Sistemnye issledovania 1969, p SYSTEMS COMPARABLE TO THE INVESTIGATOR IN THEIR DEGREE OF PERFECTION. Vladimir A. LEFEBVRE

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1 1 Sistemnye issledovania 1969, p SYSTEMS COMPARABLE TO THE INVESTIGATOR IN THEIR DEGREE OF PERFECTION Vladimir A. LEFEBVRE A large number of investigators believe now that functional similarity between a technical device and a live organism does not help us to understand what is human psyche, mental domains, reflexion. Concepts and models that were elaborated in humanities acquire attractiveness for investigators in natural sciences and cybernetics. The cybernetics is being criticized for not developing special means for studying intellectual processes. Instead, it has always attempted to reduce them to elementary physical or technical patterns. Let us consider an example from Ashby s paper Principles of Self-Organization [1]. A Rat lives in a sewer; someone wants to poison it. But it is difficult to do so fast. The Rat is suspicious about bait, it takes it by very little portions, and only after being sure that the bait is harmless, the Rat would take a large piece. Ashby analyzes two types of rats: those of the first type have short memory, and those of the second type have long memory. It turns out that the rats with long memory are more vulnerable than the rats with short memory. A Poisoner trains the Rat by giving it small portions of harmless pre-bait. After the Rat grows bolder, the Poisoner adds poison to the bait and wins. He would not be able to train a rat with short memory, it will keep taking the bait by small portions and survive. But is a rat with long memory in the hopeless situation? In order to survive, the Rat must become aware of the situation. What is hidden behind the term to become aware of which clear and vague at the same time? This term is used for expressing two things. On the one hand, to become aware means to broaden one s mental horizon, to include new previously hidden mechanisms of a process into consideration. On the other hand, to become aware means to include oneself together with one s research tools and mental pictures generated by the tools into one s mental model. Let us broaden the second meaning and use the term awareness also for inclusion of other persons with their mental tools and pictures into one s mental model, and any person s mental pictures may contain other persons mental pictures etc. To register these structures the author provided a special language (Lefebvre, 1965, 1967). In Ashby s example, the Rat and the Poisoner are investigating each other. Symbol X will designate the Rat, and Y - the Poisoner. The sewer and the material world around will be designated T. The Rat s Poisoner s bodies will be also included in T. Their mental models are Tx and Ty. The following symbolic sums will represent the Rat and the Poisoner: X = T + Tx, Y = T + Ty. The author heard questions of the type, Why do you sum such different things as reality and a person s picture of it? The answer is, They are not as different as it seems at the first glance. Reality, T, and picture, Tx, are pictures in front of an external observer. Such an observer, in

2 particular, can be I, when I register T and Tx separately. After realizing this, I might write TI + TxI, that is, T from my point of view plus Tx from my point of view. Therefore, reality, T, and picture of reality, Tx, are descriptions from an external observer s point of view, and in this sense are similar. To simplify the narration, the symbol I will not be used. Here are the three rules for working with the polynomials. 1. Summands can be situated in any order. 2. Summands can be reproduced, i.e., T = T + T where is any finite sequence of letters. This is a natural rule, because we do not obtain additional information with reproduction of the text we have already known. 3. The right outmost letter common for several summands can be taken out from brackets; a letter out of brackets can be put in brackets as in T + Ty + Txy = T + (T + Tx)y. This rule allows us to distinguish inner domains. For example, T+Tx in the above expression is reality from Y s position. Let us return now to the Rat and Poisoner and depict the situation described by Ashby. The Rat can see only the material field in which it lives, while the Poisoner, in addition, can reflect the Rat s picture of the field. We designate the entire situation with 1 : 1 = T + Tx + (T + Tx)y. The Poisoner s activity consists of giving a certain picture of the reality to the Rat and then using the fact that it has the picture he gave it. With symbols, we can write the process of transfer the picture of the reality as follows: Txy Tx. What if the Rat became aware of what is going on? Then the situation changed, and the new one appeared: 2 = T + 1 x + (T + Tx)y. The naive Poisoner keeps seeing T + Tx, while the Rat sees the entire previous situation: 1 = T + Tx + (T + Tx)y. The Poisoner s actions are doomed to failure because the polynomial s change means that the Rat guessed. We may stop using uncertain terms guessed or become aware of and introduce special operations with polynomials instead. An operation of realizing is an operation similar to finding indefinite integral. The rules for polynomials transformations allow us to write a polynomial depicting two persons relations as follows: = T + x + y, 2

3 3 where and are polynomials depicting each person s mental world. We will designate the integral symbol for an operation of awareness: x x C, C T " y, X became aware of the situation; y y C, C T ' x, Y became aware of the situation. xy, T x y, X and Y simultaneously became aware of the situation. This formalism allows fixation of the processes of awareness. It is possible to describe the dynamics of the situation with the sequence of integration operators. This symbolics also let us specify the types of relations between an object and an investigator or, more precisely, between two objects-investigators, because the most interesting are the cases, when the objects are investigators the self. The simplest case is T+Tx. The investigator sees a physical reality that, from his point of view, is inanimate. The investigator is building physics. More complicated case is Y+Yx. Here Y may be, for example, T+Ty. Then X investigates not only physical reality but also Y s picture of this reality. This is a situation psychiatrist-patient. To identify pathology, the psychiatrist must find the patient s picture of the world. Sometimes, he has to deal with more complicated structures, for example, Y = T + Ty + Txy + Tyxy. Txy is the picture that, from the patient point of view, the psychiatrist has, and Tyxy is the picture that, from the patient s point of view, the psychiatrist recreated about the patient s picture. Sometimes a psychiatrist must analyze a set of tangled reflexive structures, which are no less real for him than brain tissue for a neurophysiologist. For a psychiatrist, an object to investigate is more complicated than the one that, for example, a physicist has. The object s properties which a physicist studies may depend on the physicist s tools, while a reflexing object, which is under study by a psychiatrist, may enter the psychiatrist s mental world. This is the case, when the theory about an object has influence on it [4]. For example, the patient studied books on psychiatry and his ailment manifestations have changed. In his studies, an investigator must assume that his object knows the theory. (Who knows, perhaps theoretical physics also influence on its objects?) Let us analyze another type of relations: Y + (X + Xy)x. X s mental world contains his model of the self and the model of his object of investigation. But this object is such that he imitates any X s thought (everything from X s point of view), so X believes that the object excels him in intellectual perfection. This structure of a mental world is

4 typical for religious thinking. It is obvious that X cannot take a task to study Y, because from his point of view, someone who excels him imitates him together with the task. But X can influence Y, since Y s reflexive structure (a polynomial depicting Y) depends on X. If X becomes aware of this and changes his state, he influences Y. Similar structures appear in human conflicts as well. A player with this type of mental world has to choose the Maxmin principle, i.e., he has to make such a decision that even by knowing it his adversary would harm him the least. In some cases there is no such decision. Then the one who makes decision must neutralize the adversary s deduction. He must not know the decision he would make; he must cast dice. So, by imitating his thoughts the adversary would not know his decision (it is considered that a single result of dice casting is impossible to imitate). But the adversary (the one who imitates every thought) would guess it and will also cast dice. The game theory developed by John von Neumann explains how to cast dice optimally in such situations. In using the tools, which allow us to conduct typological analysis of relations between objects-investigators, we depict an object as Y = T + Ty + Txy +... But there are more complicated cases. An object under investigation may have more than one picture of T, for example, Ty 1 and Ty 2. Actually, they are Y s different views on T taken from different position. They may be not connected or sometimes Y is aware of their difference and even formulate a task of their connecting with the help of taking third position or the one of already existing, i.e., a configurator appears [2]. Let Ty 1 be schematization of the object using cybernetics, and Ty 2 by using physics. Three cases are possible: (Ty 1 + Ty 2 )y 1, (Ty 1 + Ty 2 )y 2, (Ty 1 + Ty 2 )y 3. The first notation describes Y s awareness from the cybernetics point of view; it means that Ty 2 is reduced to Ty 1. The second notation describes the awareness from the physics point of view, i.e., the picture generated with the tools of cybernetics is reduced to physical models. These processes of awareness are much more complicated that those used in reflexive games, in which real persons are involved, and something can be borrowed from them. This is the case of positional awareness. If we use the analogy of the reflexive games, this is a constructing of a new player who can become aware of pictures used by players already built. Perhaps, scientific knowledge can be represented as a reflexive polynomial, and its member would correspond to various research positions. In this sense, the very connecting to science is the beginning of investigating a reflexive object. Education would mean taking positions, and creative activity would look like aggression toward the entire structure: eliminating some personas, introducing new ones, constructing a set of competing scientific contra positions. Note that a contrast between scientific and nonscientific depends on the way of 4

5 representation of an object. The idea of an object comparable or, more than that, excelling the investigator in perfection is alien to the present scientific thought, which was formed in studying simple mechanical phenomena. It is inclined to reduce a live object to an inanimate thing and then proclaim that attributes pertinent to live and intelligent can be deduced from inanimate. To study objects which are only little distinguishable from investigators we have to revise our research ideology and try to create new tools designed especially for studying such objects. References 1. William Ross Ashby. Principles of Self-Organization. In: Principles of Self-Organization, Pergamon Press, Lefebvre, V. A. Konfliktuyushchie Structury (Conflicting Structures), Moscow, Lefebvre, V. A. The Basic Ideas of Reflexive Games Logic. In: Problemy Issledovania Sistem i Structur, Conference Proceedings, Moscow, Lefebvre, V. A. The Elements of Reflexive Game Logic. In: Problemy Ingenernoy Psikhologii, Leningrad,