"The Integral Algorithm of Organization and Evolution of the Living Up to Culture - the Possible Instrument for Genetic Programming". V.L. Kalmykov Institute of Cell Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142292, Russia E-mail: kalmykov@venus.iteb.serpukhov.su Abstract The paper present correct physicomathematical formulating the invariant operational scheme of organization (space correlations) and evolution (time correlations) of the living, including a new generalized conception of information. This new methodological innovation would permit the creation of a programs that solve problems in the full sense (in essence and integrally), and not only as imitation. The chief elements of the proposed operational schemes are as follows: - elementary operations on information, energy and matter; life is realization of some combinations of these operations; the combinations form a mathematical group; - general definitions of control, reproduction and creation operations; interdependence of these integrative operations (on elementary operations) in the organism; - generalized conception of information; - consecutive stages of arising and evolution of the organisms; - the generalized criterion of the life evolution direction; - the generalized definition of life, culture, functional elements of culture ... ************************************************** Introductory Explanations * About significance of the abstract theoretical biology. It may be impossible to find a thought and reflection in the neurons or in the brain or anywhere else by use of scalpel, test-tube, electrode and concrete-theoretical modeling only without innovations from the abstract theoretical biology. * Unlike the most present works in Computational Biology this study was not aimed at using computers in biology, but it was the attempt of a biologist to formulate the logic of the living for its probable use in Genetic Programming. The logic has been fulfilled as a strict theoretical model, which integrally reflects the universal functional organization of the living. The essence of the method was the invention of ideal objects that are still absent for a sufficient understanding of the living. * The science still don't know what is information in a main point. A "little bit" is known only about the bits (the information capacity) and some manipulations with them. This problem is the main in the questions how nervous system to compute and what is the cognition. * The logic of the functional organization and evolution of the ideas and of the biological systems is similar. ******************************************* This paper shows some attempt to invent and formulate the general logic of the functional organization and evolution of living systems as a strict physico-mathematical theory. It is also aimed, according to John Maddox, at elucidating, to some extent "the dark side of molecular biology" [1]. The modern molecular biology mainly deals with particular details of the molecular structure of the living. This very often damages traditional biological problems. The task is close to the questions of what life is and why it is organized so. Being traditional for the theoretical biology, these questions are at present especially urgent in connection with the problems of ecological education and development of computers, robots and cyberspace. In the latter cases the development of computers with soft- or/and hardware, based in essence on the logic of organization and evolution of the living, is meant. Besides, for a valuable and justified presentation of knowledge about the living in computers its generalized (universal) functional description is necessary. This work presents such a generalized theoretical description of the living. It includes elements of axiomatic approach and is physically interpretable. A mathematical group of elementary operations, which are not reduced to each other, is suggested as a fundamental notion for the living world. The mathematical group is the functional invariant of the living organization. The regulations for mechanisms of integrational closure of elementary operations onto each other in the course of biological self-organization are examined as well. The generalized definitions of the following notions are given: organism, organization level, information, entropy, evolutionary direction, life. The suggested functional invariant of organization appears to be fundamental not only for biological objects themselves but also for any organizational levels of the living. The earlier variants of the results obtained in this direction was prepublished [2a -- 2c]. ********************************************** Part I "Axiomatic Backgrounds of the Life" Here are the main statements, notions and interpretations: 1. The set of compatible systems (M) is the basis of the living. These systems are formed by fixation of free environmental energy in their structure and, as a result, they are able to do some work. Such systems will further be called endergonic ones. Compatibility of these systems is structural homomorphism in character, i.e. they have a fundamental unity of specific morphological arrangement. In consequence, there is some easiness of their interaction up to the possibility to be interconverted. 2. The environment, as an initial source and a final drainage receiver of substance and/or energy, is necessary for existence of the living. The environment is assumed to afford some interval of conditions for realization of optimal kinetic stability of structures of the living. 3. Endergonic systems of the set M possess such a vast structural variety (polymorphism), that they are capable of establishing ten pairs of simple mutually opposite functional relations between each other, i.e. between their constituents and the environment (set R) (SEE Table 1). This set of functions is basically invariant for the living. The notion "function" used here is analogous to its use in the work by G.A.Chauvet [3]. Stressing the orientation and asymmetry of the notion "function", the word "operation" is used in this work as a synonym. The operations of set R and their combinations entirely cover all kinds of relations that are obligatory for emergence and a stable existence of endergonic systems of the set M. The operations are equally performed with substance and energy and information. ______________________________________________________________________ Table 1. Set R includes ten pairs of mutually opposite simple operations that underlie the living. ______________________________________________________________________ Direct operations Reverse operations ______________________________________________________________________ 1. Identification 1'. Identification 2. Right-hand mirror reflection 2'. Left-hand mirror reflection 3. Change of the relative 3'. Conservation of the relative position of the operation position in space (fixation object in space or return of the position) 4. Transformation of 4'. Conservation of configuration configuration (resistance to transformation; reconstruction of configuration) 5. Increase (growth, 5'. Decrease (reduction, addition ...) subtraction, elimination) 6. Entrance 6'. Going out 7. Connection (maintenance 7'. Disconnection or increase of interaction (including isolation) probability, binding, adhesion, compilation of two or more operation objects) 8. Switch-on, i.e. mediating 8'. Switch-off initiation of a specific action of the operation object, affected by a definite way 9. Source 9'. Drainage receiver 10. Concentration 10'. Scattering ______________________________________________________________________ Operations R generate the mathematical group G over all possible combinations. The proofs are: 1. In case of combinations (unlike arrangements) the sequence of operations is not significant, hence the performance of properties of associativity appears. 2. All combinations of operations belong to one group. This follows from the conditions of specifying this set, in combinations of which all possible changes in the system are embedded. 3. There is the only common unit, which is the operation of identification. 4. There is a reverse element for each element (SEE Table 1). Self-organization is a spontaneous emergence of the structures of order in the course of spontaneous processes. The structures of order of endergonic systems are in principle thermodynamically instable kinetic stabilities. During self-organization the spontaneous transitions from one structure of order to another are conditioned by thermodynamic instability (nonequilibrium). The possible types of the structures of order of endergonic systems are as follows: 1. The static ones. For instance, organic molecules (including macromolecules) and their crystals. 2. The informationally unmediated stationary structures. They are dynamic structures existing due to an informationally unmediated return to the initial position (state, form). For example, dissipative autocatalitic structures of the Beloussov - Zhabotinsky reaction type [4], whirlwinds, rivers (permanent stations based on the water circulation)... 3. The informationally mediated stationary structures. They are dynamic structures existing due to an informationally mediated return to the initial position (state, form). The kinds of such automorphic processes are: reproduction, adaptive behaviour, recovery (regeneration, repair). As it is seen from the points listed, any endergonic structure of order can be characterized by its specific group of symmetry. In particular, this appears from the fact that the set of transformations, which make the system return to its initial position (state, form), is just one of the definitions of a group of symmetry. Group G characterized here is common to all the possible endergonic structures. ************************************************** Part II "Integral Criteria of the Evolutionary Direction, Information, Life, Culture " Let us consider two neighbouring levels of the system organization: the system itself and its subsystems of the first below-lying level. When examining the system (a complex of interacting subsystems) as a single whole (as if "from outside"), we are speaking about the macroapproach. Here the inner subsystems (microlevel) are ignored, and generalized characteristics of the state only are relevant. The generalized characteristics, like free energy, symmetry and entropy, allow us to speak about the system transformations (transitional structures of order). In case of the microapproach the system is supposed to be examined from inside, and behavioral characteristics of the subsystems (microsystems) are relevant. In the macroapproach the notion "space of possible (virtual) transitional states of structures of order" is used. In the microapproach we use the notion "space of possible behavioral forms of the subsystem (microsystem) of the first below-lying level of system organization". There are certain criteria of the direction of spontaneous autonomous transformations of macrosystems, i.e. a spontaneous behavior of microsystems within an isolated macrosystem is only "permitted" when: - free energy of the macrosystem (its capability of doing some work) decreases; - entropy of the macrosystem increases; - symmetry of the macrosystem increases. Criteria 1 and 2 formulate the 2nd law of thermodynamics. Criterion 3 is a corollary of the general principle of symmetry of physical phenomena formulated by Pierre Curie [5] in 1894. This principle is also developed in the work by V.A. Kopcik [6]. Free energy of the system is defined as the ability to do some work autonomously. Symmetry of the system is characterized by an at most high group of transformations, which leave the system unchanged. As for entropy, the matter is more difficult. In this work complete entropy of the isolated system is defined as a volume of the space of possible transitional structures of order on their way to equilibrium. This definition is close to that of absolute entropy by Max Plank [7,8], which does not require any probabilistic ideas and is applicable to physical systems with any number of freedom degrees. The author believe that the conception about space of possible transitional structures of order could be defined as a space of possible transitional groups of the system symmetry. Hence it appears that complete entropy of the system is an extensive characteristic of its potential (evolutionary achievable) symmetry, which seems to be rather paradoxical. To think that the system is entirely isolated is just idealization. When extreme principles are applied to a real system, recourse to its mental isolation must be had. In fact, the system remains open. The mental isolation of the system is emphasized by means of the notion "independence" of its transformations (behavior). It is most correct to use the formulated extreme principles locally, as a criterion for choosing the direction of spontaneous processes at each concrete point of evolution, but not "on the whole". Origin and evolution of the living is self-organization of structures of order. The complexes of endergonic systems of set M act in the capacity of these structures and carry the combinations of operations of set R. Spontaneous formation of these complexes occur in such a way that the combinations, satisfying the formulated extreme principles, are realized. New self-organized structures of order are formed on the basis of the kinetic stabilities achieved earlier. So, each step within self- organization means an increase of specific contribution of new-emerging structures to realization of the formulated extreme principles, in particular the specific power and/or specific symmetry of the system continuously increase. Therefore the integral criteria of the evolutionary direction is arising of the specific product of the power of the system on its symmetry (the mass of the system is the divisor of the product of its power on its symmetry). Information is the central factor determining the stability and the functional efficiency of informationally mediated stationary structures, the living organisms belong to. Hence, the main link in the evolutionary process of the living is functional perfection for obtaining, accumulating, processing and using information. Let us consider the stages of emergence of living organisms on the basis of the set of endergonic systems M. The following steps of self- organization of endergonic systems leading to origin and evolution of the living can be discerned: 1) emergence of elementary cycles of catalysis; 2) emergence of cycles of autocatalysis consisting of elementary cycles; 3) emergence of hypercycles [9] consisting of cycles of autocatalysers; 4) formation of functional interclosures (organisms) over the operations of set R of hypercyclic, autocatalytic, catalytic and simple noncatalytic structures. Two operations of the functional interclosures finally remain open for the environment: sources and drains. Functional interclosures (organisms), formed by this process fill up the set of self-organized endergonic systems M. They belong to a higher level of organization. The new level of organization is initial for recurrence of the described self-organized logic etc. The level of organization is a stage in evolution of systems, on which the functional interclosure of their subsystems goes with a principle unity of their specific morphological conformation (with their structural homomorphism). The functional interclosure of organism subsystems makes sense that when interacting with each other, with the environment and other organisms, they provide a kinetically stable existence and development of the organism and, thereby, the existence and development of each other. It should be noted that such a functional interclosure is realized in the limit of all organisms and factors of the environment and inner medium, i.e. within the life process as a whole (biosphere). A living organism is therefore both a functional interclosure and a partial functional closer of the life process factors to a single whole. An automatic forced selection of alternative combinations of the elements under consideration goes in the direction satisfying the formulated extreme principles. Information mediating the selection of these behavioral forms appears at the points where alternative behavioral forms (combinations of dissipation flows) are equally probable or realization of hardly probable behavioral forms is necessary from the standpoint of satisfaction of extreme principles. Realization of the selection of the given behavioral form by the system occurs with the help of controlling subsystems making selective steps in potential kinetic barriers, which keep back the dissipation of free energy of the system and/or selectively lower such potential barriers in accordance with the available information. The mediating function of information becomes a participator of principle in mutual coordination of self-organized endergonic systems beginning with the stage of emergence of hypercycles. Information is reflection of a definite trajectory of behavior of the system in the space of its possible behavioral forms that allows the system an identical reproduction of the selection made by the system earlier in its behavior. It can be also said that information is an interrelation of events fixed in any way. In the last sense information and reflection of the function (operation) is one and the same. Information is the central link in the mechanisms of coordination of operations of set R within subsystems of organisms, communities of organisms and the whole biosphere. Functionally, information manifests itself in three different forms, being part of three integrating functions: control, reproduction and creation. The three functions integrate elementary operations of set R to a single whole within functional interclosures. Control is a directed change in the probability of realising alternative trajectories of the controlled object behavior. Reproduction is a cycle of the system transformations under control, which results in emergence of its copy. Creation is a combinatorial process aimed at forming a new type of information mediating the system behavior control and/or reproduction in higher ( in accordance to the extremal principles) evolutionary level. The obtained information, in particular, realizes the process of polymorphic reproduction of the system (i.e. reproduction of a new type of the system placement by introducing and/or removing its elements and/or by changing its structure). Reproduction is the hypercycle of the control cycles and creation is the hypercycle of reproduction cycles. Information, arisen in creation cycle is the base for reproduction of controlling structures. Life is a spontaneous process of combinatorial generation of the group G of functional interclosures (organisms, organizations) by combining the operations of set R above the set of endergonic systems M. Culture is the whole complex of all highest (the evolutionary most progressive) achievements in all fields of human activities. Estimation of evolutional progressivity occurs according to the evolutionary progress criterion, which has been formulated in this work. Human activities proceed within the limits of universal mechanisms of selforganization that are typical for the living (SEE the definition of life and the above context of it). In general outline these activities can be defined as the man-mediated process of combinatorial mutual enclosure of universal integrating operations: control (C), reproduction (R) and creation (Cr.). In the simplest and most general form this combinatorial enclosure is represented by all possible two-by two combinations of the three integrating operations. The 9 pairs of the combinations have been analysed, and the conclusion has been made that they correspond to the most general functional elements of culture or (the same) to the most general fields of professional human activities (SEE Table 2). The real content of individual elements of culture (professional positions) are in addition profoundly differentiated. So, each of the 9 cells in Table 2 can be divided into analogous 9 subcells. This results from the combinatorial nature of life. And according to common sense, it is clear as well, that, for instance, there are some elements of art in real policy, and there are some elements of ideology in real religion (or art). ********************************************************************** Table 2. Functional Elements of Culture (the most general fields of professional human activities) as combinatorial length two combinations of integrating operations: creation, reproduction and control ********************************************************************** * Creation (Cr) * Reproduction (R) * Control (C) ********************************************************************* Cr * 1 CrCr * 2 CrR * 3 CrC * * Religion * Science * Policy * * Art * * * * Metaphysics * * * ********************************************************************* R * 4 RCr * 5 RR * 6 RC * * Upbriging * Education * Teaching * * (Game) * (Enlightenment) * (Drill) * * * Technology * * ********************************************************************* C * 7 CCr * 8 CR * 9 CC * * Methodology * Organization * Ideology * * * Management * * ********************************************************************* CrCr: creation of creation: CR: creation of reproduction; etc. New information appears in the course of creation, and by means of reproduction it is used as the basis of control processes. Old information moves in the opposite direction. This results from the definitions formulated in this work as well as from common sense. Hence, a conclusion inevitably comes to mind: in culture new information moves from religion, art and metaphysics through science to policy and, farther on, to upbringing, education, teaching, methodology and, in the end, to ideology (SEE Table 2). Old information moves in culture in the opposite direction beginning with ideology. The report on the integral logic of organization and evolution of the living would be incomplete without an additional precision of creation mechanisms. When defining creation as a specific combinatorial process, sources of its participators and its motive forces should be considered as well. Creation can occur on the basis of a fixed number of known elements to be combined. In case the range of known (accessible) combined elements is not replenished, the creation process may reach a deadlock, and new creative prospects can arise thanks to discovery either of new, earlier unknown elements or to that of new sources of the exhausted known elements or to discovery of new properties of the old elements. Thus, discovery is a special form of the creation process replenishing it with new participators. Let us consider the motive power of the combinatorial creation process. When life is born, it is mainly a chaotic thermal motion in the primary "broth" of organic and inorganic molecules. In the most ordinary organisms the chaotic behavior is supplemented with sexual process, the essence of which is to provide genetic combinations. In the human society the sexual process mounts to the highest forms of love , which provides motivation of both creative genetic informational combinations and the tendency towards a search as well as a creative combination of information as knowledge that is the basis of human activities and creative development of techniques. REFERENCES 1. Maddox,J. Nature 363, 13 (1993). 2a. Kalmykov,V.L. "The significance of the Theoretical Biology for Biotechnology" (preprint in Russian), Pushchino, 1988, 11 pages. 2b. Kalmykov V.L. (1995) "The Functional Scheme of Organization and Evolution of the Living. The meccano of a biocomputer", SMBnet archives in directory smb/pubs as two files: and , files may be got via ftp://ftp.ncifcrf.gov/smb/pubs/README_VL_Kalmykov_FSOEL or via http://www.iam.ubc.ca/spider/spiros/smb/index.html (SMB - the Society for Mathematical Biology. Information about SMBnet: e-mail to with "HELP" in the body of mail ). 2c.. Kalmykov V.L. and Kharitonov A.S. (1996) "Theoretical Global Ecology. Integral Logic of Organization of the Living", SMBnet archives in directory smb/pubs as two files: and , files may be got via ftp://ftp.ncifcrf.gov/smb/pubs/README_VL_Kalmykov_ILOL or via http://www.iam.ubc.ca/spider/spiros/smb/index.html 3. Chauvet,G.A. Phil. Trans. R. Soc. Lond. B. 339, 425-444 (1993). 4. Jantch,E. Autopoiesis. A Theory of Living Organization (ed. Zeleny,M.) 65-88 (North Holland, N.Y., 1981). 5. Curie,P. Journ. de Phys. (III),3,393 (1894). 6. Koptsik,V.A. J. Physics vol. C, 16 (1983). 7. Planck,M. Z. Phys. 35, 49-57 (1925). 8. Planck,M. Sitzungsber. Acad. Wiss. Berlin, 442-451 (1925). 9. Eigen,M. & Schuster,P. The Hypercycle. A Principle of Natural Self- Organization (Springer-Verlag, Berlin, 1979).