The whole history of modern natural science development shows that the transition of any science from the descriptive level depends on 3 constituents:

• analysis of available facts and theoretical conceptions;
• synthesis of mathematical model (formulas, functional dependence of variables);
• experimental testing;

Any scientific trend cannot be independent unless it has its own mathematical basis. That is why the western acupuncture is so dependent on neurology.

The development of any science becomes really scientific only when transition from qualitative description of available phenomenon (i.e. pure speculative conceptions that can be innumerable) to quantitative description of interaction of different changeable facts (phenomena, values), the latter being called variables in mathematics, takes place. The short record of such interactions is called a formula or functional dependence of variables. In the easiest case the formula describes the dependence of two variables, e.g. "x" and "y" according to definite principle (law).

The "Canon of Changes" also describing the changes of variable processes in the basis of Old China medicine. It should be assumed that this treatise deals with some functional dependencies between the variable quantities.

Then each hexagram (or trigram) line is variable x (x₁, x₂ ... x₆). Only two discrete meanings Yin-Yang (O and 1 or - and +) may be given to them. Or we may say, that variable "x" aspires to either O or 1 (0 <-- x or x --> 1). The principle of making a definite hexagram (collecting of lines into a single structure) is functional dependence. Then function f(x) or y is hexagram built.

Let us consider the structure and possible applications of hexagrams. Each hexagram has six positions (lines) differing in their locations. Each position can be either in Yang or Yin location, it is shown by whole or interrupted line.

Tibet pulse diagnostics also gives six pairs of mutually opposite signs of pulse:
 

Yang Strong  Surface (superficial)  Swollen  Quick  Energetic (vigorous)  Full, strong

Yin Weak  Deep (intensified)  Flat  Slow  Flabby  Empty, mild (soft)

If we compare the pulse signs and hexagram structure we shall see that they have the same mathematical structure. We could assume that the pulse of each separate organ is described by a definite hexagram. There are 12 (twelve) organs in all, it means that simultaneously twelve hexagrams are necessary to describe the state of all organs.

Let us consider the system of twelve organs arranged in order of round - the clock - circulation of energy. Let us give a special hexagram received from the connection of two trigrams according to this organ in Fu - Xi and Wen - Wang orders to each organ.

We mark transition from one hexagram to another by means of arrows coinciding with the energy movement direction in corresponding canals (organs). The given approach allows to show graphically in the form of the appropriate changing of hexagram lines the process determined in traditional acupuncture as movement of energy through canals.

Each hexagram line corresponds to a definite point of six energies of a canal given. In this case an uninterrupted or interrupted line is interpreted as closed or open point or as excess or deficiency of energy in a canal accordingly.

Example:

Let us choose pairs of organs belonging to one original element, e.g. "C" and "iG". The upper trigrams of appropriate hexagram are the same, but the lower ones are opposite. It looks like this mathematically:

f₁(x₁, x₂ ... x₆) =

= f₁(1, 1, 0, 1, 0, 1)

or f₁(1, 1, 0, 1 ,0, 1) = f₀(1, 0, 1) + f(1, 1, 0).

    f₂(x₁, x₂ ... x₆) =

= f₂(0, 0, 1, 1, 0, 1).

 

f(1, 1, 0) and f(0, 0, 1) functions (  and  trigrams in Wen-Wang Order) are opposite. If due to some reasons their opposition disappears, process of appropriate lines changes violates when one hexagram turns into another, that process is called energy blocking in traditional acupuncture, i.e. it is impossible to achieve a clinical effect while influencing points of six main energies. In this case a pair of organs ("C" and "iG" can be described mathematically only by means of trigrams (  and  ), (f₀(1, 0, 1) and f₀(1, 0, 1) functions) to corresponding organs in Fu-Xi order. While combining, they form a new hexagram  or f₀(1, 0, 1, 1, 0, 1) function. This function describes a pair of organs ("C" and "iG") as a single whole and corresponds to a Dai-Mai wonderful canal. A hexagram can be reduced to the level of trigram  or f₀(1, 0, 1, 1, 0, 1) --> f₀(1, 0, 1).Trigram level is described by us paper [1].

Thus, such different conceptions as pulse signs, points of six main enregies, main energies, wonderful meridians can be described by means of one mathematical model,namely,hexgram or corresponding functional dependence.

The state of main energy of organ (canal) may also be described in a form of Pofessor Park's diagrams.

In this case every such diagram corresponds to a definite hexagram. There are twelve such diagrams all in all, hence, twelve hexagrams are necessary to describe them. For example:

 

Kidneys dryness excess.	Stomach wind excess.

Thus Professor Park Jae Woo proposed a graphical record of energy states of organs. This considers only a small part of hexagrams. Old China philosophy describes 64 (sixty four) hexagrams arranged in Fu-Xi and Wen-Wang orders.

Wen-Wang orders is a scheme of obviously expressed processes. That is why modern scholar of acupuncture in China use just that very order in diagnostics and treatment. In this case a definite hexagram from Wen - Wand order corresponds to an affected organ. Six hexagram lines correspond to six main points of a canal. A corresponding line of a hexagram while influencing the point turns to the opposite one and there forms already a new hexagram that must correspond to a season and be balanced.

The above conformity between diagrams of six main energies of an organ and hexagrams can also be extended to constitution of six energies describing all system of twelve organs. Very often it is impossible to use Professor Park's Jae Woo algorithms in practical work and to distinguish the central affected organ due to distribution of the excess and deficiency on the pulsegram.

Constitutions of six energies with the distinguished affected central organ:

 

Constitution of Yang - Wind.

Constitution of Yin - Cold.

 

Pulsegrams where it is impossible to distinguish the central affected organ:

 

One could solve this problem if one assumes that the system of twelve organs is described by twelve diagrams formed separately according to six dense (Yin) and six hollow (Yang) organs:

 

One hexagram describes dense (Yin) organs. Its lower line corresponds to the Liver Meridian , the second line - to the Heart Meridian , etc.

 

Another hexagram presents hollow organs (Yang). Its first line corresponds to the Large Intestine Meridian , the second one - to the Urine Bladders Meridian , etc. It is possible to determine which meridians and in what way are to be influenced changing definite lines of a hexagram to their opposite in order to have another hexagram, namely, season balanced one. The calculation is performed by means of Dzin - Phan hexagram development table.

An ordinary tactics of treatment consists in improving disbalance between organs having the clearest distinction or it consists in distinguishing an organ being the main disbalance link and in influencing organs connected. with it to improve this disbalance. The hexagram structure itself already means disbalance between organs. From this point of view disbalance between organs is quite a normal phenomenon. Thus, there are both favourable and unfavourable hexagrams, and there are favourable, and unfavourable disbalances of organs for the season given.

Thus, an Old China medicine was built up not on the mythical ideas (energy, Yin - Yang, etc.), but on the harmonious theory of mathematical analysis of changeable processes which were developed thousands years ago. In this case the terms above are the notions of definite mathematical operations. This theory can be translated into modern mathematical language but it is mush easier to use those symbols listed in it.

French nomenclature is used.

[1] "Treatment of Insulin-Dependent and Insulin-Independent Diabetes in Each Definite Clinical Case Using Wonderful Channels, 4Energy Seas,Yin-Yang Syndromes on the Base of Pulse Data and Pulsegram Analysis", The Web-Journal of Acupuncture, August 1998.