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.

Rarefied sets

Here I would like to draw your attention to the idea of independence of two possibilities: whether an element belongs to a certain set or not. This idea occurred to me while trying to understand the nature of our dreams. Walking straight by the road you will face certain events and environment, while if you walk in the opposite direction, events and environment – everything will be quite different from what you have seen before. So, the two roads (straight and back) in your dreams are a kind of an asymmetric world represented to us as increased and dynamic.
 
On the one hand, if we try to analyze whether an element possibly belongs to a certain multitude we will apply specific notions. While on the other, if we try to prove that the element does not belong to this multitude we are likely to use other indexes.
 
Certainly, all the analyzed factors have much in common. However, this interrelation is rather complicated and implicit. (Let us suppose that they are multifractals, and that we need to establish the interrelation between their primings, which we do not know). The trick is that at a subconscious level we are able to connect, apparently untied factors, while at a conscious level we have not yet learned to do that.
 
For this case we have a dream machine. So, I have chosen the way of dream formation – having broken the connection between what can be with something that cannot be. Let me draw an example with dreams. Imagine, that today you have seen a beautiful building, which has seized your attention. Accordingly, it is highly possible that today in your night dream you will see some constructions. In the evening, watching news on TV, you see unpleasant staff of some international conflict. So, the possibility of seeing constructions in your dream still remains, while the possibility of not seeing them arises, as in your dream you may experience some kind of violence, etc. As a result, if moving straight in your dream you will come across some buildings, but try walking back and you will meet the war. Does not it remind you a compromise between our view of the world and our representation of the world?
 
Further on, trying to find the message of our dreams, I found out that we deal with interpretation of our problems in dreams in some aspects, which we had not noticed before when being awake. These aspects, however, are able to influence decision-making on certain problems. Is it worth moving straight if you will never get back. Then I tried to find linkage between my vision of the world in dreams and mathematics, and consequently between the notion of problem and some mathematical instrument.         
 
It is not a secret that I am an admirer of mathematical machine of indistinct sets (fuzzy logic). Naturally, I either apply or plan to apply this instrument in all my projects. However, I often come across the problems of presence and absence of element in certain sets (actually the road back). Certainly you may assume that having calculated the probability of presence of element in the set I can easily estimate the probability of its absence in the set. Here that I supposed that these two probabilities may be absolutely different and have nothing in common. Moreover, the presence of element in the set and its absence get interrelated if we apply the same factors for analysis. While, actually it is just theory, and in practice factors influencing the presence or absence of element in a set are quite different.
 
Thus, the rarefied set can be described as follows: {e1(p1,z1),e2(p2,z2),e3(p3,z3)...en(pn,zn)} (the rarefied set), with “p” as probability of presence of “e” element in the set, and “z” as probability of its absence. I suppose, that the notion of «problem» can be well described with the help of such mathematical means. Link with concept of a problemFor this purpose let us analyze the following diagram.
 
The diagram shows the variations of uncertainty degree of analyzed sets according to the transition between the following notions: “problem — purpose — task”. One degree of probability disappears with each notion starting with the notion of problem! When analyzing problems we should consider the probabilities of fulfillment and non-fulfillment, while when analyzing purposes and tasks we should consider probability of achievement and a set of measures respectively. 
 
The notion of risk is another idea, which requires some judgment. So I am not able to make any statements on this matter yet. However, I suppose that risk is somehow related to the probabilities of presence and absence of an element in a set.
 
The next step in development of idea should be the creation of some tool permitting to apply the idea in practice (something like Gant’s diagrams). The diagram includes the following marks: “M” as a set describing this or that notion, “e” as an element of a set (the factor under analysis), “p” as probability of presence of element in the set, “z” as probability of its absence in the set (here “p” and “z” are independent figures). In case with “PROBLEM” notion we deal with a rarefied set, where the two probabilities of presence and absence do not depend on each other. I think that mathematical means of complex figures could be applied here. However, it is just my supposition.
 
Let me draw another example fro the military field. Various factors influence probability of presence and absence of enemy forces in some specific place. For example, their presence is highly possible due to the tactic expedience. While, some climatic factors can influence the probability of their absence (World War II has shown that in Russia, for example, tanks are almost no use in rainy weather and in swampy areas). I mean that weather hardly depend on the battlefield situation. 
Certainly, the idea on the rarefied sets still requires deep analysis from the point of view of the tool itself and its usage. However, its development and use in various fields of knowledge seems to be very expedient. It is enough to look at the diagram to see the variations of uncertainty degree of analyzed sets according to the transition between the following notions: “problem — purpose — task”.