LECTURES IN THEORETICAL BIOLOGY: The Second Stage (K.Kull, T.Tiivel, eds.). Tallinn, Estonian Academy of Sciences. 1993. Pp. 33-50.
© A.P.Levich

(on the centenary of E. Bauer)

A. P. Levich

1. The problem of theoretical biology

Fifty five years ago in "Theoretical Biology" E. Bauer confidently stated that biology was not applied physics or chemistry. He also stated that "all special laws, which would be revealed in certain fields of biology would display the general laws of motion, appropriate to living matter" [4, p.8]. The urgent problem of theoretical biology was, according to E. Bauer, the development of general laws of motion for living matter. It should be mentioned that this problem has not been solved up to the present day.

E. Bauer proposed that the general laws of theoretical biology would be analogous to those of theoretical physics, as an illustration he gave the examples from Newtonian mechanics and statistical physics.

In what way are the theories in advanced fields of science organized? The methodology of science shows that the theory of some part of reality is sure to include the number of components, the development of which acts, directly or indirectly, as stages of theory creation [28; 29].

The O-component is the description of the ideal structure of the theory's elementary object.

The S-component consists in enumeration of the possible theory object states. In other words, component S is described as a state space of analysed system.

The C-component fixes the ways of objects' variability (changeability) and corrects the overidealization during the isolation of the objects, since only processes rather than objects exist in the World and the notions of objects are the abstractions of these processes. C-component brings the processes, variability and the pre-time in the theory.

The examples instead of precise definitions of elementary objects and their variability are given below:

Material points along with their positions and velocities in physical space are the elementary objects of classical mechanics. The planets of the solar system can be considered as an example. The variability is determined by points' trajectories. The state space is a six-dimensional phase space which is the product of three-dimensional Euclidean space and three-dimensional velocity space.

In quantum mechanics elementary objects are the ranges of probabilities of microobject states, for example, energy states of the atom. The variability in state space is determined by the trajectories of vectors in infinite-dimensional Hilbert space.

In nuclear theory elementary objects are nucleons and some other particles with certain sets of quantum numbers. The variability is the mutual transformation of particles and radiations. The state space is restricted by those combinations of quantum numbers for the totality of changing particles, which meet the conservation laws.

In embryology the living cell acts as an elementary object, and the role of variability belongs to the cell division and differentiation processes. The state space is described by the set of morphological features.

In community ecology the elementary object is population. The variability consists of births and deaths of organisms. State space is the set of vectors (n1, n2, ..., nw), where ni is the size of the population of species i, included in the community. The vector set is limited by the available resources.

The T-component of the theory consists of bringing the clock and the parametric time into the functioning of the systems. Parametric time can be considered as the image of changing objects reflecting the variability process on linearly arranged metrized numerical set. Generally, the variability of a selected object acts as a standard in measuring other variabilities, the clock here is the standard object and the way of organizing the necessary reflection.

The traditional clock in natural science is based on physical processes. The examples of these processes are: gravity or resilient pendulum devices, astronomical systems, observing the Earth's rotation around its axis or around the Sun, caesium or other sources of the electromagnetic oscillations, recently discussed pulsar standard of superstable periods, and radioactive decay.

Here is Fridman's description of physical clock appearance [9]. Let point M correspond to certain basic movement, and let the device showing the arc lengths, t, which are the trajectories of point M in its basic movement, be the clock of point M. We will call the magnitude t the physical local time of the point M.

To begin with, consider star time. Let us assume the movement of the end of the hand of a certain length directed from Earth center to the star to be the basic motion. The distance, passed by the end of this hand would be the star time, ts .The star time is the same in all parts of space, it is the universal time.

Let us consider another time, which we will call the gravitational time. Suppose, the material point is falling in a constant gravitational field. We choose this as a basic motion. The clock shows the distance tg , passed by this material point, which is exactly the gravitational time. Related to the gravitational time the stars' movement is uneven.

Let us put in the pendulum time. Imagine many hypothetical pendulum clocks. Let the motion of the second hand of our clock placed at any point on the Earth be the basic motion of this point. Assume the distance passed by the end of second hand of our clock to be the pendulum time, tp. In contrast with the star time or the gravitational time, which are universal, this pendulum time is local, i.e., different at various latitudes.

The parametrization of variability with the help of the physical clock permeates the whole entity controlled by human consciousness, i.e., science, culture, and way of life.

The changes in the World can not be reduced to mechanical displacements. Chemical transformations, geological chronicle, the development and extinction of speices and whole communities, the Universe nonequilibrium, and sociogenesis ...

Isn't it better to assume the clock being established in frames of reference for description of natural object variability to be different, and is it possible to consider one clock, for example, physical clock, to be correct and unlike clock to be wrong?

This thought would be understandable in the case of Galilei who tried to find the laws of pendulum motion with the help of his own heartbeat.

As early as Poincare stressed that "there is no time measurement method, which would be better than another"."The accepted method is merely more suitable. When comparing clocks we can't say that one of them works properly and the other keep incorrect time. We can only say that the indications of one of these clocks are prefered" [32]. In nonphysical sciences there is a growing necessity for clocks, not to be synchronized with some physical standards. These clocks in comparison with standardized, would be much more convinient and more adequate for description of nonphysical forms of motion.

In embryology the development of organisms is effectively described by using a special unit of biological time, equal to an interval between same phases of cell division [7]. This unit, named "detlaf," depends on the temperature and is species-specific. That is why the regularities of development, observed in the detlaf time scale are undistinguishable in the astronomical time scale.

The population time in ecology [1], ethnography [3], and genetics [34] can be measured by the number of generations.

The chronostratigraphical scale of geological time is based on the sequence of rocks with standard points. These points have been chosen in opencast mines with well-conserved frontier provinces [13]. In paleobiological stratigraphy durations of geological epochs can be measured by vertical width of layers with remains of fossil species [35].

In the psychological time model [10] the durations of the intervals between personally important events are measured by the number of inter-event links.

The L-component of the theory consists of the statement of the variability law which isolates the real generalized motion in state space from all possible motions (the term "generalized motion" is used as a synonym to variability of objects).

In mechanics and theory of fields this variability law more often appears in a form of "motion equations". For example, the Newtonian equations of macroobject motions with small velocities and in weak fields, or the Schrodinger equation of nonrelativistic quantum mechanics or the Maxwell, Einstein or Dirac equations etc.

The law can be formulated not only in a form of equation, but in a form of the extremum principle. An example is the minimum action principle: trajectory is real only if its' time integral of difference between kinetic and potential energy magnitudes is minimal. Equational and extremum principle forms of the variability law are equivalent.

In many fields of natural science, for instance, in the examples given above, and in nuclear theory, in embryogenesis, and in ecology the objective of theory constructing is the formulation of variability laws. This objective can't be reached without proper solution to a set of problems, connected with the elaboration of the O, C, S and T components of the theory. In natural sciences' methodology the C and T components are still elaborated to an inconsiderable degree. There is a very close link between the choosing of these components and the way the L-component is derived. According to A.A.Sharov, the law of motion is exactly the description of the variability of the object under consideration by means of a standard clock variability. Hence, the choice of the clock adequate to the processes observed can affect the probability of revealing the variability law.

Laws of motion affect the method of time measurement if the T and L components of the theory correspond to each other [24]. For example, "the simultaneity of two events or the way in which one event follows another, the equality of the two durations should be determined in a way which provides the most simple formulations of natural laws" [32].

The difficulties of motion equations' derivation appear to be due to inconformity of physical measurement of time to the nonphysical nature of the regularities being observed.

Finally, the I-component of the theory is presented by a set of interpreting procedures. The first of these procedures is to bring the formal mathematical theory constituents into compliance with the abstract notions of reality. The second procedure consists of the rules of bringing these notions into correlation with magnitudes measured experimentally.

The apparatus of quantum mechanics deals with the complex-signed wave functions and with the operators affecting them. A transfer to the notions of macrophysical reality is conducted by some postulated rules, namely: the square of the wave function is the probability of microparticles occuring at definite points of time and space; the eigenvalue of an operator is the quantitative value of the corresponding physical characteristic. For example, interferential experiments with the particles passing through obstacles are required for the probabilistic distribution observations. Energy characteristics of atoms are determined by the distance between spectral lines in the experiments concerning the atomic emission and absorption of radiation.

The I-component is a necessary constituent of the theory. It is the complex of interpreting procedures that transform the formal theoretical scheme into realistic science. The possibilities of the I-component elaboration, paticularly its experimental identification, depends not only, or not so much on the merits of theoretical scheme and its creators, but on the sum of the technologies, worked out by civilization.

It took hundreds of years for Democritus' hypothesis to become a "verified" theory. Vast experience in X-ray structural analysis was nedeed for the hypothesis of some descrete substance of heredity to become the scientific model of a DNA double helix structure.

Interpreting procedures are very ambiguous. I-component elaboration often turns out to be the most difficult and the most vulnerable stage of capable theory's creation.

In the present-day paradigm of natural science the problem "what is time?" is considered to be naive or nonscientific. Most people think it to be absolutely clear or believe the answer to this problem can be found in some physical textbook. Actually,time is the basic idea of all our dynamic speculations, which make sense only due to the concept of time. The structure of time as a physical object is postulated to be as simple as possible [2]. " The presentation of time as an internal property of physical systems exceeds the limits of conventional physical description" [37].

Firstly, in physics time is identified with a set of real numbers, although the lack of distinct nonmathematical notions about time makes it impossible to analyse constructively the correspondence between the real straight line axiomatics and the properties of time. Secondly, physics proposes that the clock is based on the gravitational or electromagnetic interactions for any variability observations, that is, the parametric time only is used.

Thus, the biological theory construction must be preceded by investigation of time in biology, and by the development of time construction appropriate to build the T-component of laws of the living matter's motion.

The objectives of this work are:

- to show that the interpretation of Bauer's stable nonequilibrium principle might be equivalent to the hypothesis of flow existance, which generates the metabolic time of natural systems;

- to present the construction of substantial time, which would be useful in solving the biological theory problems formulated by E. Bauer.

2. Notes on the origin of the nonequilibrium sources

"Only living systems never reach an equilibrium, for they constantly work against stability" [4, p.43]. According to Bauer, the source of free energy(or"the work of structuring forces" and "structural energy" are the synonyms) is the nonequilibrium of molecular structure of living matter

What is the source of the nonequilibrium of "living matter"? Firstly it is the activation of molecules of food caused by levelling processes. Energy of these molecules maintains nonequilibrium (here the molecules of living matter in "active, deformed state" are considered [4, p.127]. However, the unavoidable result of metabolism is, according to E. Bauer, the lowering of the potential of free energy of nonequilibrium. "The more intensive metabolism is, the higher rates of the free energy depletion are. This free energy of living matter exists because of the deformed nonequilibrium structure of its molecules" [4, p.129]. "During assimilation the structural energy of a system can be used. This energy is necessary for the reconstruction of nonliving substance" [4, p.144].The total amount of energy that can be assimilated is limited. This amount of energy is species-specific parameter of organism (Rubner constant) (see [4, p.131; 37] and is "proportional to the free energy of an ovicell" [4, p.130].

This means that the problem of the source of living matter's nonequilibrium cannot be reduced to the possibility of nonequilibrium's replenishment with free energy of food. Another source of nonequilibrium is required. The utilization of this source should regulate the organism's ability to make up for free energy losses with food. Concerning deeper nonequilibrium one can propose several possibilities of its origination in organism. They might be the following:

- the law of nonincrease (or conservation) of structural energy and transfer of it from generation to generation;

- the possibility of external replenishment of structural energy during the origination or fertilization of the ovicell in addition to an explanation of Bauer's theory, according to which fetal cells, possessing maximum initial potential, originate due to dying or, in other words, dissimilation of the body tissues" [4, p. 144].

- to reject the idea of the impossibility of structural energy replenishment during the life period, and then to find the ways of such replenishment, for instance, the mechanism of structural energy assimilation by autotrophs and its farther spreading in the biosphere through the food chains.

In the second and third proposals, and in other cases, allowing the structural energy replenishment, the question about the sources of such replenishment remains.

When considering the problem of understanding the stable nonequilibrium principle, another problem arises, that is the search for the sources of nonequilibrium. This problem is connected with time, its flow and becoming. One of the possible hypotheses dealing with this problem's consideration consists of the substantial time construction [28; 29].

All natural systems are hierarchic. The replacement (or substitution) of elements takes place on every hierarchical level. Any variability of natural systems can be presented as the superposition of these replacements. The quantity of elements of a standard system, that have been substituted, may act as a substitutional clock of the systems. The origin of the elements' substitution deals with the external flow of elements on some deep level of organization. This flow penetrates the whole natural hierarchy, which contains the system. In particular, time of the Universe (or, in other words, of that part of the world, which can be measured instrumentally) originates from the generating flow of pre-elements. These pre-elements belong to rather deep levels of living matter hierarchy. The above means that the Universe is isolated, open, unstable, and that the passage of time is determined by the Universe nonequilibrium.

Generating flow appeared as the logical extrapolation of metabolic time properties. This flow helps to find the ways to solve the existing problems of natural science. The link between time flow and instability of the system, and between flow dissipation and irreversability is the instability of the system. In other words the presence of substrate-energetic flow through the system is the passage of time. An uncommon feature in this is the necessity of generating flow existence. The flow hypothesis transforms the question of the "nature" of time, the causes of its' flowing, and the mechanisms of its becoming, into the question about the origin, substrate and energetic "fostering" of the Universe. In time construction flow is a fundamental, primary standard object and it generates the sequence of time moments, i.e., time is linearly ordered because of generating flow. Irreversibility isn't an immanent property of time, it occurs only through orientation of the pre-elements' flow. This means that time irreversibility exists, while generating flow isn't reversed. The presence of the flow takes off the lable of thermal death of the Universe from the second law of thermodynamics. Increase of entropy leads to equilibrium distribution only when the global extremization of an isolated system' entropy exists. The presence of flow, limiting evolution of a system, demands the solution of a conditional extremum problem and leads to eneven distribution of parameters such as the Gibbs' distribution [25], and also to the possibility of structure producing, i.e., self-organization.

"...Every day experience makes certain that the properties of nature have nothing in common with the those of a system in equilibrium. Astronomical data make this statement correct. In the vast part of the Universe, accessible to observations" [23]. In this connection isn't the absence of equilibrium features in the Universe an argument for the hypothesis of generating flow existence?

The associations concerning the idea of generating flow are not new in philosophy or in natural science. For example, some similar notions are presented by the world views of taoism, Newton's conception of an absolute time, in the present day notion of physical vacuum, substantial conception of G.J. Whitrow's, "that there is a total basic rhythm in the Universe" [36], and in Kozyrev's idea of the flow of time.

According to N.A.Kozyrev, time is a "huge flow, comprising all material processes in the universe. These processes are the sources fostering this total flow" [19, p.96]. N.A.Kozyrev considered the intensity, or density of this flow, its energy, radiation and absorption, and also rectilinearity of its spreading, its reflection from obstacles, and its absorption by substances. All this gives the reason for identifying Kozyrev's flow with some substantial flow. the sources of this flow are, according to N.A.Kozyrev, any unstable, irreversible world processes, i.e., processes with changes of energy and thermodynamical entropy of system.

N.A.Kozyrev noticed the discrepancy between the second law of thermodynamics, postulating thermal and radiational degradation of the Universe, and the lack of any traces of stability in diversity of the Universe. He also stressed that the attempts to explain thermal death had been isolated from the real Universe, which is observed by an astronomer. In fact, celestial bodies and their systems are so separated from each other, that thermal death should occur before interference from some distant system. Thus, the degraded conditions seem to be dominant, but, actually, these conditions almost never occur. The problem is not only to explain the instability of the Universe, but also to understand why celestial bodies themselves and their systems exist inspite of small relaxation periods" [19, p.96]. It is possible to propose hypotheses, maintaining the second law of thermodynamics. An example would be to assume the present moment of cosmological time to be not far from the initial fluctuation (or singularity or cataclysm). This means that degradation is not very profound and thermal death of the Universe is to occur in the far future.

N.A. Kozyrev proposes an alternative hypothesis, that is, the Universe and its systems are not isolated, that means that the obligatory conditions of the second law of thermodynamics are not satisfied. He also states that "there are some constantly acting forces (reasons) against the entropy increase" [18]. Kozyrev's flow is the required source of a system's non-isolation and also is necessary for the explanation of the star energy's origin [16; 17].

There is much evidence of Kozyrev's flow's existence in different mechanical phenomena. Irreversible processes, such as deformation of bodies, air jet striking against obstacles, work of the sand clock, light absorption, friction,burning, some human activities, changes of the temperature of bodies, aggregate state transformations, dissolution, mixing of substances, the withering of plants, and non-light radiation of astronomical objects in Kozyrev's experiments, can affect the beam or disk of torsion balance while irradiating or absorbing Kozyrev's flow.

It has been found that the flow may be screened, or absorbed or reflected by substance. Non-resilient processes in solid bodies can change their weight and resilient processes lead to changes in quantitative characteristics of resilience. A rotating body's weight changes when it participates in additional processes, such as vibration, warming or cooling, electric current conducting, its weight changes. Many features of the shape and climate of the Earth and other planets can be explained by the influence of dissipation processes on these giant gyroscopes.

Non-mechanical pickups also register the flow accompanying non-equilibrium processes, namely: the value of resistance, mercury level in thermometer, frequency of quartz piezoelement oscillations, electric potential of thermocouple, water viscosity, work of electron exit in photoelements, and the rates of chemical reactions.

It should be mentioned that Kozyrev's thoughts hardly meet existing physical notions. The values of effects in Kozyrev's experiments are not large. Additional forces in mechanical experiments are 10-4 - 10-5 of the body weight being used in measurement; in the case of non- mechanical pickups, the relative change is about 10-5 - 10-7 of the value being measured. For torsion balance the turn may be up to tens of degrees, that correspond to forces of 10-6 - 10-7 of forces acting in a system. Kozyrev illustrates of the difficulties of detection of additional cryptic sources of star energy, the difficulties occuring because of a local minuteness of the effect [21, p.210]: "The situation here is similar to that of a physicist from a labarotory in space, far from Earth, would be. It would hardly be possible to reveal gravitational forces in that situation. However, these forces determine not only the whole dynamics of cosmic objects, but their internal structures also. The analogy is that the star, despite great energy losses, is a perfect thermos. For instance, the Sun, having an internal temperature of approximately ten billion degrees may cool down only in one degree for three years. An insignificant energy inflow for replenishment of such small losses, would be indistinguishable in laboratory conditions".

In principle, it is possible to explain Kozyrev's effects with the help of more prosaic reasons other than the influence of the "time flow" (for example, convective flows, temperature changes, induced electric and magnetic fields, etc.). N.A.Kozyrev tried to analyse the role of extraneous causes in his experiments. For example, one article of N.A.Kozyrev is devoted to the possible mechanisms of effects' appearance in weighing vibrating bodies with the help of beam balance. Kozyrev's opponents, however, may have objections concerning factors, being not observed. Besides, the reader suppose the author to analyse in detail possible errors, which could reduce the noticed effects to disappointing artefacts. Up to the present there has not been and there is no concrete disproof of Kozyrev's experimental results or their consistent explanation by means of ordinary physical factors. Only doubt of simple interpretation of experiments exists.

Experiments of N.A.Kozyrev and his colleagues have been confirmed by few enthusiasts. However, one failed to regain the results similar to those of N.A.Kozyrev in any labarotory in the world. The fact that such results have not been found, especially in many precision or other physical experiments, seems to be rather understandable. N.A.Kozyrev's experiments were specially designed for the exposing the effects, being derived from his theoretical ideas. These effects are unlikely to be revealed occidentally. They are minute and require special experimental conditions, for example, inequality of beams of the torsion balance; participation of additional irreversible processes such as vibrations, dispersion of heat or electrical current in the experiments with gyroscopes, etc. Because of the background influences certain efforts to reproduce experiments' results are required. Some deviations from what has been expected could be easily interpreted as nonsystematic errors of measurements. The desire to repeat or develop complicated Kozyrev's experiments faces the difficulties of perception of the Kozyrev's works. Kozyrev did not try to adapt his original ideas and terminology to existing scientific standards.

Scientific views of N.A.Kozyrev had been often contradictory to the paradigmal beliefs of his opponents. However, this was not an obstacle for N.A.Kozyrev to make outstanding discoveries in astronomy, for example, to reveal the vulcanism on the Moon. Perhaps, the intuition didn't fail him in the forsight of substatial nature of the time passage either.

N.A.Kozyrev stressed repeatedly that non-equilibrium in the world, created by time flow, had to affect the perception of life phenomenon.

"...Our scientific knowledge lacks a vital element. Physics, chemistry and other precise sciences can follow and predict the way of destruction of a fallen leaf rather strictly, and even derive its motion equation. Nevertheless, they are unable to explain growth or shape and properties of leaf. One must not refer to some specific characteristics of plants inappropriate to non-living nature.

Living organisms can not make anything that does not exist in nature. They can only accumulate and use some basic properties lying in the foundations of the Universe. Hence, these basic properties have to exist in non-living nature as well. They are to be searched for just there, using vast experience and methods of precise sciences" [20, p.2-3]. The experimental results show that the organizing force of the active property of time has little influence on the systems in comparison with usual destructive way of development. That is why there is no surprise that the vital element was missed of the system of our scientific knoweledge. However, being low, it is dissipated everywhere in nature, and therefore only the possibility of its accumulation is required. The process of accumulation is similar to that of maintenance of mighty rivers by tiny water drops falling over enormous areas. This possibility is realized in living organisms since vital activity as a whole counteracts the course of systems' destruction" [22, p.71].

Living organisms, according to N.A. Kozyrev, may be both emitters and detectors of substantial flow.

"Experiments with plants need more detailed description. The equipment used were thick paper rotary disk and non-symmetric torsion systems with jasmin, bamboo or glass points hang by kapron threads. The systems were enclosed in tin cylindrical casings with hermetic observation window at the top. Plants under consideration (apple-tree, pear-tree, linden, chestnut, clover, dandelion and some others) were gathered on Pulkovo territory in different seasons. The experiment was carried out in the following way: gathered plants were exposed for a while on the table in a laboratory, lying apart from each other; after that top or cut of a plant was placed by the edge of torsion balance in a position of 30 degrees from the direction of the point (or from conventional index on the disk)... Deviations of torsion balance beam and disk caused by effect of plants were observed in most cases. We failed, however, to reproduce the results. Values of these effects differed both quantitatively and in sign. Acetone evaporation used as a control process always caused repultion of the disk... Values of the effects depended on the season and varied from 1-2 degree to almost complete turn. The sign of the effect value could be different. Taken into experiment immediately after gathering, a plant causes repulsion of the beam. Values of the effects of cut or top of a plant keep the same sign and differ slightly in quantity. Taken later..., the stem still repulses the point of torsion balance with the same intensity and always regularly and moderately, while the top begins to attract it rather actively and sometimes by pulses...For example, an apple-tree in blossom before throwing the petal can display attraction of about 250-300 degrees in 5-10 minutes. Repulsive effect usually shows itself in the same period of time and lies within 10-30 degrees... In autumn, 1983, a period of increased activity of apple-trees has been detected. However, these plants are known to lay the foundation of the apple crop just at that time. Actually, next year crop appeared to be rather big. No activity was revealed by autumn observations in 1984 and only a few trees gave the apple crop in summer... It is significant that the rise of number of plants under experiment... does not augment the value of the effect."

"Usual human activity was found to have little influence in measuring devices... When ill, a human being can actively interact with measurement instruments, this interaction precedes the moment of subjective falling ill. Sometimes N.A.Kozyrev and I managed to detect a common cold one or two days before temperature rised. Similarly emotional excitement violently influences measuring instruments. For example, when reading his favourite "Faust" N.A.Kozyrev was able to cause deviation of a hand of device as much as 40 degrees. Meanwhile, mental arithmetic calculations had no effect on the hand".

These are quotations from the report "Physical Time of natural life'' (see references 3, 4, and 18), made by V.V.Nasonov on December 6, 1985 at the seminar devoted to Time problems in natural sciences at Moscow State University.

"The process of liquid nitrogen evaporation has been chosen as a resource of influence... Besides the process of snow melting took place... Actually, two processes affected the object under observation: evaporation itself and warming of nitrogen fumes... Microorganisms Pseudomonas fluorescens and microorganisms of artesian water, oats and pea seeds, and onions, growing in the water, were taken in experiments. It is known that temperature changes within 1o C don't influence vital functions much. However, permissible changes were determined to be in 0.2o C interval... Influence of the changes in nitrogen concentrations was prevented by incessant ventilation and hermetically sealed test-tubes, where objects were kept. Test-tubes had been made of glass.

Exposition time usually was 60 minutes. All experiments were accompanied by control tests, in which objects were in the same conditions exept the influence of liquid nitrogen evaporation.

For microorganisms, drastic depression of vital functions was observed on the first day of experiment, then restitution followed.

Two experiments with 80 oats seeds showed the decrease of germination to zero value, while germination of control seeds was 60 percent.

The results of experiments with pea seeds were also interesting. Six experiments with 600 seeds were carried out. Average germination in control was 92 percent, while in experiments it was 62 percent, i.e., some seeds died.

In the next set of experiments (with 60 seeds divided in 3 equal groups) seeds were not affected by liquid nitrogen evaporation process. Tap-water for seeds watering was treated instead. In all groups of seeds' germination was 100 percent. However, there was depression of growth in experiment comparing with control.

Experiment with germinated pea seeds, being affected by liquid nitrogen evaporation, was continued. Experimental and control seeds were planted outdoors. Stem growth was observed... On the fifth day of experiment depressed plants overtook and then surpassed in growth control group. Maximum overgrowth (up to 50 percent ) was observed on 8 day...

Experiments showed that considerable distant effect on living matter conditions was caused not only by such intensive process as liquid nitrogen evaporation, but also by snow melting... Healthy onions of equal size and root system development were taken in experiment. A reflector (piece of cardboard, covered with aluminum foil) was placed above the experimental group of onions. This was done in order to reflect the shining of snow outside the window on the onions. Because of reflector, light conditions of experimental and control groups were unequal; sheets of paper were pasted on the window in the area of reflection to equalize light conditions. There are the results of experiment: 50 percent of control onions were rotten without sprouting. The rest of this group rooted slowly, and there was a delay in shoot growth, and its inhibition. At the end of experiment average length of shoots was 150 mm , water in pots was turbid and with a smell of decay. Experimental group's behavior was quite different. From the very beginning impetuous growth of roots was observed. The lower parts of pots were filled with roots completely. All onions were viable. Water in the pots remained clear and odorless during all the time. At the end of experiment length of shoots was 300 mm...

From the facts given above one can conclude the following:

Irreversible processes transform distantly physical properties of surrounding substances.

Living matter is considerably sensitive to these processes...

For biological objects underwent short-term direct influence of liquid nitrogen evaporation within certain conditions complete elimination of vital activity inhibition, and their further stimulation are appropriate [5, p.101-121].

Experiments with pea seeds affected by liquid nitrogen evaporation were continued in a systematic way. "Seeds were exposed to the process on the day before sowing. Dry seeds were taken... During two field seasons four experiments (with 3 reiterations with 175 seeds in each) had been carried out. In 3 variants seeds were exposed to the influence for 15, 6, and 3 minutes. Three sources of influence were placed in line in a distance of 65 cm from each other. Seeds in paper envelopes were put exactly above them on a cotton cloth, strenched on a frame-work. Shooting, growth and development were observed, and some seed characteristics were revealed.

Let us summarize the main features of observed phenomenon. In the beginning of growth affected plants develop slower than control ones, then, sometimes, surpass in growth occured.

In the most representative class of seeds (half of all seeds approximately) affected seeds weigh more than control seeds. Weight distribution of 200 seeds is distinct, statistically reliable response of biological systems to the effect.

For most characteristics mean deviations of experimental values from control are several times higher than those of different reiterations of experiment. All characteristics under observation show an increase of variation value, all distributions of the affected plants have larger dispersions in comparison with control. This is one of the direct and permanent features of the effect's presence.

The main feature of the phenomenon under consideration should be taken into account in organization and interpretation of experiments. We study the distant influence of liquid nitrogen evaporation on biological systems. However, if the system fixed the influence, it means that this system can detect all natural and artificial irreversible physical processes, which were effectively simulated by the process of liquid nitrogen evaporation. Thus, biological system under consideration is always involved in proximal and distant irreversible processes, lying beyond the experimental control" [6, p.11-81].

V.V. Nasonov, developing Kozyrev's ideas, pointed directly that helical protein molecules were sensitive to the density of time flow.

Comparing ideas of E.Bauer and N.Kozyrev, one can assume that Kozyrev's flow of time is Bauer's source of structural nonequilibrium in living organisms.

3. Differences between living and non-living matter

In respect of the stable nonequilibrium principle the difference between living and nonliving matter is the ability of living matter to use structural energy which exists in the world. As it has been stressed above the existence of non-equilibrium source, regulating the inflow of the free energy of food in the organisms, is a necessary premise of stable non-equilibrium principle.

Let us try to outline the hypothesis of E.Bauer in more concrete, thus, in more vulnerable way within the bounds of substitutional approach. Detailed statement of substitutional approach, for natural systems' description is given in works of A.P.Levich [28; 29]. Term "metabolic" concerning time, approach etc., being used in those works is replaced by term "substitutional" in present paper. Futher we will need five following propositions.

1. On all levels of hierarchic structure of natural systems general process of system elements' substitution occurs.

2. There are substantial flows on certain hierarchic levels, which produce general processes in a system.

3. One of those flows is a substantial flow, generating time passage in the Universe.

4. Life implies the possibility to accumulate and use the non -equilibrium of flows of various structural levels, which are deeper than molecular one, in particular, from the level with flow generating time.

5. Individual existence of organism consists of the depletion of substances of the flow, generating life.

The first three postulates are taken exactly from the substitutional approach. They are helpful prerequisits for transfer to living systems description and are equivalent to the part of Bauer's principle, concerned with the necessity of non equilibrium in life description. The fourth postulate implicates specific character of living systems in substitutional approach and corresponds to the statement on the insufficiency of energetic metabolism of food for producing the potential of the structural energy's the nonequilibrium of living matter. The correctness of the fifth postulate is based in the first place on Bauer's arguments [4, p.130-133] and recent data on the existence of Rubner's constant [37].

It is possible to propose other arguments to support the fifth postulate. One of these arguments is based on assumption about the similarity of growth curves of multicellular organisms to those of population growth of unicellular organisms. Ordinary S-form of growth curves is appropriate to populations, growing on a limited nutrient substrate, for example, in batch-cultures. In continuous cultures with incessant nutrient inflow growth curve is presented by growing exponence, i.e., only by left part of S-shaped curve. From the fact that growth curve of multicellular organisms is always stationary one can draw a parallel with exhaustion of some substance subordinate to the law of conservation. The substance is consumed by the organisms for the period of their life. Let me notice that the hypothesis of consumption of embryonic cell substrate throughout the life period is not necessary for explanation of existence of sigmoidal growth curve. Only limitation of total accessible intra and extracellular substrate only is necessary. For example, batch cultivation of unicellular (coenobial, colonial) algae populations in a flask is divided into following growth stages [31]: stage A, accumulation of intracellular substrates, stage B, growth using nutrients of culture medium, stage C, growth on intracellular storage of nutrients after exhaustion of a growth-limiting nutrient in the flask. Exponential fragment of the curve involves both B stage and part of C stage. Another part of C stage is expressed by stationary branch of the curve and includes decrease of cellular limiting substrate quota down to some minimal species-specific amount.

The depletion of deep substance is not the only possible reason of the growth inhibition. One can propose several reasons of the attenuation of cells' division in multicellular organisms,for example, autometabolism, the influence of the gravitation, the limits of rates of nervous impulse conduction etc. If the life of organism consists of the depletion of some substance, then the unicellular organisms must become old, and the curve of the cellular strains' development must be sigmoidal. This has been observed by some authors (Hayflick phenomenon) and disproved by others [14].

The part of the present work connected with the sources of nonequilibrium is based on the interpretation of Bauer's ideas. This interpretation implies that free energy of food is not the only source of replenishment of the structural energy's potential. It should be mentioned that this is not the only possible interpretation. G.E.Mikhailovsky, to whome the author is greatly pleased with the explanation and critique, proposes another one. He believes that the "debasement" of living matter because of the decrease of the potential can be presented as the result of the accumulation of genetic disturbances, rather than the depletion of hypothetical substance. G.E.Mikhailovsky compares the nonequilibrium of living matter to the accumulator that can be recharged, but working period of which is limited because of the debasement of its construction.

An experienced reader can consider structural energy of E.Bauer and hypothetical substantial flows of substitutional approach to be the progeni of the ideas of vitalism, for example, of the Aristotle's entelechia, Wolff's vis essentialis or nisus of Blumenbach [8]. However, the statements of the substitutional conception are more prosaic. This conception considers quite real levels of the natural systems' structures. It is merely impossible to find these levels with the help of existing scientific technologies. Hypothetical flows of elements of those levels are necessary not for the introduction of some "vital forces", but for the derivation of the whole set of logical constructions, connected with the time phenomenon by means of substitutional approach.

Naturally, the "flask" model of life arouses a lot of questions and comments. However, at the present stage of its development the efforts should be aimed at detection and identification of hypothetic flows generating non-equilibrium state of living systems. That is why some works by Kozyrev and his followers were considered above. If the interaction revealed by them is not an artefact it will confirm the existence of flows and prove both Bauer's principles and substitutional approach. Specific metabolic flows generating non-equilibrium state of living matter can show themselves in some interactions between living objects. They are still not interpreted by biologists. Superweak intercellular interactions [15] or Gurvich's morphogenetic fields [12] may be considered as examples of these phenomena. Let me notice that the conception of morphogenetic feilds has something in common with both Bauer's views, for it regards "non-equilibrium deformated states of nucleoproteids" [11, p.392] as the elementary sources of the field, and with substitutional approach, for it states that substantial contents of "the cellular fields conception consists in ... mutual dependence of different levels, namely, organisms, cells and molecules, correcting their relations by actual fields" [11, p.392].

4. Towards a dynamic theory

Now let us return to the problem concerning possible ways of description of the motion laws of living matter.

Substitutional construction of time gives the following elements for dynamic theory:

-an elementary object, i.e., a system involving several hierarchic levels (a concrete organism);

-state space, i.e., natural hierarchy, the object under consideration being the part of it, e.g., the biological hierarchy including ... molecules, cells, organisms, populations, communities, the biosphere ...;

-unification of the ways of variability in natural systems (replacements of elements on different levels of an object);

-the metabolic clock, i.e., number of replaced elements in certain model object.

Description of metabolic motion by equations requires generalization of the substitutional construction. The point is, that formalized natural systems are usually described by structurized sets. Thus, it is suitable to use the structure of sets with subdivisions for description of ecological communities involving specimens of different species. Subdivisions correspond to populations forming the community. The notion of proximity and distance of points in empirical space is described mathematically by topological structure.

The totality of atomic states can be described by vectors of infinite-dimensional Hilbert space or, in equivalent way, by the field of infinite matrices.

Application of just these structurized sets is of special importance for systems formed of several types of elements or subsystems of the same hierarchic level. Such systems are all biological systems. For example, vital functions of a cell are connected with replacements of different molecules. The rates of exchange differ significantly. sometimes it is suitable to choose a so-called "limiting" element or total amount of all types of molecules and to assume it to be the metabolic clock. However, this does not suit in other cases.

A living organism consists of differentiated cells. Rates of cell reproduction in different tissues and organs vary significantly. Thus, it is a question which type of reproducing cells (e.g., epithelium, neurons or erythrocytes) determine the biological age of an animal.

Substitutional approach requires one to be able to calculate the number of elements in objects. Therefore, when this approach is used for analysis of structurized sets it is necessary to generalize a notion of "number of elements" for these sets. Arbitrary structurized sets can be described by the theory of categories and functors, a specially created mathematical language.

Generalization of the "number" notion for structurized sets leads from cardinal (particularly, natural) numbers to structural ones. However, structural numbers are only partly regulated. Further generalization of quantitative characteristics in terms of the theory of categories leads to the method of functor comparison of structures [26; 29; 30]. Functor invariants of structurized objects allow to suggest L-component of dynamic theory. This component is formulated as the extremum principle [27; 30]: a system turns from the given X state to that A state which has maximal entropy HX(A) within a range, allowed by available external resources. Entropy of systems is calculated using invariants of functor system structures. If functional, i.e., entropy is known, variational procedures enable us to derive equations and trajectories of generalised motion of the system. Owing to extremal principle, the value of entropy does not decrease along real trajectories of the system, i.e., succession of real states, or natural evolution of the system, is regulated by its values. Thus, entropy acts as the parametric time of the system, monotonic if related to its metabolic time. Together with the metabolic time, entropy can form T-component of the theory.

A detailed account of the case of application of methodology described above to obtain dynamic equations in community ecology is given in the author's previous works [25; 26; 27; 29; 30].


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