T O W A R D S A D Y N A M I C T H E O R Y
(on the centenary of E.Bauer)
(Moscow State University)
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" (Ба-
уэр,1935,с.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.
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 (Левич,1989а,б).
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 (n ,n ,...,n ), where n is
the size of the population of species i, included in the
community. The vector set is limited by the available
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 (Фридман, 1966,с.50-53). 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, t .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 t , passed by this
material point, which is exactly the gravitational time.
Related to the gravitational time the stars' movement is
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, t .In
contrast with the star time or the gravitational time, which
are universal, this pendulum time is local, i.e., different at
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" (Poincare,1898). 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 (Детлаф,Дет-
лаф,1982). 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 (Абакумов, 1969),
ethnography (Алексеев, 1975), and genetics (Свирежев,Пасеков,
1982) 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 (Harland et al., 1982). In paleobiological
stratigraphy durations of geological epochs can be measured by
vertical width of layers with remains of fossil species (Сима-
In the psychological time model (Головаха, Кроник, 1984)
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
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
(Le Temps et la pensee Physique contemporaine, 1968). 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"(Poincare, 1898).
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 (Акчурин, 1974). " The
presentation of time as an internal property of physical
systems exceeds the limits of conventional physical
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
- 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"(Бауэр,1935,с.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 (Бауэр,
1935,с.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" (Бауэр,1935,с.129).
"During assimilation the structural energy of a system can be
used. This energy is necessary for the reconstruction of
nonliving substance" (Бауэр,1935, с.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 Бауэр,1935,с.131; Зотин, Алексеева,1984) and is
"proportional to the free energy of an ovicell" (Бауэр,1935,
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" (Бауэр,1935, с.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 (Левич,1989а,б).
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 (Левич, 1980) 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" (Ландау, Лифшиц, 1964). 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" (1961), 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" (Козырев,
1963,c.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
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" (Козы-
рев,1963,с.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
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"(Козырев, 1958). 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 (Ко-
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
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 - 10 of the body weight being
used in measurement; in the case of non- mechanical pickups,
the relative change is about 10 -10 of the value being
measured. For torsion balance the turn may be up to tens of
degrees, that correspond to forces of 10 -10 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 (Козырев, 1977,с.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
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"(Козырев,1975,c.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"(Козырев,1982, c.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
These are quotations from the report "Physical Time of
natural life'' (see references 9,10,and 22), 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 1 C don't influence
vital functions much. However, permissible changes were
determined to be in 0.2 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
For microorganisms, drastic depression of vital functions
was observed on the first day of experiment, then restitution
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
Irreversible processes transform distantly physical
properties of surrounding substances.
Living matter is considerably sensitive to these
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 (Данчаков,1984,с.
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
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
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 (Данчаков, Еганова,1987,с.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, being sought for.
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. Levitch (Левич, 1989а,1989б). 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
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
(Бауэр, 1935, с.130-133) and recent data on the existence of
Rubner's constant (Зотин, Алексеева, 1984).
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
(Левич с соавт.,1986): 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
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 (Хохлов,1988).
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 (Дриш, 1915). 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
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 Кozyrev 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 (Казначеев, 1981) or Gurvitch's morphogenetic
fields (1944) 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"
(Гурвич, 1986, с.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" (Гурвич, 1986, с. 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
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 (Левич,1982,
1989б, 1991). Functor invariants of structurized objects allow
to suggest L-component of dynamic theory. This component is
formulated as the extremum principle (Levitch,1988; Ле-
вич,1991):a system turns from the given X state to that A
state which has maximal entropy H(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 (Ле-
вич, 1980, 1982, 1989б, 1991; Levitch, 1988).
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