The Abstract Theory of Evolution of the Living
Institute of Cell Biophysics, Russian Academy of Sciences,
Pushchino, Moscow Region, 142292, Russia
Email:
kalmykov@ibfk.nifhi.ac.ru
Abstract. The paper is the result of attempts of the biologist to formulate the logic of evolution of the living for its probable use in Artificial Intelligence, especially for purposes of Evolutionary Computing and Artificial Life. The logic has been fulfilled as the abstract theoretical model, which integrally reflects the universal functional algorithm of evolution of the living. The essence of the method was the invention of an ideal objects (a creative synthetic definitions) that are still absent for a sufficient understanding of evolution. The generalized definitions of the following notions are given:
Endergonic structures; Types of the endergonic structures of order; Information; Complete entropy; Level of organization;
Functional intraclosures (organisms, organizations);
Criterion of the life evolution direction (Parameter of the comparative evolutionary progress of the structures);
Creation; Life; The invariant cognitive cycle; ...
Introduction.
This work presents a generalized theoretical description (functional scheme) of the living. 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 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 groupoid of elementary operations, which are not reduced to each other, is suggested as a fundamental notion for the living world. The mathematical groupoid is the functional invariant of the living organization. The regulations for mechanisms of integral closure of elementary operations onto each other in the course of biological self- organization are examined as well.
The suggested functional invariant of organization and evolution appears to be fundamental not only for biological objects themselves but also for any organizational levels of the living.
Why do I try to use a group theoretical approach? As I understand, it is the only one way to formulate the main point of organization, behaviour and evolution of the living for science and technological use. The low of organization of integral structure and the structure symmetry is one and the same. The structure symmetry is the most high automorphism group of the structure [1].
The earlier variants of the results obtained in this direction were prepublished [2-4].
The main statements, notions and interpretations.
1. The set of compatible structures (M) is the basis of the living. These structures are formed by fixation of free environmental energy in their structure and, as a result, they are able to do some work. Such structures will further be called endergonic ones. Compatibility of these structures 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 of a reciprocal transformation.
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 structures 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 [5]. Stressing the orientation and asymmetry of the notion "function", the word "operation" is used in this work as a synonym.
Table 1. Set R includes ten pairs of mutually opposite elementary operations (with substance, energy and information) on the set of compatible endergonic structures of set M 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 position in space | 3'. Revertion of position in space |
| 4. Transformation of configuration | 4'. Restoration of configuration |
| 5. Increase of number of elements | 5'. Decrease of number of elements |
| 6. Provision of inlet | 6'. Provision of outlet |
| 7. Connection | 7'. Isolation |
| 8. Switching-on, i.e. mediating initiation of a specific action of the operation object, affected by a definite way | 8'. Switching-off |
| 9. Inflowing | 9'. Outflowing |
| 10. Concentrating | 10'. Scattering |
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 structures of the set M. The operations are equally performed with substance and energy and information.
Operations R generate the mathematical groupoid G over all possible combinations. The proofs are:
1. In case of combinations (unlike permutation) the sequence of operations is not significant, hence the performance of properties of associativity appears.
2. All combinations of operations belong to one groupoid. This follows from the conditions of specifying this set, in combinations of which all possible changes in the structure 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).
Conceivably the groupoid G might represent a strict group, but there is necessary to look more closely at this suggestion.
Self-organization is a spontaneous emergence of the structures of order in the course of spontaneous processes. The endergonic structures of order 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 order of the endergonic structures 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 [6], 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 structure return to its initial position (state, form), is just one of the definitions of a group of symmetry. Groupoid G characterized here is common to all the possible endergonic structures.
Let us consider two neighbouring levels of the structure organization: the structure itself and its substructures of the first below-lying level. When examining the structure (a complex of interacting substructures) as a single whole (as if "from outside"), we are speaking about the macroapproach. Here the inner substructures (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 structure transformations (transitional structures of order).
In case of the microapproach the structure is supposed to be examined from inside, and behavioral characteristics of the substructures(microstructures) 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 substructure (microstructure) of the first below-lying level of structure organization".
There are certain criteria of the direction of spontaneous autonomous transformations of macrostructures, i.e. a spontaneous behavior of microstructures within an isolated macrostructure is only "permitted" when:
- (1) free energy of the macrostructure (its capability of doing some work) decreases;
- (2) entropy of the macrostructure increases;
- (3) symmetry of the macrostructure 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 [7] in 1894. This principle is also developed in the works by A.V Shubnikov and V.A. Kopcik [1,8].
Free energy of the structure is defined as the ability to do some work autonomously.
Symmetry of the structure is characterized by an at most high group of transformations, which leave the structure unchanged. "Most high" mean "including all possible transformations"
As for entropy, the matter is more difficult. In this work complete entropy of the isolated structure of order 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 [9,10], which does not require any probabilistic ideas and is applicable to physical structures 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 structure symmetry. Hence it appears that complete entropy of the structure is an extensive characteristic of its potential (evolutionary achievable) symmetry, which seems to be rather paradoxical.
To think that the structure is entirely isolated is just idealization. When extreme principles are applied to a real structure, recourse to its mental isolation must be had. In fact, the structure remains open. The mental isolation of the structure 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 structures 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 structure continuously increase. Therefore
the integral criterion of the evolutionary direction is arising of the specific product of the power of the structure on its symmetry (the mass of the structure is the divisor of the product of its power on its symmetry).
Direction of evolution is defined as correspondence with this criterion. This criterion is one and the same for direction of evolution and for direction of progress.
Let us consider the stages of emergence of living organisms on the basis of the set of endergonic structures M. The following steps of self- organization of endergonic structures 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 [11] consisting of cycles of autocatalysers;
4) formation of functional intraclosures (organisms) over the operations of set R of hypercyclic, autocatalytic, catalytic and simple noncatalytic structures. Two operations of the functional intraclosures finally remain open to the environment: inflowing from sources and outflowing of drains.
1') Beginning of the next iteration of the self-organization. Functional intraclosures (organisms), formed by this process fill up the set of self-organized endergonic structures 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 last peculiarity - the functional isomorphism of organization of the living on any levels of organization is the property of the fractal organization of life.
It may be hypothesized that the algorithm of the cycle of self-organization from 1 to 1', etc. is the invariant not only for organisms and organizations, but and for ideas. In the last case it may be named the invariant cognitive cycle.
The level of organization is a stage in evolution of structures, on which the functional intraclosure of their substructures goes with a principle unity of their specific morphological conformation (with their structural homomorphism).
The functional intraclosure of organism substructures 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 intraclosure 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 intraclosure and a partial functional closer of the life process factors to a single whole. In the last sense the biosphere (the life process as a whole ) is interclosure of all of the intraclosures (organisms) in the united intraclosure. 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 structure occurs with the help of controlling substructures making selective steps in potential kinetic barriers, which keep back the dissipation of free energy of the structure 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 structures beginning with the stage of emergence of hypercycles.
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.
From our standpoint the physical essence of information and the physical essence of the living are in close interrelation. The well- known theory of optimal coding by Claude Shannon, based on the statistical determination of entropy, is very often called the theory of information. Yet both statistical manipulations by quantity of bits in a file and statistical manipulations by quantity of individuals in a population did not allow simply and distinctly to understand the physical essence of these phenomena un now.
A long search for physical specificity of the living did not permit to relate it either to growth, or to reproduction, or to structural regeneration, or to substance exchange ... These phenomena have been found in crystals and other purely physicochemical structures. Information is the only attribute, which specifically inheres in the living. It is a configuring mediating coordination of all processes, taking place in organism, with each other.
Coordination, organization of all living processes presume the presence of purposefulness that is intrinsic for the living. To our mind, the physical side of this purposefulness consists in that the living is not the direct way of realization of extreme physical principles, as it occurs in the common physics, but the organizationally mediated one. When considering the living a "black box", then the change in generalized physical characteristics at entrance and exit of this black box will correspond to extreme physical principles. At the same time, some processes, hardly probable from the standpoint of the common physics, may determinedly occur inside this black box. Determined realization of such hardly probable processes is the consequence of that the living is organized, which is mediated by information. Thus, information fulfills the function of mediating the co-organization of living processes. Life is, in its turn, the way of realizing extreme principles of physics through integral co-organization of behaviour of living elements.
Information is reflection of a definite trajectory of behavior of the structure in the space of its possible behavioral forms that allows the structure an identical reproduction of the selection made by the structure 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 is one and the same.
Information is the central link in the mechanisms of coordination of operations of set R within substructures 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 intraclosures.
Control is a directed change in the probability of realising alternative trajectories of the controlled object behavior.
Reproduction is a cycle of the structure 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 structure 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 structure and of the substructures (i.e. reproduction of a new type of permutation of elements by introducing and/or removing its elements and/or by changing configurations).
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 groupoid G of functional intraclosures (organisms, organizations)
by combining the operations of set R above the set of endergonic structures
M.
I thank Mr. Alexander S. Kharitonov for stimulating, helpful discussions and technical assistance in writing and Mrs. Larisa F. Kun'ieva for help in the electronic submission of the paper.
References
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ftp://ftp.ncifcrf.gov/smb/pubs/README_VL_Kalmykov_FSOEL
or http://www.iam.ubc.ca/spider/spiros/smb/index.html
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