Glad to announce the publication of our article.
«Electronic Information Systems» QUARTERLY SCIENCE MAGAZIN № 2 (21) 2019
Read this article here: https://elibrary.ru/item.asp?id=38566107
A. S. Kruchinin
About mathematics and informatics of stratagems
A version of stratagem logic interpretation is given in terms of topic “Mathematics and Informatics of Stratagem” discussion. The logic of their association with hexagrams of “The Book of Changes” (by means of numerical three-dimensional matrix of computer program SEFOR) is described. A possibility of calculations with the use of numerical basis of hexagrams for stratagems and to restore the entire (possible) set of stratagems and comments for them is set forth forcibly.
Key words: stratagems, stratagematics, hexagrams, computer program SEFOR, numerical three-dimensional matrix, selection of path version, optimal aim selection.
“Mathematics and Informatics of Stratagem” article was published in “Electronic information systems” scientific journal . Defining the relation of stratagematics to the exact science or an art is a matter of a considerable discussion. This analysis aims to lift the veil on thirty-six stratagems described in Chinese treatise . For this purpose, we consider SEFOR (Solutions Effective Formulation and Optimization targeted Research) program*  three-dimensional numerical matrix based on two-dimensional 8x8 Square, in Chinese tradition known as Lo Shu Square  and used in traditional Chinese medicine to identify the location for therapeutic modalities by the "Complicated Spatial Balance" method. However, neither this method, nor its calculations or logic has no application to SEFOR program.
Converting two-dimensional numerical matrix into three-dimensional and comprising it hexagrammatically (Note: Hexagram being a figure composed of six stacked horizontal lines where each line is either broken (open) or unbroken (solid) also possesses properties of numbers those are atypical) made obvious that the entire sequence of I Ching (Note: Book of Changes) hexagrams is mathematically interlinked. Moreover, mathematical operations within the matrix involve both quantitative and qualitative components of these numbers. Hexagram names and their descriptive comments are calculated. Mathematical calculations connect all stages of the changes.
Nowadays there is no necessity in applying divinatory approaches for hexagrams generating. This can be achieved by questionnaire surveys when analyzing psychoemotional state or converting body state measurements resulted from acupuncture research into hexagrams.
Identifying the exact location in the matrix (hexagram), that describes current situation or state, gives six optimum options of the first step of problem solution (Pic. 1).
*SEFOR program creator – D.V.Trubitsin
Pic. 1. SEFOR program three-dimensional numerical matrix
Each option of the transition (step) is a change in one line of hexagram. Any step leads to another hexagram and therefore to situation or state change. Six hexagram lines represent six transitions.
Choosing the exact transition gives recommendation (advice), what exactly is required to make this transition. In other words, we get the plan of actions aimed at situation or state change, which is also calculated.
Now, let us proceed with stratagems. Stratagem 17 “Tossing out a brick to get a jade gem”, for example. It refers to Group 3: Attacking Stratagems. The meaning of this stratagem consists in “converting a small gain to get a bigger one to gain benefit”. It represents an unequal exchange, a mousetrap. Intention is to bait someone by making him believe he gains something and obtain something valuable from him in return.
The meaning of this stratagem in accordance with I Ching is associated with hexagram 4 “The young shoot”. However, the comments to hexagram fail to reflect the meaning of stratagem.
However, from Hexagram 4 we can move on to Hexagram 41 (Pic. 1). A vector arrow (action required for transition) shows this transition, which is calculated, corresponding to hexagram 24.
Let us review the comments to hexagram 24 “Return (The Turning Point)” and hexagram 41 “Decrease”:
Hexagram 24.6 - Missing the defining moment will result in misfortune. Missing fateful time will defeat your plans.
Hexagram 41 - A time of decrease, restraining yourself and controlling anger. Something you donate today, the fate will return with interest tomorrow. It might seem that you are much too wasteful, shower someone with gifts, this feeling will soon disappear and you will be generously rewarded.
Stratagem 14 “Borrow a corpse to resurrect the soul” refers to the same Group 3: Attacking Stratagems. The meaning of this stratagem consists in attracting and applying positive ideas, technologies, traditions of the past, in other words drawing on experience in current issues solution. In accordance with I Ching, this stratagem is also associated with hexagram 4 “The young shoot” and again the comments to hexagram do not reflect the meaning of stratagem.
At the same time, the comments to hexagram 24 and hexagram 41 contain the following:
Hexagram 24.3 - Reversion can reflect the unsafety of current situation. Reoccurrence. Go back to the beginning. Convert threat to own use.
Hexagram 41 - Something important is coming back. Latent possibility to return to the source.
Similar analysis was repeatedly performed with relation to all thirty-six stratagems.
Conclusion: associating stratagems of “The Thirty-Six Stratagems” treatise with hexagrams reflects only the “departure point”, but not the “path” or “place of arrival”. The comment to stratagems consists of the combination of comments to “path” and “place of arrival”.
We cannot but agree that applying brief and detailed comments to I Ching hexagrams is problematic. To solve this we had to analyze nearly ten of the best comments of different authors, summarize them, exclude apparent inconsistencies and verify by change theory logic and mathematics.
For the purpose of situation or state change, where there are six optimum alternative solutions (six arrows from hexagram pic. 1), and for stratagem logic there are six optimum options (direction vectors) of “place of arrival” to each particular hexagram. Consequently, there should be three hundred and eighty four general stratagems. A few more with consideration of coincidences as the one analyzed above.
There is an obvious correlation between six direction vectors and six groups of stratagems:
- Group 1: Winning Stratagems
- Group 2: Enemy Dealing Stratagems
- Group 3: Attacking Stratagems
- Group 4: Chaos Stratagems
- Group 5: Proximate Stratagems
- Group 6: Desperate Stratagems
Six direction vectors are those particular clues to uncovering the logic of stratagems. Their reference to Wu Xing six elements (Note: Traditional Chinese system of five elements with sixth transitional element binding the phases) is also noticeable.
There are two hundred and fifty six additional stratagems with sixty-four including passive behavioral options, as “To wait patiently by the river, to see the body of your enemy floating by”. These sixty-four options with comments are already implemented in SEFOR program. A fourth of general stratagems is also interpreted. When the changes theory logic and the essentials of mathematics are meaningful, it becomes an achievable goal.
If SEFOR program solves the problem of the right path selection for situation change or state correction, stratagem logic focuses more on setting the optimum goal and identifying the ways toward achieving them (which is important in both competitive battles and war pursuance). Additionally the program engages the same logic, mathematics and three-dimensional numerical matrix.
Apparently, much of changes theory was lost. Only the hints of ancient knowledge reached us. Mathematical background elimination reduced the entire knowledge to divinatory practices and mantics.
Today work on reconstruction of this theory is ongoing. In 2017, a binding of psychological types categorizing based on Myers-Briggs type indicator (MBTI) theory  logic to SEFOR program matrix was established. Work on binding of European tone row major and minor tonalities distribution to program matrix along with correlation of Lusher Color Test logic is completed.
In the context of stratagematics, according to the research, if hexagrams allocation three-dimensional development had never existed and there had been no understanding of their numerical basis, logic of stratagems and their classification as they were described in “The Thirty-Six Stratagems” treatise would not have appeared.
It is no coincidence that it says: “Interpreting art of war only as an art and neglecting the fact it is based on precise calculations, - means not to know how to practice the art. <…>. Calculate many times and do not rely on principles. These principles will reveal in your calculations, but the essence of these calculations is beyond explanation”.
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