The common version of "Book of Changes" contains a complete set of six-line symbols corresponding to the hexagram names. The sequence of the sixty-four hexagrams is analyzed using mathematical and symbolic methods, which can prove that the set of hexagrams is one. Set a rigorous

Personal " Zhouyi "Honormal Mathematical Logic Analysis

Mathematical Logic, a discipline that uses mathematical method to study logic or formal logic. It belongs to the logic of formal logic formally symbolized and mathematical, and belongs to the category of intellectual logic. The common version of "Book of Changes" contains a complete set of six-line symbols corresponding to the hexagram names. The sequence of the sixty-four hexagrams is analyzed using mathematical and symbolic methods, which can prove that the set of hexagrams is one. Set a rigorous logical system.

Shen Youding "The Great Idea of ​​the Zhouyi Gua" Excerpted by

Yi has sixty-four hexagrams, the main hexagram, and the scattered hexagram. Any internal and external hexagrams with the same order as the main hexagram, and the internal and external hexagrams with the same order as the scattered hexagram. Old and old, old and old, middle and middle, young and young, are called the same order. There are also types of hexagrams and responses. The same type of internal and external hexagrams are called combinations of different types, and the same type is called combinations of responses. Similar types are Yang Gua and Yang Gua, Yin Gua and and Yin Gua. The main hexagram of similar combination is that the eight trigrams are self-respecting. If this is the case, there is no corresponding line, Qian, Kun, Kan, Li, Zhen, Gen, Xun and Dui. The main hexagram of the response and combination is that the six lines of the hexagram are all responding, and the number is eight. If it is good or not, it is good or bad, and it is always profitable and loss-making. There are six main hexagrams, and the bone structure of the order hexagrams are established, and the other forty-eight hexagrams are all scattered hexagrams. The main hexagrams are totally six groups: Qian and Kun are one, Tai and Fu are two, Kan and Li are three, since they are good and good, and four, Zhen, Gen, Xun and Dui are five, and Xian and always gain and losses are six. The first article starts with Qian and Kun, and the middle is the intersection of Qian and Kun, and the ends with Kan and Li; the next article ends with Kan and Li, and the intersection of Kan and Li has not been improved, but the middle is Zhen and Gen and Xun and Dui, and the beginning is Zhen and Zhen. The intersection of Gen, Xun and Dui is always profitable and loss. One is right and the other is wrong, all of which are in harmony and in harmony. ...The second chapter of the scattered hexagram is Qian and Kun, the second chapter of the scattered hexagram is Zhen, Gen, Xun and Dui, the second chapter of the scattered hexagram is also the eight trigrams, and the second chapter of the scattered hexagram is half...; the second chapter of the scattered hexagram is half.... The second part of the scattered hexagram in the previous article is the six hexagrams...; the second part of the scattered hexagrams have constant profit and loss, and the second part of the scattered hexagram has half...; the second part of the scattered hexagram has constant profit and loss... This is the bone structure of the sutra hexagram.

Symbolic mathematical deduction example diagram interpretation

, starting source diagram. "Easy Square Chart" is a logical Yi diagram with complete hexagram and coordinated hexagram and mathematics. The three-line two-way small horizontal diagram is the two axes of the meridian and latitude, the three upper and three lower lines of the six-line hexagram are the meridian and latitude coordinates of the hexagram items. The two diagonal lines are eight hexagrams that cover themselves and eight hexagrams that cover one-pieces. , the four hexagrams are intricately changed into a regular quadrilateral distribution. The six-line coefficients of the Yi hexagram are consistent with the order of the hexagram values ​​and sizes of the hexagrams in the chart, which correspond to the first nine, nine two, nine three, nine four, nine five, and the upper nine. The sum of the values ​​of the two hexagrams is an integer multiple of 9, and the difference is an integer multiple of 7; the sum of the values ​​of the two hexagrams is an integer multiple of 7, and the difference is an integer multiple of 9; the sum of the values ​​of the two hexagrams is an integer multiple of 7, and the difference is an integer multiple of 9; the values ​​of the two hexagrams are incorrect Sum of 63. The "Easy Square Chart" is divided into four areas according to two diagonal lines, the outer ring and the corners of the secondary outer ring, the edges of the outer ring, and the rest of the parts, with two hexagram groups in each area. The "Yi Square Chart" combines hexagram theory and mathematics. It is not only the starting source diagram of the symbolic interpretation of the hexagram sequence in the popular version of "Zhouyi" and it is also the basic source diagram of the overall logic of the hexagram sequence.

information points: Liuyao coefficient, hexagram value and arrangement order; relationships between hexagrams and mathematical characteristics; intricate changes in relationships and point characteristics; hexagram combinations and regional distribution.

, three-axis magic square . "Easy square three-axis magic square" is the most critical link in the overall thinking of hexagram order mathematics and logic analysis. The magic square is based on the sixty-four hexagram sequence numbers of the "Yi Square Chart" as the data set, and is bound by the "Morning and Synthesis Layout", "Qian Kun is in charge, and the Four Cores of Shaolong". The whole picture is divided into two areas: the upper half and the lower half. The horizontal symmetrical hexagrams in the half picture are incorrect and the vertical symmetrical hexagrams are comprehensive. In order to implement the "bone structure of the general purpose" and "two-ton coupling is either unblocked or changed" Rules create conditions. "Shaochang Four Cores" refers to the eight hexagrams of "Zhen Gen Xun Dui and Jian Gui Mei Zhongfu Xiaoguo". The last four hexagrams are the core four hexagrams of "Yi Square Chart".

information points: "Qiankun is in charge, Shaolong four cores" ensures the uniqueness of the magic square plate; the coordination between the two forms of the two forms of the simultaneous and latitude are both reversed and changeable.

, correct and reset. hexagram term intricate changes and reasonable matching of hexagram group are the two obvious characteristics of the "Easy Square Chart". Although the "Yi Square Three-axis Illusion Square" has a comprehensive and staggered meridian and latitude formula that is coordinated with either overturning or changing, the magic square plate system focusing on data balance has failed to take into account the original configuration of the hexagram group. To this end, on the premise of maintaining the basic structure of the Magic Square Pan Bureau, a hierarchical treatment method is adopted to reposition the 64 hexagram items to solve the reasonable placement of the hexagram group. ⑴ Direct positioning of the 32 hexagrams that account for 50% of the total number; ⑵ Positioning of the 16 hexagrams that account for 25% of the total number is "non-overturning or changing two positions"; ⑶ Resetting of the other 16 hexagrams, focusing on solving the hexagram joint hexagrams Groups are reasonably placed.

This link implements the point ownership of 48 hexagram items, and also implements the regional ownership of resetting the 4 hexagrams of the sixteen hexagrams, re-emerging the "Yi Square Chart" hexagram group matching relationship and making it more clear and intuitive, vertical combination Then the unity is consistent with the established form in the middle, that is, the columns in the half chart are inlaid with different hexagrams.

information points: The magic square guides 48 hexagram items to determine the position, 32 direct positioning, and 16 pairs of two positions; the purpose of resetting Sixteen hexagrams is to properly configure the hexagram couplets and hexagram groups; hexagram couplets and hexagrams The rational configuration of the group refers to the hexagram group pairing and hexagram couplet inlay; forming a "new game" under the reset concept.

, New disk-bit and serial number. According to the rhythm of Mr. Shen's careless bone structure, he combined the main hexagram points of the "New Pan Bureau" and tried to make a sequential trajectory of 64 serial numbers. The principle is: rhythmic rhythm, roughly two points, smooth macroscopic, less roundabout, and seek symmetry.

This link not only gives 48 confirmed hexagram items with serial numbers, but also reserves serial numbers for resetting the sixteen hexagrams. clarifies the hexagram couplets of reserved serial numbers, the ownership of the hexagram group, and the hexagram theory relationship between the serial numbers .

Key information: the hexagram connection belonging to reserved serial numbers; the hexagram relationship between reserved serial numbers.

, full cycle, three graphs and two rings. Fully loop is both a concept and a logical method. As a concept, full cycle refers to two different situations arranged by the same combination of elements, deduced from "situation 1" to "situation 2" in the form of element translocation. The translocation trajectory of all elements can form a single closed cycle; as logic The method is because the deduction between situations is a special situation. In this case, the composition of "situation 1", "situation 2" and "deduction Circle" is certain. If you know the second one, you must have it. Third. This is a situation where a full cycle is achieved by "one-to-one".

If it is "one to many" and there is an association in the "many" situation, then this "one" situation can be regarded as a co-solving of the associated situation under sufficient circulation conditions, and "one to many" forms a system. The "one" situation as the co-solve has a mathematical logical background. "Three pictures and two rings" specifically refer to the situation where "one to two" achieves a full cycle.

This article analyzes the mathematical logic of the common "Zhouyi" hexagram order, and the use of "one-to-many" is divided into two levels. One level is used to solve the problem of resetting the sixteen hexagrams, adopting the "three pictures and two rings" multi-round audition selection and resetting the sixteen hexagrams potential plan; the other level is used to show the overall logic of the hexagram sequence, divided into "one to four" and "One to Nine" two forms.

Information points: Fully loop and a separate loop; full loop is established, "two pictures" and "one ring" are determined; "one to many", common solution and "three pictures and two rings".

, known condition source and known condition graph. uses the "three pictures and two rings" method to try to reset the sixteen hexagrams. There is a pair of known conditions maps and a known condition source map.

Known condition source diagram is also called reset hexagram layout, which comes from "Yi Square Chart". The reset 16 hexagrams are arranged in the fourth-order square chart in the order number of "Yi Square Chart" and are branded with each hexagram item. Hexagram group color mark. This picture has its own source, model, and compliance, and the picture is objective and natural.

Known conditions are generated by resetting the hexagram layout according to the principle of "most prominent feature and minimum variation": the outer four corners are each made of diagonal translocation. This picture has its own source, model and compliance, and the picture is objective and natural.

7, 16 serial number hexagram layout. The 16 hexagrams reset by must have their own hexagram properties. The layout of the sixteen hexagrams is naturally a hexagram relationship layout diagram, and this hexagram layout diagram can be inferred in advance, because the "new board" is pre-existing While leaving the serial number, it also clarifies the hexagram couplets of the reserved serial number, the ownership of the hexagram group, and the hexagram theory relationship between the serial number.

6 serial number hexagram theory layout: 16 serial numbers are arranged in order in the fourth-order square diagram according to their size, which is exactly the four hexagrams of upper, lower, left and right; they naturally form two ways of error. This picture has its own source, model and compliance, and the picture is objective and natural.

Information points: hexagram couplet has been fixed, and intricately has been fixed .

8, audition frequency. If the 6 hexagrams are fully arranged without restrictions, their number will reach 16! =2.09228E+13, human resources cannot be auditioned. The actual situation in this example is that the arrangement of 6 hexagrams is bound by the 16-sequence hexagram theory layout, and the 4 hexagrams in each hexagram can only have 4 arrangements . Each hexagram couplet is named after the one with the smallest sequence number in the "Yi Square Chart", and there are four hexagram couplets: "Shi", "Qian", "Fu", "Sheng". Taking into account the variables in the regional layout of the two hexagrams "complex" and "support", the number of arrangements of the 16 hexagrams has been limited to 4×4×4×4×2=512. This number of audition manpower is fully qualified. In addition, the existence of hexagrams in the known conditional square diagram, the actual audition number was once again greatly reduced to 96 cases.

In order to clarify the caliber, I will briefly introduce the implementation method of resetting the arrangement of sixteen hexagrams in this article.

initial arrangement: "Shi", "Qian", "Fu", "Sheng" four hexagram couplets are bound by the 16-serial hexagram theory and layout, each one goes to one side, "Shi", "Qian", "Fu", "Sheng" four hexagrams are in the hexagram couplet. Lead the lead, ranks first in the upper left corner.

variant order: the hexagram couplet is marked by the lead hexagram "Shi", "Qian", "Fu", "Sup" and "Chang", and is clockwise as the order, with a total of four steps; the hexagram couplet is also clockwise as the order, with the "Shi" in the upper left corner "The hexagram couplet starts. The arrangement of

variants is carried out by the sequential superposition method. The situation in the first unit (1-256) is explained as follows: (1) initial arrangement; (2-4) superimpose the "Shi" hexagram couplet in sequence and the following three steps of variation; (5- 8), (9-12), (13-16) Three steps after superimposing the "Qian" hexagram couplet; (17-32), (33-48), (49-64) After superimposing the "Sheng" hexagram couplet Three-step variations; (65-128), (129-192), (193-256) Three-step variations after superimposing the "Fu" hexagram couplet.

second unit and so on.

9, review verification. 16 cases of 96 trials achieved "three pictures and two rings". How to choose? It is necessary to examine the interpretation of "Yi Square Three-Axis Illusion Square" to "Gauze Sequence Pan Bureau". The rules for counting adjustment steps between the disk bureaus are interpreted:

Rated steps: Specify that each hexagram item is dispatched on average by 1 step, and all 64 hexagrams are calculated. The total number of dispatch steps in the whole world is 64.

"One-step" definition: symmetrical positioning of upper and lower half diagrams, left and right half diagrams once, or straight adjacent positioning of 1 time.

effective steps: the hexagram item is adjusted with the minimum number of steps between the end and the beginning points as the effective number of steps.Based on this, 16 potential plans were reviewed and verified. The situation is as follows:

48 hexagram items were confirmed in the early stage, of which 16 items "not overturn or change two positions" occupied 16 steps of dispatch, so the rating of sixteen hexagrams was reset. The number of dispatch steps is 48. The above 16 verifications show that the only 121st example meets the requirements. The 16 hexagram terms in the arrangement of this example correspond to the 16 sequence numbers. The sequence numbers in the hexagram theory layout are the correct explanation of the hexagram sequence of the common "Zhouyi". The review and verification situation also shows that the analysis method and analysis path of this article are accurate.

Personal version of the "Zhouyi" hexagram sequence

The above mathematical and symbolic deduction completes the accurate analysis from "Easy Square Chart" to hexagram sequence. This is a path-like deduction, which is strip-like. So is there a horizontal and comprehensive logic in the hexagram order? Or can the above-mentioned deduction elements form an organic and complete logic system? The answer is yes. In fact, the entire path of the deduction process was closed during the review and verification process. Further research shows that the basis of the hexagram sequence is the square of the square, the destination is the square of the square, and the core is the square of the square. The common "Book of Changes" hexagram order not only has the nature of "four directions and harmony" to the square of Yi, but also is the hub of "the thoroughfare of the nine states".

Fourteen sides of the world are in harmony. "Four-side Tongji" refers to the four magic squares with the hexagram sequence number as the data set, with the "Easy Square Chart" as the core, and jointly achieve a "one-to-four" full circulation system. One of the four magic squares is a composite magic square with a mid-abdomen transposed composite magic square, and the other is an ordinary eighth-level magic square, which has a unified orientation.

9th 9zhou thoroughfare. "Jiuzhou thoroughfare" refers to a "one to nine" full cycle system with the square of the Yi and the square of the Yi and the full hexagram as the source diagram. The formal logic of nine series of easy pictures:

, unified whole picture four parts, single-room flowers are heterogeneous, the whole picture of the change point is positively symmetric, and the phase is incorrect or inverted;

, the variation range of each group of easy pictures exists from The law of incremental circles inside and outside;

, nine-picture layout and group diagram relationship. The upper corner position is a pair of inner rings in the core (4 flowers), the horizontally flipped relationship between the two figures; the lower corner position is a pair of inner two rings in the range isomeric (16 flowers), the horizontally flipped relationship between the two figures; the left and right median , a pair of inner three ring range isomeric (36 flowers), two pictures transpose relationship; upper and lower median, single-frame flower isomeric (64 flowers), two pictures vertical flip relationship; the whole picture isomeric (64 flowers), the whole picture isomeric; the whole picture isomeric, upper median The mid-abdominal transposition pattern of the figure (64 flowers);

. Various types of pictures have unified orientation.

is a systematic "nine figures" that use the expression of adding variable points in the original square diagram, among which 36 flowers are phase-integrated translocations and the rest are phase-interferences.

Public version of "The Book of Changes" Key ideas briefly describe the key ideas of the hexagrams

In short, the four-character policy - approaching step by step. ⑴ Convert the 64 hexagram sorting problem to reset the 16 hexagram arrangement; ⑵ Reduce the 16 hexagrams to 4×4×4×2=512 rational auditions; ⑶ Compress the 512 rational auditions to 96 Necessary audition; ⑷ Select 16 potential plans from 96 necessary auditions; ⑸ Accurately identify and confirm the only positive solution from the 16 potential plans.

specific brief description:

. Interpret the order of the progressive position of the line, estimate the easy square, understand the easy square; understand the "hexagram-number" fit, understand the "hexagram-number-position-order" relationship.

. Based on the simple square, mathematical equilibrium as a means, we use the "three-axis magic square" to create a new layout architecture according to the "comprehensive and comprehensive latitude error".

. Restore the relationship between the square hexagrams and group matching, and the reasonable layout in the new layout. For the sixty-four hexagrams, most of them are still, partially adjust and partially reset strategies are adopted, and the magic square is transformed into a new pattern of hexagram couplet inlay and hexagram group pairing.

, "Use sequence instead of diagrams", compile the serial number trajectory for the new layout according to the "bone structure pattern". adopts the strategy of resetting the hexagram "to wait for the hexagram in order", so converts the 64 hexagram sorting problem into the resetting the 16 hexagram arrangement problem .

. Copy the existing hexagrams, orders, hexagram couplets, hexagram groups, relationships, distributions, and combinations, and make full use of known information to reduce the necessary arrangements for resetting the sixteen hexagrams to the minimum range to clear the clear Lu Ming.

. Using the principle of "one-to-many" and "full cycle", we select a potential solution to reset the sixteen hexagrams, and use the "June 4th Schedule" to identify the correct layout of reset the sixteen hexagrams to complete the "setting the hexagram into order".

7. Using the principle of "one to many" and "full cycle" as a means, examine the direct logical relationship between the hexagram order and the square of the square, and display it in the form of a series of easy diagrams.

To sum up, the general "Book of Changes" is bounded by the "bone structure fixed pattern" on a map originating from the square of Yi, the latitude and latitude of the meridians, the two-center three-axis, the hexagram inlay, and the hexagram group pairing. , implement a complete sixty-four hexagram system with rigorous logic formed by "two-ton coupling is either over or changing".

Appendix 1: Simple map of parsing points

Appendix 2: for Mr. Shen Youding Mathematical induction of "Yi"

Advanced chapter

public version "Zhouyi" hexagram sequence mathematical logic analysis focuses on resetting the implementation of the order numbers of each hexagram item in the sixteen hexagrams. The original analysis article explains that under the "16 serial number hexagram layout" specification, the "three pictures and two rings" audition and "June 4 dispatch" verification were obtained to obtain the only correct solution, and the "16 serial number hexagram layout" was used. The decisive role is to compress the number of large numbers into the necessary hundred cases.

original article "16 serial numbers hexagram theory layout": 16 serial numbers are arranged in the fourth-order square diagram according to their size, which is exactly the four hexagrams of the upper, lower, left and right; they naturally form two ways of error.

More in-depth research shows that there is also a ready-made "16 serial number hexagram layout", which is to directly use the established orientation of the preset 16 serial numbers to form a picture:

The same is true for this picture, this "16 serial number hexagram layout (2 )"The number of arrangements for resetting the sixteen hexagrams under " is also 512, and the number of necessary auditions is 168.

In order to clarify the explanation of the caliber, the implementation method of resetting the sixteen hexagrams arrangement in this article is similar to the original article. Initial arrangement: The four hexagram couplets of "Shi", "Qian", "Sheng" are subject to the "16 serial number, hexagram theory, layout (2)" are bound by each position, and the four hexagrams of "Shi", "Qian", "Qian", "Sheng" are in the hexagram Lead the couplet, and the upper left corner of the hexagram couplet.

variant order: the hexagram couplet is marked by the lead hexagram "shu", "qian", "renew" and "sup", and in the order clockwise, there are four steps; the hexagram couplet is based on the upper middle, upper outer, lower middle, and lower outer; In the order, the upper middle hexagram couplet begins. The arrangement of the variants is carried out by the sequential superposition method. The situation in the first unit (1-256) is explained as follows:

(1) initial arrangement; (2-4) superimpose the "Sheng" hexagram couplet in sequence and the three steps after the three steps of variation; (5- 8), (9-12), (13-16) Three steps after superimposing the "Fu" hexagram couplet; (17-32), (33-48), (49-64) After superimposing the "Qian" hexagram couplet Three-step variations; (65-128), (129-192), (193-256) Three-step variations after superimposing the "Shi" hexagram couplet.

second unit and so on.

two pictures of "16 serial number hexagrams" and two ring auditions are two independent systems. The layout (1) 16 potential schemes and layout (2) 20 potential schemes, "serial number - hexagram items" There is only one example that is completely consistent, namely No. 121 of the layout (1) and No. 161 of the layout (2). The 16-hexagram sequence number scheme is not only a common solution of the two audition systems, but also a regular solution to reset the sixteen hexagrams. The discovery and effective use of the second "16-serial number hexagram layout" above

above directly changed the method and path of number analysis, pushing the overall level of analysis to a new height.

. The dual system co-solving proves that the "three pictures and two rings" solves the problem of resetting the sixteen hexagrams with accurate methods and effective methods.

. The dual system unique solution directly obtains the conclusion of resetting the Sixteen hexagrams. The conclusion is more natural and irrefutable.

. The result of the dual system is generated first, indicating that the original "June 4th Arrangement" was not artificially defined, but resetting the internal logic of the hexagram sequence system that can be derived from the correct explanation of the sixteen hexagrams.

, each of the 512 variants of the dual system have been screened and investigated. The only common explanation proves that the order of the hexagram in the "Book of Changes" is the only composition of the "two-ton coupling or non-overlapping" bone structure that originates from Yiping Square.

Handbook "Zhouyi" is a complete hexagram system based on the innate and acquired patterns of the Zhouyi, suitable for "simplified compilation" and expressing the basic hexagram relationship, and "using sequence instead of diagrams". The text of " Yi Jing " is a Yao Ci for this set of hexagram system.