Model of stable conditions and developments of a system (states, parties, firms)

If the person knows, that he does not know, — learn he. If the person does not know, that he knows, — wake he. If the person knows, that he knows, — listen to he. If the person does not know, that he does not know, — escape from him.
In the article about the rarefied sets, I tried to reflect very little that will be, if probabilities of presence and absence of elements in some system have boundary (low and high) significances. In the same place I have assumed, that the system can have four stable conditions. And the Chinese popular wisdom has considerably helped me to understand with the given problem, on what I to you now and I shall tell.
Up to understanding of essence of processes which condition influences or this or that factor with some probability does not influence, I supposed, that the system can have three stable (in time) conditions (for example: «in the name of the father, the son and sacred spirit», «three sons was at the father», «three desires»). However with preparation of materials on the rarefied sets it became clear to me, that equilibrium conditions at a system should be four. What have I overlooked in the reasonings (or whom)? And the god who sends sacred spirit. And father at whom was three sons. And gin which grants three desires. So, there is a fourth stable condition of a system. For me that fact became amusing, that popular wisdom not only describes stable conditions of a system, but also and our behaviour for each of these conditions (look an epigraph), as some strategic planning.
For obvious understanding of a problem, I have drawn some figure, some kind of « magic quadrate Bobrovnikova ». On it the rectangle broken on four equal parts (component quadrates) is represented, each of which describes one of stable conditions of an arbitrary system. The parties of my rectangle intersected under a right angle are probability scales of realization and not realization of the script of development, a membership of an element, influence of the factor and to that similar, depending on researched object.
three scripts of development of systemLet's conduct the analysis of the diagram submitted in figure, by the example of an epigraph to this article. And at the same time also we shall consider possible three scripts of development of a system, both aside progressions, and aside regressions (arrows 1, 2, 3).
So, « the person knows, that he knows ». That is, the probability of comprehension of that fact, that low probability of absence of knowledge (YES-YES is great; KNOWLEDGE OF KNOWLEDGE). Sufficient for translational development a condition of a system at which the greatest well-being and prosperity of the majority of its elements (a green small square) is observed. It is confirmed and planned behaviour — «listen to he, and you will live also well, as well as he». And differently, what for at him to study? An example from area of management. If we know, that one thousand screws will be twisted, if there is an order to twirl one thousand screws and how such performing discipline such condition of any company and corporation can be characterized as satisfactory and progressive as the development of the company is possible to plan very precisely is reached.
The following case if « the person does not know, that he knows ». That is low probability of understanding of that fact, that low probability of absence of knowledge. The knowledge is present, but it is not used in complete force. Hence, it is necessary «to wake» knowledge to life to improve life (a blue small square — NO-YES; IGNORANCE ABOUT KNOWLEDGE). As applied problems of management in a situation with screws the following is received — we do not have knowledge of how the order will be precisely executed to twirl one thousand screws (absence of effective administration managerial control). In this case it is important to understand, that the company is controlled in technological sense, but thus we know nothing about how it is reached. Hence, it is necessary to make use expert experience which will help us to understand, how our company copes, and as it to use for the good (to wake). Situation not too bad though hides in itself dangers, as, not knowing as we have organized management, we can disorganize all control system of our company (state). And also at the further development we cannot make use completely our successful performing experience of management.
«If the person knows, that he does not know» That is, the probability of understanding is high, that the knowledge is absent (high probability of absence of knowledge) learn he. This acceptance of that fact that it is necessary to develop strenuously self-organizing of a system (a yellow small square — YES-NO; KNOWLEDGE OF IGNORANCE). There is a real need to learn to cope and live well for we recognize, that affairs at us go at random. All is not too bad and from the point of view of management. We understand with all evidence what operate our company we cannot. We do not know, that will happen, if the order will be given will screw up one thousand screws, perhaps, instead of screws to be screwed up nuts. Hence, it is necessary to learn to operate the company in technological sense, will learn to plan production. For crash of our enterprise hereinafter can follow.
At last a gloomy grey small square at the very bottom, a condition of a system at which very much it would be desirable to escape. « If the person does not know, that he does not know » (NO-NO; IGNORANCE ABOUT IGNORANCE). It already probably occurred crash of a system. These are revolutions and shocks, it is change of an authority and anarchy. It is distemper. Well if is where to run (for example: for ocean). And if there is no place? There are only two possible outputs from crisis, or the system starts to collapse (is destroyed) or to revive, but already in the other qualitative condition (to regenerate). And actually, the states apparent by an eternal stronghold break up, dictators come to power, fires of inquisition blaze, archipelagoes Gulag are under construction. The manager does not know and at all does not assume (or incorrectly assumes) that will happen if will return the order to screw up one thousand screws. « Go there, I do not know where. Bring that, I do not know that » — only in a fairy tale this problem can have acceptable and good solution. Imagine the company which not only is unguided, but its management at all does not know about it. The situation is extremely dangerous both to it, and for those who tries to cooperate to it for its behaviour is absolutely unpredictable. And popular wisdom learns «to run» at such state of affairs. 
The big happiness was for Russia, that within the hardest tests country was headed by the genius and unshakable commander Stalin (U.Churchill)
Known a policy I have reduced expression not casually. From my diagram logically follows, that in a condition of a crisis situation (a grey small square) if not crash of a system as such should appear (to be generated) a certain force which will supply movement of a system in a direction of a green small square is possible. It is confirmed by remarkable articles Lev N. Gumilev from a series «the Ethnoorb and passionarity » in which it is proved, that in complicated historical periods in any human community always there is the certain political movement headed by its chief and providing development of company in a progressive direction.
Three outcomes (arrows 1, 2, 3) for revival of a system (the state, the enterprise) are possible: through self-knowledge (development of own knowledge — ignorance about knowledge), through tutoring (import knowledge — knowledge of ignorance) and passing intermediate conditions, directly to the light future (tunnel effect — knowledge of knowledge). Similar reasonings remind national fairy tales when the main hero should choose three paths, thus he always something risks to lose. And always the fastest path of reaching of the purpose, it the most dangerous, and circumscribed as « road which goes directly ». It is impossible to assert univalently which of directions of development is the best. All of them are not deprived defects and acceptable only in strictly certain conditions. I have reduced the reference to fantastic characters not simply so. We, people, intuitively have the given knowledge, but only they are not hardly formalized to the full to use them in practice.
Let's talk about screws. There is a path of development 1, through tutoring of the company to screw up one thousand screws if there is such order. It is possible, when the administration accepts that fact, that in the company there is no efficient control engineering procedures which is possible for acquiring as external knowledge. And actually it means tutoring a performing level of an authority to exact performance of orders and orders of managers. Delay of time of realization of similar plans results in devaluation of the managing staff and destruction of the upper echelons of management as corollaries of outflow of the staff in a technological orb.
The following path of development (2) passes through comprehension of that fact, that « so further to live it is impossible » though the performing level of an authority works rather effectively. Hence, it is necessary to acquire knowledge of how to generate such direction of development at which orders on screwing up thousand screws (which will be correctly returned will be screwed up). In this case also it is impossible to delay terms as already technological level of management by virtue of incompetent commands will collapse.
The most favourable and expensive path is directly to the light future (3). A complicated solution as it is necessary to change not only technological component managerial processes, but also understanding of how it is done (administration managerial control). High expenditures of labour at all levels of management will be necessary and the managing centre should be formed highly to supply exact performance of the order on screwing up thousand screws and as such order correctly to generate.
It is necessary to understand, that each of the submitted possible directions of development at all has no such smooth structure as I have drawn. They have discrete structure. For each plot there is a certain directedness and length of distance from one point up to other (some kind of a vector). The distance, in this case, can be considered as magnitude proportional to certain resources (for example: to money) which are necessary for expending for transition in our probability space. There is one more measurement which is not present on my diagram. This time. Yes, to move from one point in other the certain resources and time are required.
Here the principle of indeterminacy which is circumscribed by me in one of articles starts to work. It is formulated as follows — product of a resource for a while always more or is equal the certain magnitude. Actually it means, that in probability space the outcome is not always predicted. However that it to reach for the certain time in any case it is necessary to expend the certain resources (for fulfilment of the indicated inequality).
Our system would be desirable to change the condition aside a green small square for the certain time. For this purpose we are compelled to spend some of resources according to the indicated equation. But in practice it is become clear, that it was required from us to time more, than we planned. And if we have planned sequential actions (the following one after another)? And if even one of line-ups is infringed, all our gains in outcome on all paths of development can appear vain. So affairs go at random.
If we can mathematical evaluate a position of our enterprise on the basis of an offered technique accordingly we can plan and behaviour of our system in probability space. Application of the similar tool if a horizontal axis to present by the way a certain scale of efficiency of administration managerial control, and horizontal — by the way scales of technological backwardness can be more interesting. Accordingly, planning transition in a direction of a green small square and comparing the obtained outcome, it is possible to judge progress (recourse) of the human community entrusted to us.

Together with system or scientific fortunetelling

This story was told to me by one of my acquaintances long time ago. It touched my soul so deeply that I have remembered it for years. Moreover, this story had strongly changed my outlook. This is what I am going to tell you about right now. Let me begin with the story itself. It happened in the times of the Soviet Empire. Though I cannot tell you the name of my acquaintance and what train crash could have happened and when, I can tell you for sure that this is a true story. So, let me present to your attention a play in three acts with epilogue and prologue. 
Prologue and Background
In some sense the trip could decide the fate of my acquaintance. It was supposed to be a long railway trip. As usual, my acquaintance arrived at the station far before the train’s departure, made himself comfortable in the compartment and started to read a newspaper. “Then suddenly my stomach gurgled and a nightmare began – I felt terrible gripes”. As you surely know, the lavatory in Soviet trains was closed at stops. What should he do? His neighbor advised him to visit the lavatory at the station, as there were still fifteen minutes left before the departure. “Can you imagine, I felt so bad that I had to use his advice”. Though he assured me that he had had aches in his stomach before, still he had never felt so bad. “Then my watch stopped as ill lick would have it. I noticed it only at the platform. You know, a second-hand in my watch was so thin that I had never paid attention to it. Looking at my watch I was happy at having so much time left before the departure.” When my friend came back to the platform, his nightmare went on – the train had already left with the luggage and all the documents. “It was the moment when I noticed my watch stop. I got so angry that I smashed them into pieces, though it was my good friend’s present”. Then he surely turned for help to the railway administration and police. But there was nothing they could do unless running after the train. “The most interesting thing is that the pain disappeared immediately after I saw that the train had left. Later I thought that it had happened because of fear.” Upset, my friend had to come back home to make his trip next time. “My hair rose when I learned that there had been a terrible train crash and no one from my van survived. Then I thought that I would have placed the watch, which was already in the dump, under the icons if I could find it”. From that very moment on my friend became a very faithful person and his life really changed for the better. 
Act 1 or General Reasonings
“Mysticism” was my first thought, while some people would suppose it was a good luck. Is it a fate or is there anything more about that? To analyze this story I applied my experience in system analysis (a system approach to things and events). Finally I came to the conclusion that everything has its reason.
Of course, from the point of view of an ordinary observer, it was just a coincidence, a very lucky chance, which saved the life of my friend. But let us imagine a ball rolling down the gutter. With a certain probability we can foresee the ball’s position in the near future – where it will be and when; applying a simple formula from the course of general physics we can guess the moment when it falls down from the gutter. The main conclusion from this experiment is that both the ball and the gutter compose a mutual system, isolated in a sense.
Using the same line of reasoning like in the physical experiment, we come to the conclusion that my friend did not belong to the system of the crashed train, but he played a certain role in another system where he was not supposed to perish (as his system was far more stable).
Now let us imagine that we can predict the fate of any system and we can choose what system to belong to. Thus, we can control our future in a sense. If my friend had known what would have happened he would have put a monument to his watch.
So, the main conclusion we can draw from this story is that we are all screws, constituent parts of a system functioning and developing according to its own rules. Thus, being aware of all the secrets of our system, we can predict the future. And the influence of the system as well as our influence on the system can be of different kinds (physical, chemical, biological, etc.). 
Act 2 or Drawing Schemes
hypothetical ratio between arbitrary systemsThe scheme demonstrates a hypothetical ratio between arbitrary systems. The intersection of their boundaries is just my supposition. One should consider that the boundaries may not intersect but at the same time the systems may interact, and that the boundaries may be of any kind (geographic, demographic, financial, and political).
The scheme shows that if an object under analysis is located in the intersection area, it is attracted by the centers of several systems, though it belongs just to one of them. Belonging to one system is just a temporary factor, which depends on any influence redistribution among the systems. Thus, in the near future the object can be expected to move to another system.
By analogy, the same happened to my friend: he did not enter the system of the train, though the attraction was very strong (he had to make his trip by train). Obviously, he was used (or attracted) by another system, so he was not to leave by that train. 
It is well-known that systems can apply various means of influence to cooperate with their elements. It can be physical, physiological as well as any other type of influence. For example, previously I had serious doubts regarding the fact that icons could help win battles (that was quite often in the Ancient Russia). However, now I have changed my view on this problem. There can be no trifles in the life of system and its elements, so an icon in the battlefield could strengthen the impact of center (the faith) on the final elements (the soldiers), that raised the morale of the army and finally lead to victory.  
Act 3 or Predicting System’s Condition

the simplest time system
A ball rolling down the gutter is the simplest system. We can predict its position at any moment in the future, as we obtain all the information on the considered phenomenon. Now let us imagine a break in the gutter the ball can fall down through. For a system where the ball is supposed to constantly roll down, such break can be a disaster especially if the ball is flimsy (made of thin glass, for example), as it can fall into pieces. So, we have just predicted the ball’s crash (an important event) with a high probability.
In reality we all belong to some systems, which lead us to falls, rises or something else. In order to foresee the future we just have to see the whole of a system (systems) we cooperate with now or will cooperate with in the future and the way this system (systems) is (are) likely to function in the future. You may say that it is almost a mystery. But in fact, to be able to see and guess the consequences of some events, it is enough to be a good observer and analytic.
To my opinion, a phenomenon of famous foretellers does not exist, but there are just gifted people able to see the general course of things and to predict its future behavior. If a gipsy fortuneteller has such a gift, you can rely on her without any doubt. Various attributes of fortunetelling like playing-cards or stars are just means of building correlative patterns of our system on the time axis. And the more accurate the correspondence between the system’s behavior scale (here a ruler and a set square) and the physical system (the ball and the gutter), the more precise the fortunetelling.
So, is it possible to control the future? It is you to decide, as some things are actually under our control, but others are not. It depends on the strength of the system’s influence and on how we can control the latter. Imagine, that you have foreseen that your system is near to a catastrophe, so why don’t you move to another system (see the scheme above)? If you feel that a plain is likely to crash, then maybe you should better stay at the airport (or not go to work or to your friends’ home). If we set a magnet near the break in the gutter, the ball will get magnetized and will not fall into pieces. 
Epilogue or Ode to Rarefied Sets
Now let us discuss the foretelling with the help of scientific approach. Here we will apply the notion of probability (its Majesty the probability). 
possible variant consisting of two systemsThe picture represents a possible variant consisting of two systems, one of them supposed to be more preferable (perfect career, good health or saving life, etc.). The picture shows that we are being influenced by various systems. Thus, we have to estimate the development trends of these systems as well as the probability of our presence in any of them.
We cannot determine strict boundaries between the fields, so each field is probabilistic. At the same time we can estimate the risk of our belonging to any system and, what is more important, we can guess the probability of our participation in some event. Everything here depends on the precise description of both the system and its development, as well as on the observer’s abilities, the means he uses, and on whether the development pattern of the considered phenomenon corresponds to reality. (Indeed, in physics experiments on correspondence of mathematic patterns to real physical processes play a very important role).
I have divided these probabilities (probability of belonging and probability of participation) intentionally. Actually, the factors determining our position relative to systems “A” and “B”, are quite different. This is the essence of rarified sets, which are widely represented in one of my articles. The mathematical machine, that I proposed, helps analyze our position relative to quite different systems at the level of probabilistic descriptions. This is the method the fortunetellers apply, as they just need a probabilistic means somehow correlated with our fate (!). Further they just have to predict which events you will participate in and which not. However, this process requires detached substances (“queens”, “aces”, “kings” and other cards correspond to certain patterns of behavior — love, health, traveling, etc.). The preciseness of correlation between the cards sequence (stars arrangement) and our experience (character, problem) depends on the degree of competence of the observer (the fortuneteller).
Any system we deal with always (!) sends us some signals of this or that form. My personal experience proves the idea, and I am convinced that you can also draw certain situations from your life when a system sent you alarm signals and you just neglected them and got into trouble. My pictures also illustrate a certain power that influences us, which means that we can feel it. The latter proves the idea that we can predict our own future. To do that we just have to see the essence of systems and feel their influence (like Nostradamus). We can also try to describe our future through some mathematical patterns. Anyways, we are likely to get one and the same result — “together with system”, which means that one should not swim up-stream, but he should gain profit from any situation so that being in any system he could choose the best position both inside this system and relative to other systems.