THE GENERALISED THEORY OF LIFE

(The Abstract Theory of Spontaneous Organising and Evolving of Complex Systems - Towards a General Physical Understanding and Integral Computer Simulation of Life).

V.L. Kalmykov

(For the latest version of this project paper see:Author's Web Site)

Abstract

This paper is the result of attempts by a biologist to formulate the logic of organization and the evolution of life for its probable use in Artificial Intelligence, especially for purposes of Artificial Life and Evolutionary Computing. The essence of the method is the invention of ideal objects (creative synthetic definitions) that are still missing from a sufficiently good understanding of life. Generalized definitions of the following notions are given:

• Endergonic structures

• Types of the endergonic structures of order

• Information

• Complete entropy

• Level of organization

• Ten pairs of mutually opposite elementary operations (operations form a mathematical groupoid) that underlie the living

• 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

• Culture

• Functional elements of culture

• Discovery

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. Whilst traditional in 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 a generalized (universal) functional description is necessary. This work presents such a generalized theoretical description of life. It includes elements of an axiomatic approach and is physically interpretable. A mathematical groupoid of elementary operations, which are not reducible to each other, is suggested as a fundamental notion for the living world. The mathematical groupoid is the functional invariant of life and organization. Rules for the mechanisms of integral closure of elementary operations onto each other in the course of biological self- organization are examined also.

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, this is the only viable way to formulate the main points of organization, behaviour and evolution of life for science and technological use. The law of organization of integral structure and the structure symmetry is one and the same. The structure symmetry is the highest automorphism group of the structure [1].

Some earlier variants of the results obtained in this direction were prepublished [2-6].

Group Theoretic Approach

The main statements, notions and interpretations.

1. A set of compatible structures (M) is the basis of the living. These structures are formed by the fixation of free environmental energy in their structure (e.g. organic molecules) and, as a result, they are able to do some work. Such structures will further be called endergonic ones. The compatibility of these structures is structurally homomorphic in character, i.e. they have a fundamental unity of specific morphological arrangement. In consequence, this eases their interaction encouraging the possibility of reciprocal transformations.

2. The environment, as an initial source and a final drainage receiver of substance and/or energy, is a necessary condition for the existence of the living. The environment sets the parameters under which living systems realise optimal kinetic stability in their structures.

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 are the basic invariants for the living. The notion "function" used here is analogous to its use in the work by G.A.Chauvet [7]. 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 orthogonal elementary operations (with substance, energy and information) on the set of compatible endergonic structures of set M that underlie the living

Operations R generate the mathematical groupoid G over all possible combinations. The proofs are:

1. In the 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 one common unit, which is the operation of identification.

4. There is a reverse element for each element (SEE Table 1).

Organization

Self-organization is the spontaneous emergence of structures of order in the course of spontaneous processes. The endergonic structures of order are in principle thermodynamically unstable yet kinetically stable (in other words far from equilibrium, yet maintaining a constant state). During self-organization the spontaneous transitions from one structure of order to another are conditioned by this 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 (lifeless). They are dynamic structures existing due to an informationally unmediated return to the initial position (state, form). For example, dissipative autocatalytic structures of the Beloussov - Zhabotinsky reaction type [8], whirlwinds, rivers (permanent stations based on the water circulation)...

3. The informationally mediated stationary structures (alive). They are dynamic structures existing due to an informationally mediated return to the initial position (state, form). Examples of such automorphic processes are: reproduction, adaptive behaviour, recovery (regeneration, repair).

As can be 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), are 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 lower 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 the generalized characteristics of the state only are relevant. These 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 lower level of structure organization".

There are certain criteria (extreme principles) for 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 [9] in 1894. This principle is also developed in the works by A.V Shubnikov and V.A. Kopcik [1,10].

Free energy of the structure is defined as the ability to do some work autonomously.

Symmetry of the structure is characterized by the highest group of transformations, which leave the structure unchanged. "Highest" means here "including all possible transformations"

Entropy

As for entropy, the matter is more difficult. In this work the complete entropy of an 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 [11,12], which does not require any probabilistic ideas and is applicable to physical structures with any number of degrees of freedom. The author believes that the conception about the 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 an idealization. When extreme principles are applied to a real structure, we isolate it as a mental abstraction. In fact, the structure remains open. The mental isolation of the structure is emphasized by means of the notion of the "independence" of its transformations (behavior). It is valid 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 a self-organization of the 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 in the 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 arises as 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).

The direction of evolution is defined as correspondence with this criterion. This criterion is one and the same for both the direction of evolution and for the direction of progress.

Emergence

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 the 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 [13] 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 to 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 basic for the 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 an invariant not only for organisms and organizations, but also for ideas. In the latter case it may be named 'the invariant cognitive cycle'.

A new 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, so that when interacting with each other, with the environment and with 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 at one level and a partial functional closer of the life process factors to a single whole at a higher level. 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

Information is the central factor determining the stability and the functional efficiency of informationally mediated stationary structures that living organisms belong to. Hence, the main link in the evolutionary process of the living is a 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 us simply and distinctly to understand the physical essence of these phenomena until now.

A long search for physical specificity of the living did not permit us 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 organisms, and with each other.

The coordination and 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 a direct way of realizing extreme physical principles, as these occur in traditional physics, but an organizationally mediated one. When considering the living as a "black box", then the change in generalized physical characteristics at the entrance and exit of this black box will correspond to our extreme physical principles. At the same time, some processes, hardly probable from the standpoint of traditional physics, may deterministically occur inside this black box. Determined realization of such hardly probable processes is the consequence of living organization, 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 a 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 mechanism of the coordination of operations of set R within the 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.

1. Control is a directed change in the probability of realising alternative trajectories of the controlled object behavior.

2. Reproduction is a cycle of the structure transformations under control, which results in emergence of its copy.

3. 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, arising in the 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.

Cultural Implications

Culture is the whole complex of all the highest (the evolutionary most progressive) achievements in all fields of human activities. Estimates of evolutional progressivity occurs according to the evolutionary progress criterion, which has been formulated in this work.

Human activities proceed within the limits of the universal mechanisms of self-organization that are typical for the living (SEE the definition of life and the above in context). 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 length two permutations of the three integrating operations. The 9 pairs of the permutations 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 formulated 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 length two permutations of integrating operations: creation, reproduction and control

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 upbringing to methodology and, farther on, to science, education, organisation, policy, teaching 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 united logic of organization, behaviour and evolution of the living would be incomplete without some additional details about creation mechanisms. When defining creation as a specific combinatorial process, sources of its participators should be considered as well. Creation can occur on the basis of a fixed number of known elements to be combined. Where the range of known (accessible) combined elements is not replenished, the creation process may reach a deadlock, and new creative prospects can only arise due to the discovery of either new, earlier unknown elements, 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.

I thank Mr. Alexander S. Kharitonov for stimulating, helpful discussions and technical assistance.

References

2. Kalmykov, V.L.: "The significance of the Theoretical Biology for Biotechnology" (preprint in Russian) Pushchino (1988) 11 pages

3. Kalmykov V.L.: "The Functional Scheme of Organization and Evolution of the Living. The meccano of a biocomputer", SMBnet archives (1995) in directory smb/pubs as two files:
README_VL_Kalmykov_FSOEL and VL_Kalmykov_FSOEL.tar.Z.; files may be got via:
ftp://ftp.ncifcrf.gov/smb/pubs/README_VL_Kalmykov_FSOEL
or http://www.iam.ubc.ca/spider/spiros/smb/index.html
or in text format locally vlkfsoel.txt

4. Kalmykov V.L. and Kharitonov A.S. "Theoretical Global Ecology. Integral Logic of Organization of the Living", SMBnet archives (1996) in directory smb/pubs as two files:
README_VL_Kalmykov_ILOL and VL_Kalmykov_ILOL.tar.Z; 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
or in text format locally vlkilol.txt

5. Kalmykov V.L.: "The Integral Algorithm of Organization and Evolution of the Living Up to Culture - the Possible Instrument for Genetic Programming". In Proceedings of the First Online Workshop on Soft Computing (1996) pp. 284-289 Nagoya University
available in text format locally vlkiaoe.txt

6. Kalmykov V.L. (1997) "The Abstract Theory of Evolution of the Living" in Proceedings of AISB 1997 Wokshop on Evolutionary Computing, 7th - 8th April 1997, Manchester, pp. 25-30.
available http://sun.ipr.serpukhov.su/~vvv/IBK_RAN/kalmikov.html

7. Chauvet, G.A.: Phil. Trans. R. Soc. Lond. B. 339 (1993) 425-444 8. Jantch, E.: Autopoiesis. A Theory of Living Organization (ed. Zeleny (1981) 65-88 (North Holland, N.Y.)

9. Curie, P.: Journ. de Phys. (III), 3 (1894) 393

10. Koptsik, V.A.: J. Physics vol. C (1983) 16

11. Planck, M.: Z. Phys. 35 (1925) 49-57

12. Planck, M.: Sitzungsber. Acad. Wiss. Berlin (1925) 442-451

13. Eigen, M. & Schuster, P.: The Hypercycle. A Principle of Natural Self-Organization (Springer-Verlag, Berlin) (1979)

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