Information and biology

J. Social

Biol.

Struct.

1978

1, 95-108

Information M. V. Volkenstein Institute

of Molecular

Biology

and

and biology and D. S. Chernavskii

Physical Institute Moscow, USSR

of the Academy

of Sciences

of USSR,

The statistical sense of information is treated using the phase space. The reception of information is connected with the non-equilibrium and non-stability of the receptive system. The tentative definition of the value of information can be introduced according to the results of its reception. Just the value of information is of importance for biological processes. The value of information depends on the level of its reception and is directly connected with the redundancy and indispensability of information. Some biological examples are presented. Biological development both phylogenetic and ontogenetic involves an increase of the quantity and of the value of information.

Introduction The evolution of the Universe, biological evolution as a specific expression of the evolution of the Universe, the ontogenetic development of a living organism and the creative activity of man mean the creation of new information. In other words, in every one of these various phenomena exist situations of some choice between several possibilities made by the system. Such a situation means the existence of instabilities in the state of the system; the choice carries the system into one of several relatively stable states. These transitions are irreversible-evolution does not go back, an adult organism does not transform into a zygote, the words which form a verse do not go back into their initial chaotic mixture. The concept that irreversible creation of information is the result of instabilities allows one to treat the most general dynamic laws governing the Universe and man in a unified manner. As was shown by Quastler (Quastler, 1964; Bl umenfeld, 1974) the creation of new information is the ‘memory’ of accidental choice. This means the irreversible transition from the unstable (‘choosing’) into the stable (‘chosen’) state. Such a process is different from the recognition of information masked by noise, for instance, if a previously unknown regularity is discovered (Quastler, 1964). In this sense, the theory of the self-organization of biological macromolecules proposed by Eigen (1971) does not describe the arising of new information. Prebiological selection in this theory is based not on the accidental choice but on the selection of the macromolecular chains which possess the maximal selective value a priori for the given boundary conditions. A homogeneous world lacking structural organization would not contain any information. No imaginable form of life would be possible in such a world. According to contemporary theories, such was the initial state of the clot of plasma from which the Universe arose lOi years ago. However, this state was unstable.

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M. V. Volkenstein and D. S. Chernavskii

The further development of the Universe, the formation of its heterogeneity, means the creation of the new information. The aim of this paper is the treatment of the notion of levels of information. As will be shown, information in biology must be used in a broader sense than is usual. The following characteristics of information require definition and analysis : (i) the quantity of information, (ii) macroscopic and microscopic information, (iii) the redundancy of information, (iv) the indispensability of information, and (v) the value of information. We meet with the greatest difficulties in the treatment of the value (sense, context) of information. However, just this characteristic is the most important one in the studies of biological development (Volkenstein, 1977).

The theory

of information

and statistical

thermodynamics

As is known, the choice of one event from r events possessing equal probabilities gives the quantity of information (called further information): I = logsl?. I’ is the number of microstates or the statistical entropy is expressed in a similar way S = klnl?,

(1) weight of the initial system. The (2)

where k = 1.38 x lo-ls erg grad-l or 3.31 x 10mz4 entropic units (e.u.), i.e. cal grad-l. Expressions (1) and (2) are equivalent in the same sense as mass and energy in the relation E = mc2 (Blumenfeld, 1974). Correspondingly, the information can be calculated in e.u. and the entropy in bits. The sense of this equivalence is that the entropy expresses the information which is lacking for the total description of a statistical system. Therefore the conservation law is valid (Layzer, 1975): I+ S = const.

(3)

According to the Nernst theorem, during the cooling of an equilibrium ideal crystal from the temperature T to 0 “K the entropy decreases from S, to zero and the information increases by the quantity AI = S,. In the reverse process the entropy increases to S, which is maximal at this temperature and AI decreases to zero. If we compare the crystal with its melt, the information obtained during the crystallization is equal to the loss of entropy. The equivalence of entropy and information means the possibility of a statisticalthermodynamic treatment of information. Entropy is a macroscopic characteristic of a statistical system. Obviously, in these examples, we have to do with the macroscopic information. The loss of information, let us say in the heating of a system, involves an equivalent increase of entropy because of transformation of the macroscopic information into the microscopic information (Layzer, 1975). Let us consider the evaporation of a liquid contained in a vessel. Before the evaporation, there exists macroscopic information about the localization of the molecules in a definite part of the phase space. After the evaporation the phase volume, occupied by the molecules, becomes strongly expanded and the initial macroscopic information is transformed into the microscopic information, in particular into the information about the correlations between the velocities of molecules in the gaseous phase,

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97

arising as the result of their collisions. This information cannot be registered because of the instabilities in the motions of the single molecules determined by collisions. The ‘microscopic information’ cannot be memorized. The statistical character of the system is determined just by the instabilities and therefore the system can be described by the value of entropy (cf. Romanovsky, Stepanova & Chernavskii, 1975). From the conservation law (3) it follows that during the evaporation of liquid (Z-liquid, g-gas) : I macro(2)+ S”’ = Imacro

+ S(U),

(4)

whereas I macro(CT) = Imacro -I&,,,, S(g) = S(‘) + Imicro. When the whole information, I becomes microscopic, and S becomes maximum in the given conditions. If the probabilities pi of the accessible microstates of a physical system are known, then the quantity b, = -logapt (5) is the number of bits necessary for the message about the observed existence of the microstate i. The quantity @) = - ~P,log,p,

(6)

equal to the information, according to Shannon, has the sense of entropy and coincides with the thermodynamic entropy if the set of p, corresponds to the thermodynamic equilibrium distribution or to the adequate non-equilibrium distribution, The difference bi’ - bi = lOg,p,/p*’

(7)

expresses the number of bits about the change of probabilities average value of this difference:

from p’ to p. The

K(P, P’) = -
due to the transition

from p’ to p. As

CP, = CP,’ = 1 i i

the quantity K(p,p’) is always positive and becomes zero only if pi = p,’ (see Schliigl, 1971). The analysis of relations between information and entropy must be based on the study of the behaviour of a system, which is able to receive or create information, in its phase space. The phase space of such a system must possess the following properties. A part of the dynamic variables (i.e. of the co-ordinates of the phase space) must form the subspace which contains a discrete multitude of the stable points. The transition of the system into the stable state from the unstable one means the reception or the creation of information. Correspondingly, the subspace, containing the unstable points, is the carrier of entropy. If it is known that the system is localized 7

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M. V. Volkenstein and D. S. Chernavskii

in a given stable point of the ‘informational subspace’, we possess the maximum possible information about the system. The information about the localization of a system in an unstable point cannot be ‘memorized’. Hence it is the microinformation, i.e. the entropy. The regions of attraction of the stable points are separated by separatrices. Every one of these regions can be treated as ‘elementary in the informational sense’. Other dynamic variables must form a totally unstable subspace which cannot be the carrier of information. This subspace is the carrier of entropy. A simple model of such a system is the so-called Chinese billiards-a board with nails and holes. A solid ball rolls on the board. The holes correspond to the stable states; if the ball hits a hole we get the whole information about the system. The stability of the ball in the hole is determined by the forces of gravity and friction. If the ball hits a hole, its kinetic energy transforms into heat, i.e. into the entropical subsystem of dynamic variables. Separatrices are the trajectories at which the ball hits a nail. If the initial co-ordinates and velocity of the ball are at a separatrix then its motion is unstable and it is impossible to predict the final result. Information is formed only if the ball hits a hole. The board of Halton is like the Chinese billiards without holes. This is a model of a globally unstable system. Evidently, in any real system formed by atoms and molecules, the phase volumes of the ‘informational’ and ‘entropical’ subspaces are incomparable-the second is much greater than the first one. The large ‘entropical’ subspace is necessary for the dissipative character of the system and therefore for the possibility of informational transitions from the unstable states into the stable ones.

The levels of reception

and the redundancy

of information

In real systems, information is contained in a message coded by some language in the general sense of this word. In particular, the language can be the usual language of a nation. The reception of the information by a real system occurs at different levels determined by the information which is already memorized by the system. The quantity of the stored information is different at different levels. Correspondingly, the quantity of the memorized information is different at different levels. It is natural to assume that the hierarchy of the reception levels is determined by the increased complexity and specialization, i.e. by the increased quantity of the stored information. Therefore the increase of the reception level corresponds to the increase of the redundancy of information contained in the perceptible message. A good example is the reception of the usual message written in some language. The first level of reception is determined by the ability of the receptor to distinguish the letters-the coding symbols of the language. At this level the receptor knows only the number N of the different letters. The appearance of every letter possesses equal probability. Hence the system gets the quantity of information II = log, N per letter. For the latin alphabet, N = 26. At the second level, the receptor possesses the knowledge about the elementary structure of the language-the probabilities p, of the appearance of single letters.

Information In this case the information

and biology

99

must be calculated with the help of Shannon’s formula:

(11) and

It is easy to show that I, < Ii, i.e. at the second reception level the message possesses redundancy equal to

R, = 1 -(&/I,).

(13)

This is the definition of redundancy according to Shannon (see Iaglom & Iaglom, 1973). At the next levels, the double, tertiary, quaternary, etc., correlations between the letters are taken into account. The redundancy

Rj = 1 -&/Ii) increases with language :

increasing

level. According

I1

I2

I3

I4

4.76

4.03

3.32

3.10

(14) to Shannon

.. .

I,

. ..

~2.1

...

(1951) for the English

I8 ~1.9 bit.

The quantity of the perceived information per letter decreases with increase of the level. Correspondingly, the redundancy increases :

R,

R,

R,

R,

.. .

R,

. ..

R,

0

0.15

0.30

0.35

.. .

~0.56

. ..

~0.60.

This means that, at the ninth level, 60 per cent of the letters contained in a message are redundant; the remaining 40 per cent of the letters are sufficient for the reception of the message. The subsequent analysis (which is much more complicated) defines the correlations at the level of words. This analysis must endeavour the sense of the message. For instance, a telegram has been sent: ‘Cannot live without you, I am thinking about you all the time, am awaiting you, burning with impatience, come, we shall be together at last . . .’ etc. Evidently most of the words here are redundant. the simplest level of reception by two words

This text can be substituted

at

‘Love, come.’ Of course we are distracted here by the emotional coloration of the text due to the ‘redundant’ words. Evidently the increase of the level, the increase of redundancy, means the increase of indispensability of the remaining non-redundant elements of the message. The same message can be perceived by different receptor systems with different sequences of levels. For the usual reader, the information contained in a book does not depend on the kind of edition of this book-on the type of printing, of paper, of cover, etc.

M. V. Volkenstein and D. S. Chernavskii Any new edition of the same book gives only the redundant information-the editions are interchangeable. For a librarian, who classifies the books according to the years of publication and other indications, different editions of the same book are not interchangeable, only the books of the same edition are redundant. For a bibliophile, only one definite edition of the book is indispensable or only one definite copy; all other books are redundant. We meet with such situations in many different fields, e.g. in philately. The redundancy of information is determined by the reception level of a given receptive system. It follows from the examples considered here that the level of reception is connected with its goal. The sequential levels in the consideration of a linguistic message mean the successive approximation toward the understanding of the structure of language and toward the understanding of the sense of the message. But the existence of a goal means the possibility of choice, and therefore the existence of unstability-the achievement of some purpose is equivalent to the transition of the receptive system from an unstable into one of the stable states (Volkenstein, 1976). The ‘conservation law’ (3) is valid if the entropy and information are determined at the same consideration level, i.e. the level of reception. At the level corresponding to the chemical reaction, the calculation both of entropy and information can be separated from the differences of the isotopic molecules. In the chemical reactions the content of isotopes practically does not change. But at the level of the nuclear reactions the identification of the isotopes, e.g. U238 and U235, is possible. The notion of identity and therefore of the redundancy of information is directly connected with the reception level. This does not mean, of course, that, for instance, the identity of particles with even spin in Bose-Einstein statistics has a relative character. The reception of information is a real physical process of interaction of a receptive system with the physical signals. Hence the identity of the objects forming a message is in the end determined by their genuine physical nature. In classical physics all objects are non-redundant in principle and the acknowledgement of them as identical or different depends on the level of reception. Therefore the notions of entropy and information are relative in classical physics. The absolute value of entropy can be established only at the level of quantum mechanics. It is determined by the discrete structure of the phase space, by the principal identity of microparticles. These problems are directly connected with the paradox of Gibbs (see Gelfer, Luboshits & Podgoretsky, 1975). The reception of information is an irreversible process proceeding in a nonequilibrium system, which possesses the non-stable and stable regions of the phase space. We must distinguish the reception of the coming information and the formation of the new information in the system under the influence of an external signal. In both cases the transition occurs from an unstable state into one of the several stable states; for the choice, the plurality of the stationary states is necessary (cf. Lavenda, 1972). However, the information obtained by the system in the first case is quantitatively connected with the information of the message and is adequate to the message in this sense. In the second case, the new information can be formed in the system independently on the external signal, as the result of fluctuation which is reinforced to the macroscopic level. This change of the system is not adequately represented by internal information and is not connected quantitatively with it. It is determined by the properties of the receptive system itself and the signal plays the role of a fluctuation. An example of such a trigger system is the ass of Buridan staying between two bundles of hay and dying from hunger because it cannot

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decide which bundle to choose. One bit of information (‘go to the right’ or ‘go to the left’) produces the transition of the ass from the unstable, hungering state to the stable state-eating hay. The same result can be obtained by chance as the result of fluctuation. The information formed in the system is not equivalent to one bit obtained. The receptive system is always a dissipative one, being not only non-equilibrium but far from equilibrium (cf. Glansdorff & Prigogine, 1973 ; Prigogine & Lefever, 1975; Prigogine & Nicolis, 1971). The value of information The quantity of information in a message can be determined at the given level of reception independently of the consequences which can be produced by the reception of this message by a real system. This is the basis of the theory of communication developed by Shannon and others. However, the reception of a message at every level means the occurrence of some events in the receptive system, i.e. a change of the system. If the receptive system does not change under the action of the message, then there is no reception. Hence the theory of information which concerns not only the transmission of messages but their reception also, must consider the events occurring in the receptive system under the influence of the message. Therefore the information has to be characterized not only by its quantity but also by its quality, or sense, or contents or value. We shall use the last word. The processes occurring in the dissipative systems are determined by the reception, storage (‘memorizing’) and creation of information. Such are the processes at every level of biological organization (the next section). The application of the theory of information to biological phenomena as also to any other processes of development require the consideration of the value of information. The qualitative discussion of this problem is given in the paper by one of us (Volkenstein, 1977). The value of information is determined by the consequences of its reception. These consequences being different at different reception levels, the value of information correspondingly varies. As already mentioned, the reception of information is an irreversible and nonequilibrium process-the information does not possess any value in the conditions of equilibrium. The quantity of information can characterize a message independently of its reception, and hence the quantity of information being complementary to entropy can be an equilibrium property. Information can possess value only if there are stable and unstable regions in the phase space of the receptive system. The value of information appears as the result of the possible transmission from the unstable state into some relatively stable state, produced by the reception of information. At a given level, only the non-redundant information is valuable. At increasing levels of reception, the redundancy of a message increases; so also does the value of information. The tentative definition of the value can be formulated. We have a message which contains Nr ‘letters’ and the quantity of information N1 1r. At the next level, the received information decreases to Nr I, (1s < 1r) because the system already possesses the information, which can be expressed as Nr(1r - I,). Let us substitute the decrease of the quantity of information per letter by the decrease of the number of letters in the message to N, < Nr. This is equivalent to neglecting the redundant letters. The total information, i.e. the information of the

102

M. V. Volkemtein and D. S. Chernavskii

message plus the stored information,

can be treated as constant.

Then

N, _ 43 = l-R,. Nl - K

(15)

The number of letters is decreased (1 - R,)-l times and the total information per letter is increased by the same ratio. Therefore the value of information and its indispensability are increased. The ratios of the values at the subsequent levels are 1 l-R,

1 : iYj&

1 : 1

1 : **- :I-R,-

In the case of the English language quoted on p. 99 these numbers are 1 : 1.18 : 1.43 : 1.54 or, multiplied

: . . . : 2.28 : . . . : 2.50

by I1 = 4.76 bit, 4.76 : 5.61 : 6.81 : 7.33 : . . . : 10.85 : . . . : 11.90 bit.

The ratios of the non-redundant

letters N,, N,, Na, . . . are

l-R, : I-R, : l-R, : . . . : l-R,, and in our case 1 : 0.85 : 0.70 : 0.65 : . . . : 044 : . . . : 0.40

. . ..

This tentative definition of the value does not contradict the definitions corresponding to such situations where the probability of the achievement of some purpose can be defined and depends on the obtained information. These definitions are given in a series of works (Bongard, 1967; Kharkevitch, 1973; Stratanovich, 1975). The value of information in this case is expressed by the increase of probability of the achievement of the purpose, i.e. as 1 = l0&P,/P,~

(16)

where p, is the probability of the achievement of the purpose before the reception of information and pi is the probability after reception. Evidently the value I can be negative, if p,
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103

achievement of a purpose produced by this substitution. The corresponding biological example is considered in the next section. Hence the definition of the value of information can be only relative and conventional, as the value depends on the level of reception, on the purpose. However, this discussion can be useful for the understanding of a series of problems, in particular of the problems of theoretical biology.

The informational

aspects of theoretical

biology

The biological system at all levels of organization-an enzymatic system, an acting genome, a cell, tissue, organ, organism, population, biocenose (biogeocenose), the biosphere as a whole-is a dissipative system, which exists far from an equilibrium and is characterized by a series of stable and non-stable states. The phase space of the biological system always contains the entropical (statistical) and informational (dynamic) part. In contrast with the engines built by men, let us say, with the steam-engine, these parts are combined in a biological system both spatially and functionally. In a natural way, the fundamental problems of the mathematical modelling of the biological processes are solved by means of the study of the behaviour of the model in the phase space, by construction of the ‘phase portrait’, i.e. by the finding of the stable and non-stable singular points and separatrices (cf. Romanovsky et al., 1975). The biological system creates, stores (‘memorizes’), transmits and receives the information. The properties of the system are determined by the reception of information. The biological system is characterized by the multilevel structure and behaviour. The study of one kind of problem is based on a definite hierarchy of levels, the study of other problems takes another hierarchy into account. The biological system is always historical-it is a result of development (both phylogenetic and ontogenetic) and is developing further. In the language of information theory, this means the memorizing of information and the creation of new information. The complexity of treatment of the biological system is in particular connected with the realization of both cases described above-both the reception of information with its adequate translation and the creation of the new information, i.e. the spontaneous ordering of the system in space and time. Development implies the creation of new information, the occurrence of the new, higher reception levels. Therefore, development is connected with the increase of the value of information. The higher reception levels are formed as the result of the non-stability of the systems at the lower levels. Let us consider the reception of the genetic information coded by the sequence of nucleotides in DNA. At the level of the reception of this ‘text’ we can disregard the information determined by the regular disposition of the atoms in every nucleotide and consider the similar nucleotides as identical. In reality the atoms, let us say, in two adenines of the chain, vibrate in different phases and this gives a contribution to entropy. At this level of reception, the quantity of information in a DNA chain which contains n nucleotides is equal to I1 = log,+’

= 2n bit.

(17)

This information possesses a value for the translation process if the corresponding gene is not repressed. The biosynthetic system, containing a total set of amino-acids and t-RNA molecules, ribosomes and the necessary enzymes is in a non-stable

104

M. V. Volkmtein

and D. S. Chernavskii

state because it can synthesize any protein chain under the influence of the DNA chain. The quantity of information in the protein chain, calculated also as information of the text, is equal to I, = log,20n’g = in x 4.32 bit = 144 The redundancy

due to the degeneration

bit.

(18)

of the code is

R, = 1 - (Z.JI,) = 0.25,

(19)

and the ratio of the values of I, and I1 is equal to Ii : &, i.e. 1.39 : 1. At the next level, we take into account the fact that the substitution of some amino-acids by similar ones does not practically change the properties of the synthesized protein. Let the number of the non-exchangeable amino-acids be N< 20. Then I3 = log, N n’3 = +z log, N < 12. (20) The redundancy

at this level is R, = 1 - (1J1i) = [l - (log, N/6)] > R,

(21)

and the ratio of the values of 1a, I, and I1 are 1 1 l-R,:l-R,:l-R,=log,N:

1

6

1.39:

1.

If, e.g. N = 16, then these ratios are 1.50 : 1.39 : 1.00. At the fourth level, we take into account the possibility of substitution of proteins, e.g. of proteases. Let us suggest that DNA chains of two kinds are introduced in the system, containing n, and na links. Correspondingly, the protein chains with n,/3 and n,/3 links will be synthesized. Let ni = 0*75n,, N = 16 for both proteins. Then I1 = 2n, + 2~2, = 4*67n,, I, = 144n,+

144n, = 3.36n1,

(22)

I3 = 1*33n,+ 1*33n, = 3*10n,. 1 If the proteins are interchangeable, I, = l-33?+

(23)

The redundancies R,, R,, R, and R, are 0.72, 0.34, 0.28 and 0. The relative values are 3.56, 1.50, 1.39 and 1.00. We have considered a relatively simple system with a series of levels of reception of the genetic information. The simultaneous consideration of other biological phenomena and singularities gives other levels of reception and, correspondingly, different values. Treating the possible mutations of DNA and their biological consequences we obtain another scale of values of the elements of a genetic message -of the codons (Volkenstein, 1974, 1976). The value of the codon can be defined as the average change of the hydrophobicities of the coded amino-acid as the result of the mutational substitutions of the nucleotides in the codon. We build a scale, where the lowest value corresponds to the codons GAA, GAG (Glu) and GGC, GGU (Gly) and the highest to the codon UGG (Trp). The degeneracy of the code

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105

is decreased in this scale as the codons corresponding to the same amino-acid can possess different values in the sense of the consequences of mutations. For instance, the values of the codons corresponding to Gly: GGA, GGC, GGG, GGU are equal to 1.7, 1.4, 2.5, 1.4 in conventional units. Evidently in all these cases the criterion of value, i.e. of the irreplaceability of the message or of its elements, is the conservation of the biological function. The biological system is characterized by the coexistence of a series of hierarchies of the discrete levels of reception. We suggest that the clear differentiation of levels determines the regulatory possibilities of the system. In ontogenetic development the specialization, the irreplaceability of the informational messages increases, and hence the value of information increases. Simultaneously, the quantity of information increases at the higher levels of organization. Together with the initial genetic information, the new information is formed in the system, coded not by the sequence of nucleotides but by the organization of the cellular structures, by the morphology of the organism, etc. The statement about the repression of the definite genes and of the activity of the remaining genes means the new information. The recapitulation (Bar’s law of embryonic similarity, the biogenetic law or Haeckel) means, in this sense, the increase of the value (of the irreplaceability) of information during embryogenesis. At the earlier stages of ontogenesis a similar phenomenon is observed in the classical experiments of developmental biology. The properties of some part of the frog’s egg can be defined; it is known, for instance, that a definite part of the late blastula or of the early gastrula takes part in the formation of the eye of the adult animal. This part is the presumptive eye. If a piece of ectoderm from the presumptive eye is transplanted into the more adult embryo, the further development of this piece depends on the locus of transplantation-in the region of the head of the host it can form the brain or eye; in other regions of the embryo it forms other organs and tissues, characteristic for these loci in the normal development. At the stage of neurula the presumptive eye becomes the determined eye-it forms the eye in every locus of transplantation. Hence in the development totipotency is replaced by the unipotency. We meet with the specialization, with the increase of the irreplaceability, of the value of information. Contemporary molecular and developmental biology investigate the molecular nature of these processes. Evidently, the new levels of reception are formed at every stage of ontogenesis, the hierarchy increases, and thus the means to increase both the quantity and value of information. Similar processes occur in biological evolution. In contrast to ontogenesis, we meet here with an increase both of the value and quantity of genetic information at every level of development. There exists some similarity between biological evolution and games, such as chess. In general, the contemporary theory of games is a source of valuable ideas concerning the process of development (cf. Eigen & Winkler, 1975). The most important difference between a strategic play and evolution consists of the absence of the player in nature (if we exclude divine intervention). For example, consider the changes produced by moves on the chess board. Every move usually means a new level of development of the game, corresponding to new possibilities for further movement and new states of the medium. In chess the number of possible moves changes at one level while at a higher level the number of reasonable moves changes in varying ratios. Thus, in the initial position, 20 moves are possible for the whites 8

M. V. Volkenstein and D. S. Chemavskii but no more than 8 of them can be considered as reasonable. In the further development of the play, the number of possible moves increases and can become 40-50, but the number of reasonable moves decreases to 2-5. Hence at the higher level, most of the possible moves become redundant and the value of the reasonable moves increases. Of course, at the same time, situations occur corresponding to only one reasonable move (e.g. in the case of the exchange of pieces). Later, when the number of the pieces on the board is decreased, so also is the number of reasonable movesin the Endspiel it becomes l-3. The value of the move increases further, because of the increase of the value of the created information. Therefore games like chess can be considered as models of evolution. The systematic study of games based on such informational value levels has not been done; it would be instructive. About

artistic

information

A short discussion of some informational aspects of aesthetics is in place in this paper, as there are important features of similarity between an artistic work and a living organism. We suggest that the further development of scientific aesthetics will depend on our understanding and appreciation of theoretical biology. An artistic work is the result of human vital activity and, hence, the result of biological development. It contains the traits which are determined by the prehistory of the author and by the history of humanity as a whole system. After being created, an artistic work obtains self-dependent existence and enters into interactions with the external world-with its audience, i.e. with readers, spectators or listeners. The artistic work acts on the author-there is a feedback between the author and his creation. In this sense, the artistic work can be treated as a non-closed system which communicates information to the surrounding world. It is a complicated system possessing many levels both in the internal structure and in the communication of information. Simultaneously, with these features of similarity, the artistic work differs from an organism because it does not change itself. A verse, a picture, a sonata, are stable and they do not change-the non-stability characterized the state of an artist during the creation of these works. The act of creation consists in the free choice, i.e. in the transition from a non-stable state into one of the stable states and therefore in the formation of a new information. The artistic work is a whole informational system. All levels and elements of this system have informational meaning. Thus the information, communicated by a verse, consists of its contents in the usual sense of the word (the contents can be, in principle, communicated also in prose), in the system of images, in the rhythm, rhymes, metrics, etc. The problems of poetical information have been studied by one of us earlier (Volkenstein, 1970). The reception of artistic information is the process determined by the level of reception, i.e. by the supply of the preliminary information by the receiver (the so-called thesaurus). It is impossible to perceive the information contained in a verse written in language which is not known by the reader. The reception of artistic information is always a non-equilibrium process, the achievement of some goal, i.e. the choice of the way from the non-stable state to one of the stable states. The receiver must desire to obtain this information; without such desire he will not perceive it. Correspondingly, the value of artistic information is determined by its irreplaceability at a given level of awareness of the receiver. Hence the value differs for various receivers and varies in time because the mind of the receiver changes.

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The level of awareness increases with age. The same work is also perceived in different ways in different historical periods. The wholeness of an artistic work means the irreplaceability of its elements. In this sense, the value of the word in a verse is higher than that in a scientific text. The same scientific notion can often be expressed in many ways, with the help of synonyms, etc., but the substitution of one word in a good verse usually destroys its informational structure. The complexity of the informational analysis of an artistic work is connected with the dual character of its reception. Firstly, there occurs the transcription of information into the totality of the thoughts and emotions of the receiver which are somehow adequate to the perceived message. Secondly, the artistic information is simultaneously the source of the new information in the mind of the receiver due to the new associations which are subjective. This process of formation of new information can be defined as the co-creation of the artist and receiver. The brighter and richer are these associations, i.e. the greater the changes of the consciousness of the receiver under the influence of the artistic information, the higher is its subjective value. Using these ideas, we can give a definition of the value, i.e. of the talent, of an artistic work. The talented work serves as a source of new information during every reiteration of its reception and it possesses, in this sense, unlimited informativeness. For four centuries, the plays of Shakespeare have created new thoughts and motions in millions of men, and we do not foresee the end of this process. Religious scriptures have this same property. In a pithy book by Moles (195S), two kinds of information in an artistic work are discussed-the semantic and the aesthetic information. The first can be formulated in an exact way, obeys the universal logics and can be translated into another language. The semantic information gives rise to the definite actions of the receiver. On the other hand, the aesthetic information cannot be translated into another language, it provokes the definite states of the receiver, and its reception is subjective. From our point of view such a division of these two types of aesthetic information is not valid. An artistic work is an integral system and therefore their elements, both translatable and non-translatable, cannot be divided. An aesthetic influence can be produced also by an oral description of a picture. The change of the state of the receiver is also an action, thus the emotion felt by a listener to a symphony is his action. The real sense of the division, suggested by Moles, is the separation of the directly perceived information from the formation of the new information in the receiver’s brain. References Blumenfeld, L. A. (1974). The Problems of Biological Physics. Moscow: Nauka (in Russian). Bongard, M. M. (1967). The Problem of Recognition. Moscow: Nauka (in Russian). Brillouin, L. (1956). Science and Information Theory. New York: Academic Press. Eigen, M. (1971). Naturzoissenschaften 58, 465; Q. Rev. Biophys. 4, 149. Eigen, M. & Winkler, R. (1973). Das Spiel. R. Piper Verlag. Gelfer, J. M., Luboshits, V. L. & Podgoretsky, M. I. (1975). The Gibbs Paradox and Identity of Particles in Quantum Mechanics. Moscow: Nauka (in Russian). Theory of Structure, Stability and Glansdorff, P. & Prigogine, I. (1973). TI lermodynamic Fluctuations. London, New York, Sydney and Toronto: Wiley-Interscience. Iaglom, A. M. & Iaglom I. M. (1973). Probability and Information. Moscow: Nauka(in Russian). Kharkevitch, A. A. (1973). The Theory of Information. Recognition of Images. Moscow: Nauka (in Russian).

M. V. Volkenstein and D. S. Chernavskii Lavenda, B. (1972). Q. Rev. Biophys. 5, 429. Layzer, D. (1975). Scient. Am. 233(6), 56. Moles, A. (1958). Thkorie de l’lnformation et Perception Esthe’tique. Paris: Flamrnarion. Prigogine, I. & Lefever, R. (1975). Adv. Chem. Phys. 29, 1. Prigogine, I. & Nicolis, G. (1971). Q. Rev. Biophys. 4, 107. Quastler, H. (1964). The Emergence of Biological Organization. New Haven and London: Yale University Press. Romanovsky, J. M., Stepanova, N. V. & Chernavskii, D. S. (1975). The Mathematical Modelling in Biophysics. Moscow: Nauka (in Russian). Schlagl, F. (1971). Z. Phys. 249, 1. Shannon, K. (1951). Bell Systems Tech.J. 30(l). Stratanovich, R. A. (1975). The Theory of Information. Moscow: Sovietskoje Radio. Volkenstein, M. V. (1970). Nuuka iJizn No. 1, 72 (in Russian). Volkenstein, M. V. (1974). Dokl. Akad. Nauk SSSR 216, 1395 (in Russian). VoIkenstein, M. V. (1976). Molek. Biol. 10, 498, 737 (in Russian). Volkenstein, M. V. (1977). Foundations of Physics.