 decimal places can ensure correct because of its sensitivity to the diagnosis of disease. #

Remark 2. Western Economics is different from TCE because the TCE has a concept of Chi or Qi as a form of energy. From the energy concept, that one organ or subsystem of the economic society is not running properly (or disease, abnormal), is that the energy deviation from the average of the organ is too large, the high (real disease) or the low (virtual disease). For the normal range of a GDP inflation rate of some economic society as $-\left(\rho \left(x\right)+\rho {\left(x\right)}^3\right)\le -\left(1-\rho {\left(x\right)}^3\right)$, in TCE, if $c\ne 1$, the economy is considered as a real disease since the GDP inflation rate is too high; if $0\le {\rho }_3=c\rho \left(x\right)<\rho \left(x\right)={\rho }_1$, the economy is considered as a virtual disease since the GDP inflation rate is too low. Thus TCE identifies an important indicator for an economic society’s health: the value of the GDP inflation rate, which, under normal conditions, ranges from 5.8114% to 16.359%. Outside this range (too low: Yin condition; too high: Yang condition), disease appears. Almost always absolutely, when there is a virtual disease, the condition of the GDP inflation rate is a Yin condition; when there is a real disease, the condition of the GDP inflation rate is a Yang condition. But there do not exist these concepts of both real diseases and virtual diseases in Western Economics. #

Remark 3. Obviously, when applying the hypothesis of Theorem 2.1 and Corollary 2.1 to other fields rather than economic society’s health, it is necessary to identify a global parameter in each field. It is able to yield a general Yin or Yang condition in relation to the average behavior of the studied phenomenon, and it maintains the equations at a sufficiently simple level of writing and application. In fact, let $0\le c<1$ where the values min and max are the minimum and maximum acceptable the index ${\rho }_3$. Denoted the value $\left({\rho }_1-{\rho }_3\right)=\rho \left(x\right)\left(1-c\right)>0$ is the target as the expectation of the index $\left({\rho }_2-{\rho }_1{\rho }_3\right)=\rho {\left(x\right)}^2\left(1-c\right)>0$ such that $-\left({\rho }_2-{\rho }_1{\rho }_3\right)=-\rho {\left(x\right)}^2\left(1-c\right)<0$. In Equations (3) and (4), replace $\begin{array}{l}\Delta \phi {\left(K_X\right)}_2=\Delta \phi \left(K_X\right)+\Delta \phi {\left(K_X\right)}_1=\left({\rho }_1-{\rho }_3\right)\Delta =\rho \left(x\right)\left(1-c\right)\Delta >0,\\ \Delta \phi {\left(X_K\right)}_2=\Delta \phi \left(X_K\right)+\Delta \phi {\left(X_K\right)}_1=\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =\rho {\left(x\right)}^2\left(1-c\right)\Delta >0,\end{array}$ by $\Delta \phi {\left(X_S\right)}_2=\Delta \phi \left(X_S\right)+\Delta \phi {\left(X_S\right)}_1=-\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =-\rho {\left(x\right)}^2\left(1-c\right)\Delta <0,$, respectively. The equivalent condition of a healthy economy $1>c\ge 0$ can be obtained as $\left({\rho }_1-{\rho }_3\right)\ge \left({\rho }_2-{\rho }_1{\rho }_3\right)\ge -\left({\rho }_2-{\rho }_1{\rho }_3\right)\ge -\left({\rho }_1-{\rho }_2{\rho }_3\right)\ge -\left({\rho }_1+{\rho }_2{\rho }_3\right).$,$\left(1-{\rho }_2{\rho }_3\right)\le \left({\rho }_1+{\rho }_2{\rho }_3\right)$, where

$\begin{array}{c}\left({\rho }_1+{\rho }_2{\rho }_3\right)\ge \left({\rho }_1-{\rho }_2{\rho }_3\right)\ge \left({\rho }_1-{\rho }_3\right)=\rho \left(x\right)\left(1-c\right)\\ \ge \rho {\left(x\right)}^2\left(1-c\right)=\left({\rho }_2-{\rho }_1{\rho }_3\right).\end{array}$

and

$\Delta \phi {\left(X\right)}_2=-\left(1-c\rho {\left(x\right)}^3\right)\Delta \ge -\Delta =\Delta \phi (\; X\; )$

3. Relationship Analysis of Steady Multilateral Systems

3.1. Energy Changes of a Steady Multilateral System

In order to apply the reasoning to other fields rather than society economy’s health, Zhang & Zhang (2013) have started a steady multilateral system imitating a society economy. A most basic steady multilateral system is as follows:

Theorem 3.1 (Zhang & Shao, 2012) For each element $x$ in a steady multilateral system V with two incompatibility relations, there exist five equivalence classes below:

${\uparrow }^0$

$\phi (\; X\; )$

which the five equivalence classes have relations in Figure1. #

It can be proved by Theorem 3.2 below that the steady multilateral system in Theorem 3.1 is the reasoning model of Yin Yang Wu Xing in TCE if there is an energy function $\Delta \phi \left(X\right)=\Delta >0$ satisfying

$\Delta \phi \left(X_S\right)={\rho }_1\Delta >0$

if increase the energy of ${\uparrow }^{+}$, where $\Delta \phi \left(S_X\right)={\rho }_2\Delta >0$,${\uparrow }^{-}$,$\Delta \phi \left(X_K\right)=-{\rho }_1\Delta <0$,${\downarrow }^{+}$,$\Delta \phi \left(K_X\right)=-{\rho }_2\Delta <0$.

It is called the Yin Yang Wu Xing model, denoted by $V^{\text{5}}$.

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

Define

${\downarrow }^{-}$

corresponding to wood, fire, earth, metal, water, respectively, and assume

$\Delta \phi \left(X_K\right)=-{\rho }_1\Delta <0$ where $x\in \left[a,b\right]$.

And take $1\ge {\rho }_1=\rho \left(x\right)\ge {\rho }_0$ satisfying

${\rho }_1+{\rho }_2{\rho }_3=\rho \left(x\right)+c\rho {\left(x\right)}^3\ge 1-{\rho }_2{\rho }_3=1-c\rho {\left(x\right)}^3$

where $1\ge c\ge \left[1-\rho \left(x\right)\right]/\left(2\rho {\left(x\right)}^3\right)>0,\forall x\ne t_0$ is the Descartes product in set theory and $\Delta \phi {\left(X_K\right)}_1={\rho }_3\Delta >0$ is the multiplication relation operation. The relation multiplication of ${\Uparrow }^0$ is isomorphic to the addition of module 5. Then $V^{\text{5}}$ is a steady multilateral system with one equivalent relation $R_0$ and two incompatibility relations $\Delta \phi {\left(K_X\right)}_1={\rho }_1{\rho }_3\Delta >0$ and ${\Uparrow }^{+}$ where the inverse relation operation is $\Delta \phi {\left(X_S\right)}_1={\rho }_2{\rho }_3\Delta >0$. The Yin and Yang means the two incompatibility relations and the Wu Xing means the collection of five disjoint classifications of ${\Uparrow }^{-}$.

Figure1 in Theorem 3.1 is the Figureof 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 complex systems can be used in economic society complex systems.

By non-authigenic logic of TCE, i.e., a logic which is similar to a group has nothing to do with the research object by Zhang & Shao (2012), in order to ensure the reproducibility such that the analysis conclusion can be applicable to any a complex system, a logical analysis model which has nothing to do with the object of study should be chosen. 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.

Western Economy is different from TCE because the TCE has a concept of Chi or Qi (气) 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 steady multilateral systems’ life. It is also believed that an individual is born with an original amount of Chi at the beginning of steady multilateral systems’ life 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 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 (Jing-Luo (经络) or Zang Xiang (藏象)) 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 $\Delta \phi {\left(S_X\right)}_1=-{\rho }_1{\rho }_3\Delta <0$,${\Downarrow }^{+}$ and $\Delta \phi {\left(X\right)}_1=-{\rho }_2{\rho }_3\Delta <0$.

For example, in TCE, a society economy as the first physiological system of the steady multilateral system following the Yin Yang Wu Xing theory was classified into five equivalence classes by Zhang & Zhang (2013) as follows:

${\Downarrow }^{-}$

${\rho }_3={\rho }_1=\rho (\; x\; )$

$c\to 1$

$\begin{array}{c}\Delta \phi {\left(X\right)}_2=\Delta \phi {\left(X\right)}_1+\Delta \phi \left(X\right)=\left(1-{\rho }_2{\rho }_3\right)\Delta \\ =\left(1-c\rho {\left(x\right)}^3\right)\Delta \to \left(1-\rho {\left(x\right)}^3\right)\Delta >0,\end{array}$

$\begin{array}{c}\Delta \phi {\left(X_S\right)}_2=\Delta \phi {\left(X_S\right)}_1+\Delta \phi \left(X_S\right)=\left({\rho }_1+{\rho }_2{\rho }_3\right)\Delta \\ =\left(\rho \left(x\right)+c\rho {\left(x\right)}^3\right)\Delta \to \left(\rho \left(x\right)+\rho {\left(x\right)}^3\right)\Delta >0,\end{array}$

$\Delta \phi {\left(X_K\right)}_2=\Delta \phi {\left(X_K\right)}_1+\Delta \phi \left(X_K\right)=-\left({\rho }_1-{\rho }_3\right)\Delta =-\rho \left(x\right)\left(1-c\right)\Delta \to 0-,$

$\Delta \phi {\left(K_X\right)}_2=\Delta \phi {\left(K_X\right)}_1+\Delta \phi \left(K_X\right)=-\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =-{\left(x\right)}^2\left(1-c\right)\Delta \to 0-,$.

There is only one of both loving and killing relations between every two classes. General close is loving, alternate is killing.

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. It means that “the same energy attracted to 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 complex system. The stability of any a 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 complex system, if the killing force is large, i.e., $\Delta \phi {\left(S_X\right)}_2=\Delta \phi {\left(S_X\right)}_1+\Delta \phi \left(S_X\right)=\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =\rho {\left(x\right)}^2\left(1-c\right)\Delta \to 0+.$ becomes larger by Theorem 3.3 below, which needs 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 complex system more stable. If the killing force is small, i.e., $\Delta \phi {\left(X\right)}_2=\left(1-{\rho }_2{\rho }_3\right)\Delta =\left(1-c\rho {\left(x\right)}^3\right)\Delta >0$ becomes smaller by Theorem 3.3 below, 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 complex system becoming unstable.

The second physiological system of the steady multilateral system controls the first physiological system of the steady multilateral system, abiding by the following rules.

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

In mathematics, suppose that the sub-economy of X is healthy. If X is intervened, then the second physiological system will attain the Chi or energy from X directly.

Suppose that the sub-economy of X is unhealthy. If X is intervened, then the second physiological system will attain the Chi or energy from X indirectly. If virtual X is intervened, it will attain the Chi or energy (Yang energy) from the son X_S of X. If real X is intervened, it will attain the Chi or energy (Yin energy) from the mother S_X of X. #

Affording Rule: The second physiological system of the steady multilateral system will work by using Affording Rule, if the first physiological system of the steady multilateral system runs hardly. The work is in order to afford the Chi or energy for the first physiological 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 physiological systems will begin to run normally.

In mathematics, suppose that the sub-economy of X is healthy. The second physiological system doesn’t afford any Chi or energy for the first physiological system.

Suppose that the economy of X is unhealthy and the capability of self-protection is lack, i.e., $x\in \left[a,b\right]$ and $1\ge {\rho }_1=\rho \left(x\right)\ge {\rho }_0$. The second physiological system will afford the Chi or energy for X directly, at the same time, affording the Chi or energy for other subsystem, 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., $\left(\rho \left(x\right)+\rho {\left(x\right)}^3\right)\ge \left(1-\rho {\left(x\right)}^3\right)$ and $c\ne 1$, to drive the first physiological 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 physiological system must make the first physiological system intervened, namely exercise. It is because only by intervention on the first physiological system, the second physiological system is able to get food.

Energy concept is an important concept in Physics. Zhang & Zhang (2013) introduce this concept to the steady multilateral systems imitating economy. And the image mathematics by Zhang & Shao (2012) uses these concepts to deal with the steady multilateral system diseases (mathematical index too high or too low). In mathematics, a steady multilateral system is said to have Energy (or Dynamic) if there is a non-negative function ${\rho }_3=c\rho \left(x\right)<\rho \left(x\right)={\rho }_1$ which makes every subsystem meaningful of the steady multilateral system. Similarly to Zhang & Zhang (2013), unless stated otherwise, any equivalence relation is the liking relation, any neighboring relation is the loving relation, and any alternate relation is the killing relationship.

Suppose that V is a steady multilateral system having an energy, then V in the steady multilateral system during a normal operation, its energy function for any subsystem of the steady multilateral system 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 a subsystem of the steady multilateral system 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, TCE is also often considered a kind of relation diseases. The relation disease is defined as the relation of two sick subsystems. In general, a relation disease is less serious if the relation satisfies one of both the loving relationship and the killing relationship of the steady multilateral system. In this case, in general, the GDP inflation rate $0\le c<1$ which means ${\rho }_3$. This relation disease is less serious because this relation disease can not undermine the loving order or the killing order of the steady multilateral system. The less serious relation disease can make the intervention increasing the sizes of both the intervention reaction coefficients $\left({\rho }_1-{\rho }_3\right)=\rho \left(x\right)\left(1-c\right)>0$,$\left({\rho }_2-{\rho }_1{\rho }_3\right)=\rho {\left(x\right)}^2\left(1-c\right)>0$ and the self-protection coefficient $-\left({\rho }_2-{\rho }_1{\rho }_3\right)=-\rho {\left(x\right)}^2\left(1-c\right)<0$.

But the relation disease is more serious if the relation not only doesn’t satisfy the killing relationship of the steady multilateral system, but also can destroy the killing order, i.e., there is an incest order. In this case, in general, the GDP inflation rate $\Delta \phi {\left(X_K\right)}_2=\Delta \phi \left(X_K\right)+\Delta \phi {\left(X_K\right)}_1=-\left({\rho }_1-{\rho }_3\right)\Delta =-\rho \left(x\right)\left(1-c\right)<0,$ which means $\Delta \phi {\left(K_X\right)}_2=\Delta \phi \left(K_X\right)+\Delta \phi {\left(K_X\right)}_1=-\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta =-\rho {\left(x\right)}^2\left(1-c\right)<0,$. This relation disease is more serious because the relation disease can destroy the killing order of the steady multilateral system if the disease continues to develop. The more serious relation disease can make both the intervention reaction coefficients $1>c\ge 0$,$\Delta \phi {\left(S_X\right)}_2=\Delta \phi \left(S_X\right)+\Delta \phi {\left(S_X\right)}_1=\left({\rho }_2-{\rho }_1{\rho }_3\right)=\rho {\left(x\right)}^2\left(1-c\right)\Delta >0$ and the self-protection coefficient $1>c\ge 0$ decreasing response to intervention.

There are also many relation diseases which cannot destroy the loving order or the killing order of the steady multilateral system although the relation doesn’t satisfy strictly the loving relationship or the killing relationship of the steady multilateral system, i.e., there is not an incest order. These relation diseases are called rare since they are hardly occurrence for a healthy economy.

The purpose of intervention is to make the steady multilateral system return to normal state. The method of intervention is to increase or decrease the energy of a subsystem.

What kind of intervening should follow the principle to treat it? Western economics emphasizes directly mathematical treatments on the sick subsystem after the disease of subsystem has occurred, but the indirect intervening of oriental economics of TCE is required before the disease of subsystem will occur. In mathematics, which is more reasonable?

Based on this idea, many issues are worth further discussion. For example, if an intervening has been implemented to a disease subsystem before the disease of subsystem will occur, what relation disease will be less serious which does not need to be intervened? what relation disease will be more serious which needs to be intervened?

3.2. Kinds of Relation Disease of Steady Multilateral Systems

For a steady multilateral system V imitating an economy with two incompatibility relations, suppose that the subsystems $-\left({\rho }_1-{\rho }_3\right)\le -\left({\rho }_2-{\rho }_1{\rho }_3\right)\le \left({\rho }_2-{\rho }_1{\rho }_3\right)\le \left({\rho }_1-{\rho }_2{\rho }_3\right)\le \left({\rho }_1+{\rho }_2{\rho }_3\right).$ are the same as those defined in Theorem 3.1. Then the relation diseases can be decomposed into the following classes:

Definition 3.1 (involving in (相及) and infringing upon (相犯)) Suppose that both X and X_S having the loving relationship fall ill. Consider a relation disease occurred between X and X_S.

The relation disease between X and X_S is called less serious if X is a virtual disease and so is X_S at the same time. The less serious relation disease between virtual X and virtual X_S is also called a mother’s disease involving in her son. The mother is the cause of disease.

The relation disease between X and X_S is also called less serious if X is a real disease and so is X_S at the same time. The less serious relation disease between real X and real X_S is also called a son’s disease infringing upon his mother. The son is the cause of disease.

The relation disease between X and X_S is called rare if X is a real disease but X_S is a virtual disease at the same time, or if X is a virtual disease but X_S is a real disease at the same time. The rare relation disease implies that they cannot destroy the loving order although real X cannot love virtual X_S or virtual X cannot love real X_S. #

Definition 3.2 (multiplying (相乘) and insulting (相侮)) Suppose that both X and X_K having the killing relationship fall ill. Consider a relation disease occurred between X and X_K.

The relation disease between X and X_K is called less serious if X is a real disease and X_K is a virtual disease at the same time. The less serious relation disease between X and X_K is also called a multiplying relation.

The relation disease between X and X_K is called more serious if X is a virtual disease but X_K is a real disease at the same time. The more serious relation disease between X and X_K is also called an insulting relation. It means that X has been harmed by X_K through the method of incest.

The relation disease between X and X_K is called rare if X is a real disease and so is X_K at the same time, or if X is a virtual disease and so is X_K at the same time. The rare relation disease implies that they cannot destroy the killing order from X to X_K although real X cannot kill real X_K or virtual X cannot kill virtual X_K.

The relation disease between X, X_K and K_X is called more serious if X is a real disease, and X_K is a virtual disease but K_X is also a virtual disease at same time, i.e., not only real X multiplies in virtual X_K, but also insults virtual K_X by using the method of incest. It is because the energy of real X is too high. The more serious relation disease between X, X_K, and K_X is also called a multiplying-insulting (乘侮) relation.

The relation disease between X, X_K, and S_X is called more serious if X is a real disease, and X_K is a virtual disease but S_X is also real disease at same time, i.e., not only real X multiplies in virtual X_K, but also real S_X insults virtual X_K by using the method of incest. It is because the energy of virtual X_K is too low. The more serious relation disease between X, X_K, and S_X is also called a multiplying-insulting (乘侮) relation.

Only the more serious relation disease can destroy the killing relationship order of the Yin Yang Wu Xing system. All the therapeutic principles need to prevent the more serious relation disease occurrence in the first place. #

The disease of multiplying-insulting relation will result in more than three subsystems falling-ill. Generally, three or more subsystems falling-ill, it will be difficult to treat. Therefore, the multiplying-insulting relation disease should be avoided as much as possible. In Chinese words, it is that “Again and again, don’t allow to the repeated to four” (只有再一再二, 没有再三再四)-Allow one or two subsystems falling ill, but Don’t allow three or four subsystems falling ill.

3.3. First Transfer Law of Diseases of Steady Multilateral Systems with a healthy Economy

Suppose that a steady multilateral system V imitating an economy having energy function $\left(1-{\rho }_2{\rho }_3\right)\le \left({\rho }_1+{\rho }_2{\rho }_3\right)$ is normal or healthy. Let x be the GDP inflation rate of V. Assume that $\begin{array}{l}\left({\rho }_1+{\rho }_2{\rho }_3\right)\ge \left({\rho }_1-{\rho }_2{\rho }_3\right)\ge \left({\rho }_1-{\rho }_3\right)=\rho \left(x\right)\left(1-c\right)\\ \ge \rho {\left(x\right)}^2\left(1-c\right)=\left({\rho }_2-{\rho }_1{\rho }_3\right).\end{array}$,$\Delta \phi {\left(X\right)}_2=\left(1-c\rho {\left(x\right)}^3\right)\Delta <\Delta =\Delta \phi \left(X\right)$, and $a=\text{5}\text{.8114\%},b=\text{16}\text{.359\%},t_0=\text{10}\text{.208\%}$ where ${\downarrow }^0$ and $\phi \left(X\right)$ is defined in Equations (3) and (4). The healthy economy means that the conditions $\Delta \phi \left(X\right)=-\Delta <0$ and $\Delta \phi \left(S_X\right)=-{\rho }_1\Delta <0$ hold, which is equivalent to the normal range ${\downarrow }^{+}$ or the healthy condition $\Delta \phi \left(X_S\right)=-{\rho }_2\Delta <0$. That ${\downarrow }^{-}$ implies that the body is without the ability of self-protection, i.e., $\Delta \phi \left(K_X\right)={\rho }_1\Delta >0$. Of course, the body cannot be healthy. It is because for any ${\uparrow }^{+}$, when $\Delta \phi \left(X_K\right)={\rho }_2\Delta >0$, there is

${\uparrow }^{-}$,

such that the healthy condition $\Delta \phi \left(K_X\right)={\rho }_1\Delta >0$ cannot hold.

By using Corollary 2.1 and Theorems 2.1 and 3.1, the following Theorem 3.2 can be obtained as the first transfer law of occurrence and change of diseases with a healthy economy.

Theorem 3.2 Suppose that a subsystem $x\bar{\in }\left[a,b\right]$ of a steady multilateral system ${\rho }_0>{\rho }_1=\rho \left(x\right)>{\rho }_2=\rho {\left(x\right)}^2>0$ falls a disease. Let the GDP inflation rate $\left({\rho }_1+{\rho }_2{\rho }_3\right)<\left(1-{\rho }_2{\rho }_3\right)$ which is equivalent to the conditions ${\rho }_3=c\rho \left(x\right)$ and $0<\left({\rho }_1-{\rho }_3\right)=\rho \left(x\right)\left(1-c\right)\to \rho \left(x\right)={\rho }_1$ .

In this case, almost always, the less serious relation disease will occur and change. If the disease continues to develop, the change can make a more serious relation disease occur.

The occurrence and change of diseases with a healthy economy has its transfer law: The first occurrence and change of the loving relationship and the killing relationship after the loving relationship disease. In other words, the following statements are true.

If a subsystem X of a steady multilateral system V falls a virtual disease, the transfer law is the first occurrence of the virtual disease of the mother S_X of X with a less serious relation disease between virtual S_X and virtual X, and secondly the real disease of the bane K_X of X after the virtual disease of S_X with a less serious relation disease between real K_X and virtual X, and thirdly the real disease of the prisoner X_K of X with a more serious relation disease between virtual X and real X_K, and fourthly the virtual disease of the son X_S of X with a less serious relation disease between virtual X and virtual X_S, and finally the new remission virtual disease of the subsystem X itself, and for the next round of disease transmission, until disease rehabilitation.

If a subsystem X of a steady multilateral system V encounters a real disease, the transfer law is the first occurrence of the real disease of the son X_S of X with a less serious relation disease between real X and real X_S, and secondly the virtual disease of the prisoner X_K of X after the real disease of X_S with a less serious relation disease between real X and virtual X_K, and thirdly the virtual disease of the bane K_X of X with a more serious relation disease between virtual K_X and real X, and fourthly the real disease of the mother S_X of X with a less serious relation disease between real S_X and real X, and finally the new abated real disease of the subsystem X itself, and for the next round of disease transmission, until disease rehabilitation.

All first transfer laws of diseases with a healthy complex system are summed up as Figure2 and Figure3. #

Remark 4. Theorem 3.2 is called the transfer law of occurrence and change of diseases with a healthy economy, simply, the first transfer law. For a real disease, the first transfer law is along the loving relationship order transmission as follows:

$0<\left({\rho }_2-{\rho }_1{\rho }_3\right)=\rho {\left(x\right)}^2\left(1-c\right)\to \rho {\left(x\right)}^2={\rho }_2$

For a virtual disease, the first transfer law is against the loving relationship order transmission as follows:

$c\to 0$

The transfer relation of the first transfer law running is the loving relationship, denoted by ®. The running condition of the first transfer law is both ${\rho }_3=c\rho \left(x\right)\to 0$ and $c\to 0$.

By Theorem 2.1 and Corollary 2.1, the running condition is nearly equivalent to both ${\rho }_0>{\rho }_1=\rho \left(x\right)>{\rho }_2=\rho {\left(x\right)}^2>0$ and $\begin{array}{c}\Delta \phi {\left(X\right)}_2=\Delta \phi {\left(X\right)}_1+\Delta \phi \left(X\right)=-\left(1-{\rho }_2{\rho }_3\right)\Delta \\ =-\left(1-c\rho {\left(x\right)}^3\right)\Delta \to -\Delta <0,\end{array}$. The best-state condition of the first transfer law is $\begin{array}{c}\Delta \phi {\left(S_X\right)}_2=\Delta \phi {\left(S_X\right)}_1+\Delta \phi \left(S_X\right)=-\left({\rho }_1+{\rho }_2{\rho }_3\right)\Delta \\ =-\left(\rho \left(x\right)+c\rho {\left(x\right)}^3\right)\Delta \to -{\rho }_1\Delta <0,\end{array}$ where $\begin{array}{c}\Delta \phi {\left(K_X\right)}_2=\Delta \phi {\left(K_X\right)}_1+\Delta \phi \left(K_X\right)=\left({\rho }_1-{\rho }_3\right)\Delta \\ =\rho \left(x\right)\left(1-c\right)\Delta \to \rho \left(x\right)\Delta ={\rho }_1\Delta >0,\end{array}$ which is the best state of $\begin{array}{c}\Delta \phi {\left(X_K\right)}_2=\Delta \phi {\left(X_K\right)}_1+\Delta \phi \left(X_K\right)=\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta \\ =\rho {\left(x\right)}^2\left(1-c\right)\Delta \to \rho {\left(x\right)}^2\Delta ={\rho }_2\Delta >0,\end{array}$ for a healthy economy. To follow or utilize the running of the first transfer law is equivalent to the following method. For dong so, it is in order to protect or maintain the loving relationship. The method can strengthen both the value $\begin{array}{c}\Delta \phi {\left(X_S\right)}_2=\Delta \phi {\left(X_S\right)}_1+\Delta \phi \left(X_S\right)=-\left({\rho }_2-{\rho }_1{\rho }_3\right)\Delta \\ =-\rho {\left(x\right)}^2\left(1-c\right)\Delta \to -{\rho }_2\Delta <0.\end{array}$ tending to be large and the value $x\bar{\in }\left[a,b\right]$ tending to be small at the same time. In other words, the way can make all of both ${\rho }_0>{\rho }_1=\rho \left(x\right)>{\rho }_2=\rho {\left(x\right)}^2>0$ and c tending to be large. It is because the running condition of the loving relationship $\left({\rho }_1+{\rho }_2{\rho }_3\right)<\left(1-{\rho }_2{\rho }_3\right)$ is the stronger the use, which dues to $\left({\rho }_1+{\rho }_2{\rho }_3\right)<\left(1-{\rho }_2{\rho }_3\right)$ the greater the use. In other words again, if the treatment principle of the loving relationship disease is to use continuously abiding by the first transfer law, then all of both the intervention reaction coefficients $\pm \left(1-{\rho }_2{\rho }_3\right){\Delta }_1$ and the coefficient of self-protection $\phi \left(X\right)$ where $\Delta \phi \left(X\right)={\Delta }_1>0$ will tend to be the best state, i.e., ${\Uparrow }^0$ and $\phi \left(X_K\right)$.