The work shows that the system of the Book of Changes is a timelike system. On this basis, the optimal square placement, flows of changes, and the structure of the system were determined. It is also shown that in this form the system of the Book of Changes is a model of nature that reveals cause-and-effect relationships, spaced in time.
Introduction
“All people by nature strive for knowledge. And the most worthy of cognition are the origins and causes, because through them and on their basis everything else is cognized, and not they through what is subordinate to them. With these words, Aristotle opens his works. It is also convincingly shown that the starting point of cognition of the most common in nature, the principles of nature, is their definition with the help of concepts that are opposite to each other in meaning. Thus, even in ancient times it was established that the language of opposites is a universal language for describing the principles of nature. However, even earlier, in the history of mankind, this method was intuitively applied in practice. At the same time, history has identified two opposite approaches along the way. The first approach is related to European civilization,where polar (annihilating each other in interaction) opposites were taken as a basis. The second approach was adopted and developed in the East, where opposites complementary to each other were taken as a basis in defining the whole.
The beginnings that were formulated in this way correspond to the principle of complementarity. Relatively recently, all this was confirmed in mathematics in the theory of semigroups, where it was shown that these two approaches are, on the one hand, the only possible ones and, on the other hand, completely independent.
Under the influence of this choice, two cultures, two philosophies, two systems of representing nature have developed in history. We will not discuss what is known as the European system. We will be interested in the presentation system developed in the East. The presentation of this system in its most complete and complete form is carried out in the Chinese Book of Changes, which has accumulated the work of many generations in the past to create and perfect this system.
General characteristics of the system of the Book of Changes
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Let us recall that in the Book of Changes, nature was originally designated as a whole and called the Great Limit. The starting point here is the division of the Great Reach into two complementary concepts of yin and yang. Further, this simple principle of opposing complementary concepts develops to a universal system for representing reality.
This is done as follows. By successive splitting, smaller complementary parts are formed, which leads to eight symbols - trigrams, then these symbols are placed one above the other in pairs, which makes it possible to obtain sixty-four hexagrams. Hexagrams are independent and independent entities; a certain generalized content is attributed to them, and so that they completely cover the surrounding reality. Thus, a system has been created in which each hexagram in a real situation corresponds to an event. Reality in this system is defined through a multitude of states participating in the continuous process of transformation to new states, that is, it is defined as a stream of changes or a stream of events.
Such a system as a model reproduces well-observed cause-and-effect relationships, interactions in nature, as a result of which one event after a certain time causes another event. If we try to note the most general properties of this model, then this model is asymmetric and focused on the property of the direction of time, that is, in essence it is a qualitative model. The arrow of time plays a leading role here. Time in this system is irreversible. But, perhaps, the main thing that is reflected in the model is the cycles of change that exist everywhere in nature. Another important property that is reflected in the model is the fundamentally probabilistic nature of the transition from one state to another.
However, at present, many of the properties of the model are still out of reach. There is no understanding of the main thing: the connection of hexagrams has not been traced. This is explained by the fact that, despite numerous attempts, it has not yet been possible to understand the structure of this system. This work pursues exactly this goal, and today it can certainly be done, relying on the theory of time-like systems, developed in.
The Book of Changes system as a timelike system
By the totality of the properties listed above, the system of the Book of Changes is nothing more and nothing less than the most ancient example of a timelike system. There are several grounds for this statement, but the main one is that the system uses an asymmetric beginning, when the whole precedes the part, the general precedes the particular.
For hexagrams, ordering relations are introduced in the system, reflecting the dynamics of opposites, which is also consistent with the theory. These relations are defined in the system in the simplest way, as the neighborhood relations of hexagrams. If we use the generally accepted numbers - numbers of hexagrams, then this can be written as a division of sixty-four hexagrams into pairs (1,2), (3,4),…. (63.64). The structure (hierarchy) of hexagrams described above and the relationship of hexagrams is what forms the backbone of the system of the Book of Changes, considered as a time-like system.
Movement and transformation in the process of movement are the basis for the functioning of the system of the Book of Changes. With regard to its structure, movement is the interaction and movement of the lines of graphic symbols of the hexagrams of the system.
In the theory of the timelike approach, a logical model of motion is used, which defines it as a certain algorithm [see. 4 p.5.3]. This algorithm assumes the definition of local maxima and minima by logical means, connected with each other according to certain rules, which is equivalent to sorting simplices - abstract components of the object of motion. This algorithm will be applied to transform the graphic symbols of the Book of Changes system. It turns out that with its help it is possible to eliminate inaccuracies in the information at our disposal on the structure of the system, and to determine the flows of change, which gives an answer to almost all questions about the structure of this system.
First, we give a motion algorithm for the case of trigrams, i.e. for the case of space quantized into three levels. The corresponding circuit is shown in Fig. 1.
Figure: 1. Transformation of trigrams.
For convenience, delays have been introduced into the scheme, which allow dividing the execution of the algorithm into conditional stages following each other. It is considered that the amount of delay is equal to the duration of the conversion in the logic circuits. For this scheme, we have, therefore, four stages (from a to d) of the transformation when moving from the input to the output.
In a trigram, the transformation of which is supposed to be traced, the broken lines are replaced, for example, by ones, and the continuous ones by zeros. We will call this coding method the main one. If broken lines are replaced by zeros and continuous ones, then this is an additional way of encoding. Now you can follow the stages of what happens to the trigram when moving.
The transformation process consists in the analysis of pairs of trigram lines located next to each other, and, depending on the direction of movement, either everything remains unchanged, or the lines are swapped if the pair contains lines of different types. When using the main coding method, discontinuous lines are sequentially promoted to lower levels, and continuous lines to higher levels, with an additional one - vice versa. This leads to the fact that in the process of transformation there is a sequence of trigrams following each other.
If a trigram is composed of lines of the same type, then it does not change with any coding method (qian and kun trigrams). We will call them basic. The trigrams Zhen, Gen, Xun and Dui remain unchanged in one of the encoding methods, and change in the other. Trigrams cani and li in all cases are transformed into other trigrams.
Let us now consider the square arrangement of hexagrams. From the primary sources that have come down to us, three options for such an arrangement are known. Ancient Chinese texts also testify that their diversity is exhausted by this. This location is according to Fu-si, according to Wen-wang and according to the Mawandu text, all of which are shown in the upper part of Fig. 2. Under them, in the same squares, lines are shown connecting adjacent hexagrams from each two, paired with respect to the order.
Figure: 2. Variants of the location of hexagrams.
The fact that there are several square arrangements of hexagrams suggests that the creators of the system were not completely satisfied with any of them. So in the arrangement according to Fu-hsi, the hierarchy of hexagrams is indicated by polar placement at the corners of the square of the main hexagrams (hexagrams 1 and 2, 11 and 12). In the arrangement according to Fu-hsi there is a certain system in the arrangement of pairs of hexagrams connected by the relation of order. It shows a diagonal cross, symmetry, but still it is complicated. In the arrangement according to Wen-wang, the maximum simplification is achieved in the image of pairs of hexagrams connected by the order relation, but the hierarchy of hexagrams is lost. In the arrangement according to the Mawandu text, an attempt is made to depict the hierarchy of hexagrams by dividing the square into upper and lower halves, but no system in the arrangement of pairs of hexagrams is visible. Thus, only the placement according to Fu-si is quite complete from the point of view of reflecting the properties of the system, however, it turns out that much is not taken into account in it.
So, there are two basic trigrams: qian and kun. We will only use the basic coding method. Excitation is introduced into them by replacing one of the lines of the trigram with the opposite line. Then, within the framework of the qian trigram, the most unstable trigram (generating the longest sequence of trigrams when moving) will be the dui trigram. Similarly, for a kun trigram, it will be a zhen trigram.
Taking this into account, it is possible to determine two for each basic trigrams, and only four linear sequences of trigrams differing in the direction of propagation of excitation, Fig. 1 (right side). In the figure, the direction of propagation of excitation is shown by an arrow going from the most unstable excited trigram to the stable excited trigram. This arrow is shown directly above the linear sequence.
Figure: 3. Groups of hexagrams.
We use the obtained linear sequences of trigrams in pairs and without repetitions to form hexagrams. The linear sequence, the trigrams of which are used as the upper trigram of the hexagram, will be placed vertically, the linear sequence, the trigrams of which are used as the lower trigram of the hexagram, will be placed horizontally. Then we have four groups of sixteen hexagrams, shown in Fig. 3.
Figure: 4. Transformation of hexagrams.
A hexagram formed from basic trigrams gives a name to the group. Let's list them: this is creativity, this is performance, this is flowering and this is decline. Each group unites hexagrams related in composition, and the basic hexagram of the group is its kind of pole. The figure also shows the arrows for the directions of excitation. It is clearly seen that these are four mutually exclusive options, consonant with the names of groups of hexagrams.
Consider the hexagrams of groups from the point of view of their stability and variability during movement. The scheme of the movement algorithm for hexagrams is built according to the same principle as the scheme for trigrams, but the number of levels must be increased to six. We will assume that two types of movement are possible for them: when the interrupted line moves from top to bottom and when the interrupted line moves from bottom to top (naturally, the solid line moves in the opposite direction).
Figure: 5. System of hexagrams (Model of the World).
This can be achieved in different ways, for example, if you apply either the main or the additional coding method, Fig. 4. Then we get that the basic hexagrams 1 and 2, as system-forming ones, are not subject to changes in any direction of movement. Hexagrams 43.44 and 23.24, base hexagram 11 and hexagram 34.19, as well as base hexagram 12 and hexagram 20.33 are not subject to changes in one of the directions of movement and change in the other. This is their important feature. Hexagrams with the indicated property are, as it were, concentrated at the poles of the groups. All other hexagrams of groups change both in one and in the other direction of movement.
The received groups are connected to the system. The order of connection is determined by the process of the passage of time that is uniform for all groups, which sets the directions of propagation of excitation. Let us consider according to the European tradition that the passage of time occurs in the direction from left to right, then the four groups of hexagrams Creativity, Fulfillment, Prosperity, Decline unite together as shown in Fig. 5.
Figure: 6. Pairs of hexagrams and trajectories of flows of changes.
The new placement is an arrangement with four poles: the upper is creativity, the lower is performance, the left is flowering, and the right is decline. The diagram of lines connecting the hexagrams connected by the order relation for the new system is shown in the center of Fig. 6.
The line pattern is arranged in the horizontal direction of time, i.e. agreed with him. Thus, in the system with the new square arrangement of hexagrams, along with the display of the hierarchy, a time-ordered scheme of lines is realized.
Let us set ourselves the goal of somehow more visually presenting the placement of pairs of hexagrams than is achieved in the line diagram. This can be done in different ways, but the most clear and simple method is based on two looped closed curves shown in the upper left of Fig. 6. Only those hexagrams are located on these curves, which are paired to each other. This figure is interesting because it was, apparently, invented in those distant times, when the “Book of Changes” system was created. Another method is shown at the top of the same figure on the right.
Another fundamental feature of the new location is the ability to observe the flow of change. Before we trace this, let us recall at least some of the known explanations of this term. “The situations reflected in the“I Ching”are taken directly from life - this is what happens to everyone from day to day and is clear to everyone … the gateway to the system can only be simplicity and clarity. … All of us from birth are in a single stream of development, but recognizing it and following it presupposes responsibility and free choice”.
So, changes are of two types: natural, associated with the nature of things, conditioned by the laws of nature, and spontaneous, conditioned by the choice of man, but still obeying the laws of nature. Recall that in any case, the transition from one state to another occurs with a certain probability. We'll start by discussing natural change.
The algorithm used (Fig. 4) determines all natural streams of change. To do this, it is enough to trace, using the motion algorithm for each hexagram, its transformation into other hexagrams when moving both in one (main coding) and in another (additional coding) direction of movement. We have the following two pairs of linear sequences common to all groups of hexagrams:
34-5-38-37-6-33 19-36-40-39-35-20
33-6-37-38-5-34 20-35-39-40-36-19.
For the groups of hexagrams “prosperity” and “decline” we have one common pair of linear sequences:
11-54-63-64-53-12
12-53-64-63-54-11.
Below we give separately the corresponding linear sequences by groups of hexagrams. For the group of hexagrams “creativity” we have:
61-37 30-57-6 28-50-57 44-13-10-9-14-43
61-38 30-58-5 28-49-58 43-14-9-10-13-44.
For the group of hexagrams "execution" we have:
62-39 29-52-35 27-4-52 23-8-16-15-7-24
62-40 29-51-36 27-3-51 24-7-15-16-8-23.
For the group of hexagrams “flowering” we obtain the following linear sequences:
18-64 22-64 48-64 41-22 32-48 26-38 46-40
18-63 22-60-54 48-55-54 41-60 32-55 26-5 46-36.
And, finally, for the group of hexagrams "decline" we get:
17-64 21-59-53 47-56-53 42-59 31-56 25-6 45-35
17-63 21-63 47-63 42-21 31-47 25-37 45-39.
Sequences of hexagrams are shown in pairs. The upper sequence is formed when moving from left to right (main coding), and the lower one when moving in the opposite (additional coding) direction.
Natural streams of change form peculiar but simple trajectories of movement. In most cases, these are cycles of change, but not always. For cycles of change, there are two opposite points that set limits. Limit points are hexagrams near the poles, discussed above (Fig. 3). Some of the trajectories are shown in Fig. 6 at its bottom. On the left are shown partially the trajectories common for all groups of hexagrams and trajectories for the group of hexagrams "creativity". On the right - the trajectories for the group of hexagrams "decline". Analysis shows that for trajectories there are diagonal symmetries about both the vertical and horizontal diagonal. Linear sequences arranged symmetrically form a pair of related linear sequences.
As for spontaneous changes, they are most likely chaotic, make sense of jumping from one trajectory to another, and should occur more rarely. Spontaneous changes are, of course, an important part of the formation of a stream of changes, since, for example, hexagrams 61, 26 or 42 can generally only be passed in this way.
A natural question arises: "Isn't this a new reading of the system, distorting the original meaning and how adequate is the new square arrangement to what is already known about the system of the Book of Changes?" No, it is not and, at the same time, it is more adequate to the system than the well-known square arrangements.
Let's give an example. In the division of sixty-four hexagrams into pairs, we will choose, for example, odd hexagrams and we will turn over their graphic image. It turns out that such a transformation transforms the graphic image of an odd hexagram into a graphic image of an even hexagram, which is a pair to the first one. Thus, the hexagrams in a pair are inverted in relation to each other. An exception to this rule are pairs of hexagrams with numbers (1,2), (27,28), (29,30), (61,62). Here, when turned over, the selected hexagram passes into itself. This fact had no explanation. Now it is crystal clear. Flip in terms of square placement in fig. 5, there is movement in the horizontal direction (for example, 13-> 14, 10-> 9, etc.). Exceptional hexagramsare located along the vertical of the new square arrangement and are by turning, that is, by moving in a horizontal direction, in pairs towards themselves.
At the same time, in these pairs (1,2), (27,28), (29,30), (61,62), another communication method is observed, combining them in the vertical direction. To pass in a pair from the first to the second hexagram, it is necessary to carry out the inversion of the lines, replace the solid line with a dashed one and vice versa. Thus, the new square arrangement not only corresponds to the graphic outlines of hexagrams, but also allows us to formulate the law of transformation of graphic images of hexagrams in pairs (1,2), (27,28), (29,30), (61,62).
Figure: 7. The order of using trigrams in a hexagram.
Moreover, in the process of forming a new square arrangement, in essence, the general law of the formation of graphical images of hexagrams was found. This law consists in the fact that excitement is introduced into the hexagrams adjacent to the base one, and then it begins to spread when passing to the next neighboring hexagrams in this arrangement, which makes it possible to determine their graphic outline.
Another general question: "Was the new square arrangement known to the creators of the Book of Changes system?" We are convinced that the square placement of hexagrams originally existed in this form, but the story announced not the final, but intermediate placement options.
Only very simple and clear construction ideas could be used by the creators of the system and the new square arrangement allows them to be seen. Let's go back to the graphical representation of the hexagram. The trigram, which is part of the hexagram, can be either at the top or at the bottom of the graphical image of the hexagram. Let's take a new square arrangement, in which, as before, each sub-square corresponds to a certain hexagram, Fig. 7. From each trigram, draw a line through those sub-squares where it is used in the graphic image of the hexagram corresponding to the sub-square. We will draw a line along the bottom of the sub-square, if the trigram is at the bottom of the graphic image, and along the top, if the trigram is at the top. As a result, we have an extremely simple construction order, shown in the figure,in which the bottom and top are regularly interchanged and symmetry is strictly maintained.
The Book of Changes system as a model of nature
The significance of the Book of Changes system goes far beyond the divinatory system. Following the Newtonian model, this is the second global model of nature. The second model reflects the action of causal relationships spaced apart in time in nature, due to its asymmetry. Nature in this model appears as an ensemble of processes of continuous, incessant transformation, movement from one state to another state.
This model shows that in this case, existence in nature obeys the law of cyclical changes, regardless of whether it is an individual event or the whole of nature as a whole. Built in time, this model assumes a periodic alternation of the processes of development and decline, that is, a periodic repetition of the moments of birth, expansion, contraction and contraction to the point of singularity.
Modern science, through the efforts of quantum theory and the theory of relativity, is still paving the way for this model.
Conclusion
The new theory of motion, applied to the system of the Book of Changes, made it possible to understand its structure.
This theory showed that the Book of Changes should be put in one of the first places among the universal human values. This also means that the use of the opportunities inherent in the system of the Book of Changes is most likely just beginning in practice.
Practical use. - And it is also now clear that when fortune-telling you need to use more than one randomly obtained hexagram, but it is necessary (and now you can) look at the most probable path of development from the current hexagram into the future.
Khanjyan O. A., Khanjyan A. O.