The manager as a teacher: selected aspects of stimulation of scientsfsc thinking
Selected aspects of stimulation of scientific thinking. Meta-skills. Methods of critical and creative thinking. Analysis of the decision-making methods without use of numerical values of probability (exemplificative of the investment projects).
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Evolution of our World. We always say that the objects (systems) exist in our World /Unietse/and they operate in it. Therefore it is necessary to give a definition of the concept “our World”. We call “our World” the greatest and universal system in which based on the law of hierarchy all objects exist as its subsystems which can be part of it without coming into conflict with the laws of conservation and cause-and-effect limitations. Such objects are target-oriented associations of systemic functional units (SFU, elements) - the groups of elements interacting with specific goal/purpose (systems, or rather subsystems of our World). These include both the objects which existed before and are non-existent now and those that exist now and will appear in the future as a result of evolution. Absolutely all objects of our World have one or another purpose. We do not know these purposes and we can only guess them, but they are present in all the systems without exception. The purpose determines the laws of existence and architecture (“anatomy”) of objects, limits interaction between them or between their elements and stipulates the hierarchy of both sub-goals and subsystems for the achievement of these sub-goals. But this architecture is continually found insufficient (limited) because it is determined by the law of cause-and-effect limitations. It forces the systems to continuously seek the way to overcome these limitations, develops them and determines direction of evolution of the systems. That is why the systems develop towards their complexification and enhancement of their possibilities (evolve). If there would be no limitations, there would be no sense in evolution because ultimately the goal of evolution always consists in overcoming the limitations. All objects of our World have at least two primary goals: to be/exist in this World (to preserve themselves) to fulfill the goal and to have maximum possibilities to perform the actions for the achievement of the goal. However, any object of our World is limited in its possibilities to varying extent due to the law of cause-and-effect limitations and moreover, since the objects are continually exposed to various external influences destroying them, the systems have to continually protect themselves from such destruction. Therefore, the systems at first “have invented” passive and then active ways of protection against such destructive influence. The process of “invention” of these ways of protection and the enhancement of their possibilities is what evolution of objects of our World means exactly, at that it implies not only the evolution of living beings, but evolution of everything that exists in the world. Consolidation of objects in groups strengthens them and ensures the possibility for them to co-operate against destruction in a target-oriented manner. It is for the reason of “survival” of elements that the systems came into being, and complexification of elements just magnifies their possibilities. The simplest systems are those having only simple control block. Such objects include all objects of mineral nature, as well as plants. The possibilities of elementary particles are too small, and the lifespan of many of them is too short. The lifetime and possibility of an electron, proton or neutron are tenfold. Grouping of elements not only increases their lifetime, but also increases their possibilities. What can be done by electron (proton, neutron) cannot be done by elementary particles constituting them. What can be done by atoms can not be done separately by protons, neutrons and electrons. Grouping of atoms in molecules has enabled the development of more complex systems, up to human being, construction of which would have been impossible using elementary particles. However, although in process of further consolidation of atoms and molecules in conglomerates (mineral objects: gas clouds, liquid and solid bodies) the possibilities of these objects increase, but their lifetime starts to decrease sharply because the law of negative entropy works. Destruction is the loss by the object of its SFU. There are only two ways to prevent from destruction: increase in durability of connections/bonds between the SFU, restoration of the lost SFU, prevention of the SFU losses. The first one is passive, while the other two are active ways of protection. The increase in durability of connections/bonds between the SFU (the first way) is the passive way of protection against destruction. Mineral bodies have only these passive means of protection from the destructive effect of the external medium. The weakest of them are gaseous objects, while the strongest are crystalline. But even the strongest crystal may be destroyed. Metabolism is aimed at the restoration of the lost SFU (the second way) and is the active way of protection of systems from destruction. It is carried out at the expense of capture of necessary elements from the external medium. There is no metabolism in mineral objects, but it is present in all living objects, including plants. Hence, our World can be divided conditionally into two sub-worlds: inanimate/inorganic and animate nature. The criterion for such division is metabolism - the purposeful process of restoration of the lost SFU. But for such process the system should contain corresponding elements (metabolism organs) which are not present in the objects of mineral inorganic nature, but do exist in plants. Prevention of SFU losses (the third way) is also an active way of systems' protection from their destruction. Systems may be prevented from destruction for the account of their behavioral reactions depending on the external situation. If the situation is threatening the system needs to escape from the given situation. But for this purpose it is necessary to be aware about this situation, to be able to see it, as well as to have organs of movement which are nonexistent in the systems of mineral and vegetative nature. For this purpose it is necessary to have at least complex control block. Hence, in the animate nature it is possible to single out two more sub-worlds/natures: flora and fauna. The criterion for such division is the complexity of the control block and its ability (the availability of possibility) to show behavioral reactions. The more complex the control block, the higher is the development of animal as a system. But at that, note should be taken of the fact that the development of systems from plants to animals was basically solving only one problem - to be/exist in this World. The purport of existence of plants and the majority (if not of all) of animals, except for humans, is only in the metabolism. If the system is hungry it operates, if is satiated it stays idle. Yes, with complication of the control block simultaneous increase in the possibilities of systems occurred too, but it still pursued the goals of metabolism. More adapted animal feeds better. If the system plays and lives jolly (emotional tint of behavioral reactions), such reactions as a rule are still directed towards self-training of systems for better hunting for other systems. Therefore such reactions are basically inherent in young animals. More adult individuals do not play any more. Note should be also taken of that division of animals into predators and herbivorous animals is quite conditional, since it is not eating meat that is a distinctive feature of a predator and plants may also be carnivorous (for example, sundew and the like). Absolutely all animals, and not only them, but plants as well, are predators, since they represent the systems which feed on other systems. Even among the objects of mineral nature mutual relations of a victim-predator type may be found. Some systems (plants and herbivores) feed on systems with simple control blocks (mineral objects and plants) because it is easier thing to do. However, other systems (carnivorous) feed or try to feed on systems with complex control blocks (other animals), although it is much more complex to do so. That is why the donkey is more stupid than a tiger. The human being differs from other objects of animate nature first of all in that it is not metabolism which is the main purport of his/her life, but cognition. Yes, the higher the level of knowledge, the better the nutrition. But the process of cognition in itself prevails over all other processes aimed at metabolism. And even the metabolism itself is raised to the rank of art (the cookery). It is also possible to single out the human nature in that way as well, since only a human being out of all objects of our World has second signaling system (the intellectual control block) and aspiration towards cognition. Hence, the purpose of our World was evolution which has stipulated the development of systems in the direction towards complexification of their control blocks up to a human being. And the purpose of this evolution was to develop systems to such a degree that they have learnt to cognize the World. We can look back and see the confirmation of it throughout the entire history of development of our World in general and biosphere in particular. We do not know what was before the Big Bang, and we do not even know to which extent such statement is qualified. However, after it only the emergence and complexification of systems in the Universe was taking place, at that it occurred only at the expense of complexification of their control blocks, because their primary SFU (elementary particles) practically have not changed since then neither qualitatively, nor quantitatively. And we, the people, are the consequence and the proof of this development either. The human being is the most complex system, the top of evolution which has occurred till nowadays. Experience of this evolution shows that major distinctive feature throughout the entire process of advanced development was only the development of control blocks of systems. We do not know the purposes of the majority of systems of our World, although we can fabricate a multitude of speculations on many issues of this subject. For example, nuclei of atoms of chemical elements that are heavier than iron in those quantities which exist now in our Universe, could only and only appear as the result of explosions of supernovas. Hence, is the purpose of stars with evolution of a supernova type is the production of nuclei of atoms harder than iron? It may be true, although no one would avouch for it for the present. But we can surely state that a human being in the shape it exists today and is known to us would not have been existent without the elements having atomic weight heavier that iron, because the structure of its organism requires the presence of such elements. So, there are sufficient grounds for the assumption that stars of a supernova type are necessary for the development of the humans. It sounds strange and extraordinary, but still it's the fact. But we know for sure and without speculations the purposes of some of the World's systems, in particular, the purposes of many systems of organism. We know one of the main objectives of any living organism - to survive in the environment, and we know the hierarchy of sub-goals into which this purpose is broken down. We see how living systems develop on the way of evolution, we see the differences of systems standing at different levels of evolutionary process and we can explain the advantage of some systems over the others. In other words, the possibility is opened to us to construct classification of all systems of our World, including that of living systems. Today there is no uniform classification of all objects of our World, but there are only separate classifications of various groups of these objects, including classifications of astronomical, geological, biological and other groups. At that, nowadays the underlying principle of the majority, if not of all of these classifications, including classification of both the entire animate nature and the diseases, is the organic-morphological analysis. But probably it is necessary to substitute it, as well as classification of diseases, for the classification based on systemic analysis - the analysis of the goals/purposes. And the basic principle of the new classification should be not external distinctions, such as the number of feet or cones on the teeth, but two basic differences: differences by types of control blocks and types of executive elements. Moreover, it is necessary to include all objects of our World in this classification - animate and inanimate, because our World is replete only with systems which differ from each other only in the degree of development of their control blocks and in the ways of protection against destruction by the external media. The world is uniform, because it is a system in itself. Therefore, it is necessary to create common and single classification of all systems of our World. And systems are any objects, including animate/organic and inanimate/inorganic. Then it will be possible to distinguish four worlds/natures (sub-natures) of objects in our World: the world of minerals/mineral nature/, vegetative, animal worlds/natures/ and the world of humans/the human nature/. The population of each world differs from each other, as it was repeatedly underlined, only in control blocks and metabolism. The objects of mineral and vegetative nature have simple control blocks. But the objects of mineral nature have only passive ways of protection against negative entropy (destruction). And all living subjects, including plants, have active ways of protection against the same negative entropy, i.e. active substitution of the destroyed SFU at the expense of metabolism. Animals, unlike plants, in addition to metabolism, have more complex control blocks which enable behavioral reactions and thus allow them to control in a varying degree surrounding situation. And the humans have the most complex control block which contains the second signaling system and consequently it is capable of cognizing the whole World, including themselves, but not just what happens/exists nearby. And within each type of nature classification we should also proceed further to include the criteria of complexity of control blocks and then the criteria of presence and the degree of development of executive elements, including the number of feet or cones on the teeth. In this case classification will be the one of cause-and-effect type and logical. For example, vegetative nature/the flora/ includes not only plants, but all the Earth's population which possesses only simple control block and metabolism. And those are not only plants and not only metazoan. Procaryotes and eukaryotes, bacteria, phytoplankton, sea anemones, corals, polyps, fungi, trees, herbs, mosses and lichens and many others possessing and those not possessing chlorophyll are all flora. They simply grow in space and they have no idea of it because they “do not see” it. However, some plants, for example, trees or herbs, unlike corals, fungi or polyps, contain chlorophyll (specific executive element). Such classification of systems has one incontestable advantage: it aligns everything that populates our World - the systems. The whole World around us is classified by a single scale, where the unit of measure is only the complexity of control block and executive elements used by it. In that way it would be easier for us to understand what life is. May it be so that inanimate nature does not exist at all? Perhaps, “animate” differs from “inanimate” only in that it “has comprehended” its own exposure to destruction under the influence of environment and first has learnt self-restorability and then it learnt how to protect itself from destructions? Then Pierre Teyjar De Chardin is right asserting that evolution is a process of arousal of consciousness. Currently existing classifications do not provide the answer to this question. New classification of systems based on the systemic target-oriented analysis will make it possible to understand, where the “ceiling” of development of systems of each of the worlds is and which of its subjects are still at the beginning of the evolutionary scale and which of them have already climbed up its top. But this classification is based on the recognition of the first-priority role of the goal/purpose on the whole and purposefulness of nature in particular, which idea is disputable for the present and is not accepted by all. Therefore, queer position was characteristic for the XX century: the position of struggle with nature, position which is still shared by a great many. This position is fundamentally erroneous, because the nature is not our enemy, but the “parent”, the tutor and friend. It “produced” us and “nurtured” us, having provided a cradle, the Earth for us, and it has been creating greenhouse conditions throughout many millions years, where fluctuations of temperature were no more than 100ºC and the pressure about 1 atmosphere, with plenty of place, sufficient moisture and energy, although Space is characterized by range of temperatures in many millions degrees and of pressure in millions atmospheres. It has brought us up and made us strong, using evolution and the law of competition: “the strongest survives”. It is not our task “to take from it”, nor to struggle with it, but to understand and collaborate with it, because it is not our enemy, but the teacher and partner. It “knows” itself what we need and gives it to us, otherwise we would not have existed. This is not an ode to the nature, but the statement of fact of its purposefulness. Some may object that such combination of natural conditions which has led to the origination of human being is just a mere fortuity which has arisen under the law of large numbers only because the World is very large and all kind of options are possible in it. However, that many incidental occurrences are kind of suspicious. The nature continually “puts stealthily” various problems before us, but every time the level of these problems for some reason completely corresponds to the level of development of an animal or a human being. For some reason a man “has discovered” a nuclear bomb at the moment when he could already apprehend the power of this discovery. Nature does not give dangerous toys to greenhorns. If there were no problems at all, there would be no stimulus to development and as of today the Earth would have been populated by the elementary systems, if it were populated at all. However, if the problems sharply exceed the limit of possibilities of systems, the latter would have collapsed and the Earth would have not been populated at all, if it would be existent in abstracto. And in any case there would have been no development on the whole. But we do exist and it is the fact which has to be taken into account and which requires explanation. And the explanation only consists in the purposefulness of Nature.
Systemic analysis is a process of receiving answer to the question “Why is the overall goal of the system fulfilled (not fulfilled)?” The notion of “systemic analysis” includes other two notions: “system” and “analysis”. The notion of “system” is inseparably linked with the notion of the “goal/purpose of the system”. The notion “analysis” means examination by parts and arranging systematically (classification). Hence, the “systemic analysis” is the analysis of the goal/purpose of the system by its sub-goals (classification or hierarchy of the goals/purposes) and the analysis of the system by its subsystems (classification or hierarchy of systems) with the view of clarifying which subsystems and why can (can not) fulfill the goals (sub-goals) set forth before them. Any systems perform based on the principle “it is necessary and sufficient” which is an optimum control principle. The notion “it is necessary” determines the quality of the purpose, while the notion “is suficient” determines its quantity. If qualitative and quantitative parameters of the purpose of the given system can be satisfied, then the latter is sufficient. If the system cannot satisfy some of these parameters of the goal, it is insufficient. Why the given system cannot fulfill the given purpose? This question is answered by systemic analysis. Systemic analysis can show that such-and-such object “consists of... for…”, i.e. for what purpose the given object is made, of what elements it consists of and what role is played by each element for the achievement of this goal/purpose. The organic-morphological analysis, unlike systemic analysis, can show that such-and-such object “consists of... “, i.e. can only show of which elements the given object consists. Systemic analysis is not made arbitrarily, but is based on certain rules. The key conditions of systemic analysis are the account of complexity and hierarchy of goals/purposes and systems.
Complexity of systems. It is necessary to specify the notion of complexity of system. We have seen from the above that complexification of systems occurred basically for the account of complexification of control block. At that, complexity of executive elements could have been the most primitive despite the fact that control block at that could have been very complex. The system could contain only one type SFU and even only one SFU, i.e. to be monofunctional. But at the same time it could carry out its functions very precisely, with the account of external situation and even with the account of possibility of occurrence of new situations, if it had sufficiently complex control block. When the analysis of the complexity of system is made from the standpoint of cybernetics, the communication, informo-dynamics, etc. theories the subject discussed is the complexity of control block, rather than the complexity of the system. Note should be taken of that regardless of the degree of the system complexity two flows of activity are performed therein: information flow and a flow of target-oriented actions of the system. Information flow passes through the control block, whereas the flow of target-oriented actions passes through executive elements. Nevertheless, the notion of complexity may also concern the flows of target-oriented actions of systems. There exist mono- and multifunctional systems. There are no multi-purpose systems, but only mono-purpose systems, although the concept of “multi-purpose system” is being used. For example, they say that this fighter-bomber is multi-purpose because it can bomb and shoot down other aircrafts. But this aircraft still has only one general purpose: to destroy the enemy's objects. This fighter-bomber just has more possibilities than a simple fighter or simple bomber. Hence, the notion of complexity concerns only the number and quality of actions of the system, which are determined by a number of levels of its hierarchy (see below), but not the number of its elements. Dinosaurs were much larger than mammals (had larger number of elements), but have been arranged much simpler. The simplest system is SFU (Systemic Functional Unit). It fulfills its functions very crudely/inaccurately as the law that works is the “all-or-none” one and the system's actions are the most primitive. Any SFU is the simplest/elementary defective system and its inferiority is shown in that such system can provide only certain quality of result of action, but cannot provide its optimum quantity. Various SFU may differ by the results of their actions (polytypic SFU), but they may not differ either (homotypic SFU). However, all of them work under the “all-or-none” law. In other words, the result of its action has no gradation or is zero (non-active phase), or maximum (active phase). SFU either reacts to external influence at maximum (result of action is maximum - “all”), or waits for external influence (the result of action is zero - “none”) and there is no gradation of the result of action. Each result of SFU action is a quantum (indivisible portion) of action. Monofunctional systems possess only one kind of result of action which is determined by their SFU type. They may contain any quantity of SFU, from one to maximum, but in any case these should be homotypic SFU. Their difference from the elementary system is only in the quantity of the result of action (quantitative difference). The monofunctional system may anyway perform its functions more accurately as its actions have steps of gradation of functions. The accuracy of performance of function depends on the value of action of single SFU, the NF intensity and the type of its control block, while the capacity depends on the number of SFU. The “smaller” the SFU, the higher the degree of possible accuracy is. The larger the number of SFU, the higher the capacity is. So, if the structure of the system's executive elements (SFU structure) is homotypic, it is then multifunctional and simple system. But at that, its control block, for example, may be complex. In this case the system is simple with complex control block. The multifunctional system is a system which contains more than one type of monofunctional systems. It possesses many kinds of result of action and may perform several various functions (many functions). Any complex system may be broken down into several simple systems which we have already discussed above. The difference of multifunctional system from the monofunctional one is that the latter consists of itself and includes homotypic SFU, while complex system consists of several monofunctional systems with different SFU types. And at that, these several simple systems are controlled by one common control block of any degree of complexity. The difference between monofunctional and multifunctional systems is in the quantity and quality of SFU. In order to avoid confusion of the complexity of systems with the complexity of their control block, it is easier to assume that there are monofunctional (simple) and multifunctional (complex) systems. In this case the concept of complexity of system would only apply to control block. In monofunctional system control block operates a set of own SFU regardless of the degree of its complexity. In multifunctional system control block of any degree of complexity operates several monofunctional subsystems, each of which has its SFU with their control blocks. It is complexity of control block that stipulates the complexity of the system, and not only the type of system, but the appurtenance of the given object to the category of systems. The presence of an appropriate control block conditions the presence of a system, whereas the absence of (any) control block conditions the absence of a system. Systems may have control blocks of a level not lower than simple. The full-fledged system can not have the simplest/elementary control block, whereas the SFU can.
So, the system is an object of certain degree of complexity which may tailor its functions to the load (to external influence). If its structure contains more than one SFU, the result of its action has the number of gradations equal to the number of its SFU or (identically) the number of quanta of action. The number of the system's functions is determined by the number of polytypic monofunctional systems comprising the given system. In former times development of life was progressing towards the enlargement of animal body which provided some kind of guarantee in biological competition (quantitative competition during the epoch of dinosaurs). But the benefits has proven doubtful, the advantages turned out to be less than disadvantages, that is why monsters have died out. This is horizontal development of systems. If they differ in quality it is tantamount to the emergence of new multifunctional systems. Such construction of new systems is the development of systems along the vertical axis. The example of it is complexification of living organisms in process of evolution, from elementary unicellular to metazoan and the human being. What can be done by man can not be done by a reptile. However, what can be done by reptile can not be done by an infusorian (insect, jellyfish, amoeba, etc.). Complexification of living organisms occurred only for one cardinal purpose: to survive in whatever conditions (competition of species). Since conditions of existence are multifarious, the living organism as a system should be multifunctional. The character of a new system is determined by the structure of executive elements and control block features. If there is a need to extend the amplitude or the capacity of system's performance the structure of executive elements should be uniform. To increase the amplitude of the system's performance all SFU are aligned in a sequential series, while to increase the capacity - in a parallel series depending on the required quantity of the result of action (amplitude or capacity at the given concrete moment). Polytypic SFU have different purposes and consequently they have different functions. The differences of SFU stipulate their specialization, whereby each of them has special function inherent in it only. If the structure of any system comprises polytypic SFU, such system would be differentiated, having elements with different specialization. In systems with uniform SFU all elements have identical specialization. Therefore, there is no differentiation in such system. So, the concept of specialization characterizes a separate element, whereas the concept of differentiation characterizes the group of elements. The number of SFU in real systems is always finite and therefore the possibilities of real systems are finite and limited, too. Resources of any system depend on the number of SFU comprising its structure in the capacity of executive elements. The pistol may produce as many shots as is the number of cartridges available in it, and no more than that. The less the number of SFU is available in the system, the smaller the range of changes of external influence can lead to the exhaustion of its resources and the worse is its resistance to the external influence. By integrating various SFU in more and more complex systems it is possible to construct the systems with any preset properties (quality of the result of action) and capacities (amount of quanta of the result of action). At that, the elements of systems are the systems themselves, of a lower order though (subsystems) for these systems. And the given system itself may also be an element for the system of higher order. This is where the essence of hierarchy of systems lies.
Hierarchy of goals/purposes and systems. The more complex the system, the wider the variety of external influences to which it reacts. But the system should always produce only specific (unique, univocal) reaction to certain influence (or certain combination of external influences) or specific series of reactions (unique/univocal series of reactions). In other words, the system always reacts only to one certain external influence and always produces only one specific reaction. But we always see “multi”-reactive systems. For example, we react to light, sound, etc. At the same time we can stand, run, lay, eat, shout, etc., i.e. we react to many external influences and we do many various actions. There is no contradiction here, as both the purposes and reactions may be simple and complex. The final overall objective of the system represents the logic sum of sub-goals/sub-purposes of its subsystems. The goal/purpose is built of sub-goals/sub-purposes. For example, the living organism has only one, but very complex purpose - to survive, by all means, and for this purpose it should feed. And for this purpose it is necessary to deliver nutriment for histic cells from the external medium. And for this purpose it is necessary first to get it. And for this purpose it is necessary to be able to run quickly (to fly, bite, grab, snap, etc.). Thereafter it is necessary to crush it, otherwise it won't be possible to swallow it (chewing). Then it is necessary to “crush” long albumen molecules (gastric digestion). Then it is necessary to “crush” the scraps of the albumen molecules even to the smaller particles (digestion in duodenum). Then it is necessary to bring in the digested food to blood affluent to intestine (parietal digestion). Then it is necessary... And such “is necessary” may be quite many. But each of these “is necessary” is determined by a sub-goal at each level of hierarchy of purposes. And for every such sub-goal there exists certain subsystem at the respective level of hierarchy of subsystems. At that, each of them performs its own function. And in that way a lot of functions are accumulated in a system. However, all this hierarchy of functions is necessary for one unique cardinal purpose: to survive in this world. Any object represents a system and consists of elements, while each element is intended for the fulfillment of respective sub-goals (subtasks). The system has an overall specific goal and any of its elements represents a system in itself (subsystem of the given system), which has its own goal (sub-goal) and own result of action. When we say “overall specific goal” we mean not the goals/purposes of elements of the system, but the general/overall/ purpose which is reached by means of their interactions. The system has a goal/purpose which is not present in each of its element separately. But the overall goal of the system is split into sub-goals and these sub-goals are the purposes of its elements anyway. There are no systems in the form of indivisible object and any system consists of the group of elements. And each element, in turn, is a system (subsystem) in itself with its own purpose, being a sub-goal of the overall goal/general purpose/. To achieve the goal the system performs series of various actions and each of them is the result of action of its elements. The logic sum of all results of actions of the system's subsystems is final function - the result of action of the given system. Thus, one cardinal purpose determines the system, while the sub-goal determines the subsystem. And so on and so forth deep into a hierarchy scale. The goal/purpose is split into sub-goals/sub-purposes and the hierarchy of purposes (logically connected chain of due actions) is built. To perform this purpose the system is built which consists of subsystems, each of which has to fulfill their respective sub-goals and capable to yield necessary respective result of action. That is how the hierarchy of subsystems is structured. The number of subsystems in the system is equal to he number of subtasks (subgoals) into which the overall goal is broken down. For example, the system is sited at a zero level of hierarchy, and all its subsystems are sited at a minus one, minus two, etc. levels, accordingly. The order of numeration of coordinates is relative. It means that the given system may enter the other, larger system, in the capacity of its subsystem. Then the larger system will be equalized to zero level, whereas the given system will be its subsystem and sited at a minus one level. The hierarchy scale of systems is built on the basis of hierarchy of goals/purposes. Target-specific actions of systems are performed by its executive elements, but to manage their target-oriented interaction the interaction of control block of the system with control blocks of its subsystems is needed. Therefore, the hierarchy scale of systems is, as a matter of fact, a hierarchic scale of control blocks of systems. This scale is designed based on a pyramid principle: one boss on top (the control block of the entire system), a number of its concrete subordinates below (control blocks of the system's subsystems), their concrete subordinates under each of them (control blocks of the lower level subsystems), etc. At each level of hierarchy there exist own control blocks regulating the functions of respective subsystems. Hierarchical relations between control blocks of various levels are built on the basis of subordination of lower ranking blocks to those of higher level. In other words, the high level control block gives the order to the control blocks of lower level. Only 4 levels of hierarchy, from 0 to 3rd, are presented. The count is relative, whereby the level of the given system is assumed to be zero. The counting out may be continued both in the direction of higher and lower (negative) figures/values. The notions of “order” and “level” are identical. The notions of “system” and “subsystem” are identical, too. For example, instead of expression “a subsystem of minus second-order” one may say “a system of minus second-level”. And although a zero level is assumed the level of the system itself, the latter may be a part of other higher order system in the capacity of its subsystem. Then the number of its level can already become negative (relative numeration of level). Elements of each hierarchic level of systems are the parts of system, its subsystems, the systems of lower order. Therefore, the notions “part”, “executive element”, “subsystem”, “system” and in some cases even “element” are identical and relative. The choice of term is dictated only by convenience of accentuating the place of the given element in the hierarchy of system. The notion of hierarchic scale (or pyramid principle) is a very powerful tool and it embodies principal advantage of systemic analysis. Systemic analysis is impossible without this concept. Both our entire surrounding world and any living organism consist of infinite number of various elements which are relating to each other in varying ways. It is impossible to analyze all enormous volume of information characterizing infinite number of various elements. The concept of hierarchy of systems sharply restricts the number of elements subjected to the analysis. In the absence of it we should take into account all levels of the world around us, starting from elementary particles and up to global systems, such as an organism, a biosphere, a planet and so on. For global evaluation of any system it is sufficient to analyze three levels only: the global level of the system itself (its place in the hierarchy of higher systems); the level of its executive elements (their place in the hierarchy of the system itself); the level of its control elements (elements of control block of the system itself). To evaluate the system's function it is necessary to determine the conformity of the result of action of the given system with its purpose - due result of action (global level of function of the system), the number of its subsystems and the conformity of their results of action with their purposes - due results of their action (local functional levels of executive elements) and evaluate the function of elements of control. In the long run the maximum level of function of system is determined by the logic sum of results of actions of all subsystems comprising its structure and optimality of control block performance. Abiding by the following chain of reasoning: “the presence of the goal/purpose for implementation of any specific condition, the presence of qualitative or quantitative novelty of the result of action, the presence of a control (block) loop” it is possible to single out elements of any concrete system, show its hierarchy and divide cross systems in which the same elements perform various functions. Systems work under the logical law which main principle is the fulfillment of condition “... if..., then….”. In this condition “if ..” is the argument (purpose), while “then...” is the function (the result of action). This condition stipulates determinism in nature and hierarchy scale. Any law, natural or social, requires implementation of some condition and the basis of any condition is this logical connective “... if..., then…” At that, this logical connective concerns only two contiguous subsystems on a hierarchic scale. The argument “... if” is always specified by the system which is on a higher step, whereas the function “then…” is always performed by the system (subsystem) sited immediately underneath, at a lower step of a hierarchic scale. Actions of elements per se and interaction between the elements may be based on the laws of physics or chemistry (laws of electrodynamics, thermodynamics, mathematics, social or quantum laws, etc.). But the operation of control block is based only on the logical laws. And as far as control block determines the character of function of systems, it is arguable that systems work under the logic laws. Sometimes in human communities the “bosses” would imagine they may govern/control/ at any levels, but such type of management is the most inefficient one. The best type of management is when the director (the control block of multifunctional system) controls/manages/ only the chiefs of departments (control blocks of monofunctional systems), sets forth feasible tasks before them and demands the implementation thereof. At that, the number of its “assistant chiefs” should not exceed 7±2 (Muller's number). If some department does not implement its objectives, it means that either the departmental management (control block of a subsystem) is no good because has (a) failed to thoroughly devise and distribute the tasks between the subordinates (the SFU), or (b) has inadequately selected average executives (SFU), or (c) impracticable goal has been set forth before the department (before system), or (d) the director himself (control block of the system) is no class for the management. In such cases the system's reorganization is necessary. But if the system is well elaborated and performs normally there is no sense for the director to “pry” into the department's routine affairs. A chief of department is available for this purpose. The decision of the system reorganization is only taken when the system for some reason cannot fulfill the objective (system crisis). In the absence of crisis there is no sense in reorganization. For the purpose of reorganization the system changes the structure of its executive and control elements both at the expense of actuation (de-actuation) of additional subsystems and alteration of exit-entry combinations of these elements. In such cases skipping of some steps of hierarchy may occur and the principle “vassal of my vassal is not my vassal” violated. This is where the essential point of the system reorganization lies. At the same time, part of elements can be thrown out from the system as superfluous (that's how at one time we lost, for example, cauda and branchiae), while other part may be included in the system's structure or shifted on the hierarchy scale. But all that may only happen in process of the system reorganization proper. When the process of reorganization comes to an end and the reorganized system is able of performing the goal set forth before it (i.e. starts to function normally), the control law of “vassal of my vassal is not my vassal” is restored.
Consequences ensuing from axioms.
Independence of purpose. The purpose/goal does not depend on the object (system) as it is determined not by the given object or its needs, but by the need of other object in something (is dictated by the external medium or other system). But the notion of “system” in relation to the given object depends on the purpose, i.e. on the adequacy of possibilities of the given object to execute the goal set. The goal is set from the outside and the object is tailored to comply with it, but not other way round. Only in this case the object presents a system. Note should be taken again of the singularity of the first consequence: the system's purpose/goal is determined by a need for something for some other object (external medium or other system). Common sense suggests that supposedly survivability is the need of the given organism (the given system). But it follows from the first consequence that the need to survive proceeds not from the given organism, but is set to it by another system external with respect to it, for example, the nature, and the organism tries to fulfill this objective.
Specialization of the system's functions. In response to certain (specific) external influence the system always produces certain (specific) result of action. Specialization means purposefulness. Any system is specialized (purposeful) and follows from the axiom. There are no systems in abstracto, there are systems that are concrete. Therefore, any system has its specific purpose/goal. Executive elements (executive SFU) of some systems may be homotypic (identical, non-differentiated from each other). If executive elements differ from each other (are multitype), the given system consists of differentiated elements.
System integrity. The system exerts itself as a unitary and integral object. It follows from the unity of purpose which is inherent only in the system as a whole, but not in its separate elements in particular. The purpose consolidates the system's elements in a comprehensive whole.
Limited discrecity of system. Nothing is indivisible and any system may be divided into parts. At the same time, any system consists of finite number of elements (parts): executive elements (subsystems, elements, SFU) and management elements (control block).
Hierarchy of system. The elements of a system relate to each other in varying ways and the place of each of them is the place on the hierarchic scale of the system. Hierarchy of systems is stipulated by hierarchy of purposes. Any system has a purpose. And to achieve this purpose it is necessary to achieve a number of smaller sub-goals for which the large system contains a number of subsystems of various degree of complexity, from minimum (SFU) up to maximum possible complexity. Hierarchy is the difference between the purposes of the system and the purposes of its elements (subsystems) which are the sub-goals in respect to it. At that, the systems of higher order set the goals before the systems of lower order. So, the purpose of the highest order is subdivided into a number of sub-goals (the purposes of lower order). The hierarchy of purposes determines the hierarchy of systems. To achieve each of the sub-goals specific element is required (it follows from the conservation law). Management/control in a hierarchic scale is performed in accordance with the law “the vassal of my vassal is not my vassal”. In other words, direct control is only possible at the level “system - own subsystem”, and the control by super system of the subsystem of its system is impossible. The tsar, should he wish to behead a criminal, would not do it himself, but would give a command to his subordinate executioner.
System function. The result of the system's performance is its function. To achieve the purpose the system should perform purposefully certain actions the result of which would be the system's function. The purpose is the argument for the system (imperative), while the result of action of the system is its function. The system's functions are determined by a set of executive elements, their relative positioning and control block. The notions of “system” and “function” are inseparable. Nonfunctional systems are non-existent. “Functional system” is a tautology, because all systems are functional. However, there may be systems which are non-operational at the moment (in a standby mode). Following certain external influence upon the system it will necessarily yield certain specific result of action (it will function). In the absence of the external influence the system produces no actions (does not function). When taking into account the purpose, the argument is not the external influence, but the purpose. One should distinguish internal functions of the system (sub-function) belonging to its elements (to subsystems, SFU) and the external functions belonging to the entire system as a whole. The system's external function of emergent property is the result of its own action produced by the system. Internal functions of the system are the results of action of its elements.
Effectiveness of systems. Correspondence of the result of action to the goal set characterizes the effectiveness of systems. Effectiveness of systems is directly linked with their function. The system's function in terms of effectiveness may be sufficient, it may by hyperfunction, decelerating and completely (absolutely) insufficient function. The system performs some actions and it leads to the production of the result of its action which should meet the purpose for which the given system is created. Effectiveness of systems is based on their specialization. “The boots should be sown by shoemaker”. Doing the opposite does not always result in real systems' actions that meet the target/preset results (partial effectiveness or its absence). The result of action of the system (its function) should completely correspond qualitatively and quantitatively to the preset purpose. It may mismatch, be incidental or even antagonistic (counter-purposeful); at that, real systems may produce all these kinds of results of action simultaneously. Only in ideal systems the result may completely meet the preset purpose (complete effectiveness). But systems with 100% performance factor are unknown to us. Integral result (integral function) is the sum of separate collateral/incidental and useful results of action. It is this sum that determines the appurtenance of the given object to the notion of “system” with regard to the given purpose. If the sum is positive, then with respect to the preset purpose the given object is a system of one or other efficiency. If the sum is equal to zero, the object is not a system with respect to the given purpose (neutral object). If the sum is negative, the given object is an anti-system (the system with minus sign preventing from the achievement of the goal/purpose). It applies both to systems and their elements. The higher the performance factor, the more effective the system is. Discrepancy of the result of action of the given system with the due value depends on unconformity of quantitative and qualitative resources of the system, for example, owing to breakage (destruction) or improper and/or insufficient development of its executive elements (SFU) and/or control. Therefore, any object is an element of a system only in the event that its actions (function) meet the achievement of the preset goal/purpose. Otherwise it is not an element of the given system. Effectiveness of systems is completely determined by limitation of actions of the systems.
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