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“Yin Yang Wu Xing” Theory in Traditional Chinese Medicine Chinese Medicine, 2011, 2, 6-15 doi:10.4236/cm.2011.21002 Published Online March 2011 (http://www.SciRP.org/journal/cm) Mathematical Reasoning of Treatment Principle Based on “Yin Yang Wu Xing” Theory in Traditional Chinese Medicine Yingshan Zhang School of Finance and Statistics, East China Normal University, Shanghai, China E-mail: [email protected] Received December 21, 2010; revised January 20, 2011; accepted January 28, 2011 Abstract By using mathematical reasoning, this paper demonstrates the treatment principle: “Virtual disease is to fill his mother but real disease is to rush down his son” and “Strong inhibition of the same time, support the weak” based on “Yin Yang Wu Xing” Theory in Traditional Chinese Medicine (TCM). We defined two kinds of opposite relations and one kind of equivalence relation, introduced the concept of steady multilateral sys- tems with two non-compatibility relations, and discussed its energy properties. Later based on the treatment of TCM and treated the healthy body as a steady multilateral system, it has been proved that the treatment principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model. Keywords: Traditional Chinese Medicine, “Yin Yang Wu Xing” Theory, Steady Multilateral Systems, Opposite Relations, Side Effects, Medical and Drug Resistance Problem 1. Main Differences between Traditional sively in the traditional treatment to explain the origin of Chinese Medicine and Western life, human body, pathological changes, clinical diagno- Medicine sis and prevention. It has become an important part of the Traditional Chinese Medicine. “Yin Yang Wu Xing” Western medicine treats disease from Microscopic point Theory has a strong influence to the formation and de- of view, always destroys the original human being’s velopment of Chinese medicine theory. But, many Chi- balance, and has none beneficial to human’s immunity. nese and foreign scholars still have some questions on Western medicine can produce pollution to human’s the reasoning of Traditional Chinese Medicine. body, having strong side effects. Excessively using med- Zhang’s theory, multilateral matrix theory [1] and icine can easily paralysis the human’s immunity, which multilateral system theory [13,14,19], have given a new AIDS is a unique product of Western medicine. Using and strong mathematical reasoning method from macro medicine too little can easily produce the medical and (Global) analysis to micro (Local) analysis. He and his drug resistance problem. colleagues have made some mathematical models and Traditional Chinese Medicine (TCM) studies the methods of reasoning [2-17], which make the mathemat- world from the macroscopic point of view, and its target ical reasoning of TCM possible [13] based on “Yin Yang is in order to maintain the original balance of human Wu Xing” Theory [18]. This paper will use steady multi- being and in order to enhance the immunity. TCM be- lateral systems to demonstrate the treatment principle of lieves that each medicine has one-third of drug. She nev- TCM: “Real disease is to rush down his son but virtual er encourages patients to use medicine in long term. Tra- disease is to fill his mother” and “Strong inhibition of the ditional Chinese Medicine has over 5,000-year history. It same time, support the weak”. almost has none side effects or medical and drug resis- The article proceeds as follows. Section 2 contains ba- tance problem [19]. sic concepts and main theorems of steady multilateral After long period of practicing, Chinese ancient med- systems while the treatment principle of Traditional ical scientists use “Yin Yang Wu Xing” Theory exten- Chinese Medicine is demonstrated in Section 3 and 4. Copyright © 2011 SciRes. CM Y. S. ZHANG 7 Conclusions are drawn in Section 5. conveyable (or non-transitivity) relation, of course, a non-equivalence relation. 2. Basic Concept of Steady Multilateral In the following, we consider two non-compatibility Systems relations. Let V be a nonempty set and x, y, z be none equal. In the real world, we are enlightened from some concepts There are two kinds of opposite relations, called neigh- and phenomena such as “biosphere”, “food chain”, boring relations → and alternate relations ⇒, having the “ecological balance” etc. With research and practice, by property: using the theory of multilateral matrices[1] and analyzing 1) If x → y, y → z, then x ⇒ z; the conditions of symmetry [1-2] and orthogonality [3-5, ⇔ if x → y, x ⇒ z, then y → z; 12,17] what a stable system must satisfy, in particular, ⇔ if x ⇒ z, y → z, then x → y. with analyzing the basic conditions what a stable work- 2) If x ⇒ y, y ⇒ z, then z → x; ing procedure of good product quality must satisfy [11, ⇔ if z → x, x ⇒ y, then y ⇒ z; 17], we are inspired and find some rules and methods, ⇔ if y ⇒ z, z→ x, then x ⇒ y. then present the logic model of analyzing stability of Two kinds of opposite relations cannot be exist sepa- complex systems [7-10]—steady multilateral systems rately. [13,14,19]. There are a number of essential reasoning Such reasoning can be expressed as follows: methods based on the stable logic analysis model, such x x as “transition reasoning”, “atavism reasoning”, “genetic ⇓ ⇓ reasoning” etc. z ← y y ⇒ z 2.1. Equivalence Relations The first triangle reasoning is known as a jumping- transition reasoning, while the second triangle reasoning Let V be a nonempty set and x, y, z be their elements. We is known as an atavism reasoning. Both neighboring re- call it an equivalence relation, denoted ~, if the following lations and alternate relations are not compatibility rela- 3 conditions are all true: tions, of course, none equivalence relations, called 1) Reflexive: x ~ x for all x; non-compatibility relations. 2) Symmetric: if x ~ y, then y ~ x; 3) Conveyable (Transitivity): if x ~ y, y ~ z, then x ~ z. 2.3. Genetic Reasoning If there are some x, y, z such that at least one of the conditions above is true, the relation is called a compati- Let V be a nonempty set and x, y, z be not equal one bility relation. Any one of compatibility relations can be another. If equivalence relations exist, neighboring rela- expanded into an equivalence relation [19]. tions, and alternate relations in V at the same time, then a Western Science only considers the reasoning under genetic reasoning is defined as follows: one Axiom system such that only researches on compati- 1) if x ~ y, y → z, then x → z; bility relation reasoning. However, there are many Axiom 2) if x ~ y, y ⇒ z, then x ⇒ z; systems in Nature. Traditional Chinese Science (TCS, or 3) if x → y, y ~ z, then x → z; Oriental Science) mainly researches the reasoning among 4) if x ⇒ y, y ~ z, then x ⇒ z. many Axiom systems in Nature. Of course, she also con- siders the reasoning under one Axiom system but she 2.4. Multilateral Systems only expands the reasoning as the equivalence relation reasoning [19]. For a nonempty set V, if there exists at least an non- compatibility relation, then it is called a multilateral sys- 2.2. Two Kinds of Opposite Relations tem about complexity [13,14,19], or equivalently, a logic analysis model of complex systems [7-10]. Equivalence relations, even compatibility relations, can- Assume that there exist equivalence relations, neighbor- not portray the structure of the complex systems clearly. ing relations, and alternate relations in system V, which For example, assume that A and B are good friends and satisfy genetic reasoning. If for every x, y ∈ V, at least they have close relations. So are B and C. However, you there is one of the three relations between x and y, and cannot get the conclusion that A and C are good friends. there are not x → y and x ⇒ y at the same time, then V is We denote A → B as that A and B have close relations. called a logic analysis model of complex systems, which Then the example above can be denoted as: A → B, B → is equivalent to the logic architecture of reasoning model C do not imply A → C, i.e., the relation → is a non- of “Yin Yang” Theory in Ancient China. Obviously, V is Copyright © 2011 SciRes. CM 8 Y. S. ZHANG a multilateral system with two non-compatibility rela- 3. Relationship Analysis of Steady tions. In this paper, we only consider this multilateral Multilateral Systems system. Theorem 2.1 For a multilateral system V with two 3.1. Energy of a Multilateral System non-compatibility relations, ∀ x, y ∈ V, only one of the following five relations is existent and correct: Energy concept is an important concept in Physics. Now, x ~ y, x → y, x ← y, x ⇒ y, x ⇐ y. we introduce this concept to the multilateral systems and use these concepts to deal with the multilateral system Theorem 2.2 For a multilateral system V with two diseases. non-compatibility relations, ∀ x, y, z ∈ V, the following In mathematics, a multilateral system is said to have reasoning holds: energy (or dynamic) if there is a none negative function 1) if x → z , y → z, then x ~ y; φ(*) which makes every subsystem meaningful of the 2) if x ⇒ z, y ⇒ z, then x ~ y; multilateral system. 3) if x → y , x→ z, then y ~ z; For two subsystems Vi and Vj of multilateral system V, 4) if x ⇒ y, x ⇒ z, then y ~ z. denote Vi → Vj (or Vi ⇒ Vj, or Vi ~ Vj) means xi → xj, xi∈ Vi, xj∈Vj (or xi ⇒ xj, xi∈Vi, xj∈Vj or xi ~ xj, xi∈Vi, 2.5.
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