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On the Way to Under standing the Time Phenomenon: the Constr uctions of Time in Natur al Science. Par t 1. Inter disciplinar y Time Studies. Singapor e, New Jer sey, London, Hong Kong: Wor ld Scientific. 1995. Pp. 149-192. © A.P.Levich

TIME AS VARIABILITY OF NATURAL SYSTEMS: WAYS OF QUANTITATIVE DESCRIPTION OF CHANGES AND CREATION OF CHANGES BY SUBSTANTIAL FLOWS

A. P. Levich
1. Time-metabol The task of the present study is to discuss one of the possible versions of the construction of time. More specifically, it is to prepare in a consistent way prerequisites for constructing a dynamic theory of natural systems by suggesting an elementary object of the theory, the ways of object variability, the clocks, the space of states, the ways of obtaining variability laws and, as far as possible, interpretation procedures. Another task of the study is to test the construction in an attempt to solve some of the problems of time. The suggested material does not form a complete study. One should treat it rather as an attempt to create a research programme for studying time.


1.1. The substitutional construction of time Systems and variability. Natural systems are formed from their elements in a way which cannot be called arbitrary. T h e h i e r a r c h y p r i n c i p l e : Natural systems are hierarchic: any object turns out to be an element of a higher rank object, and any element turns out to be an object consisting of pre-elements.
Thus a living cell consists of molecules, organisms ar e for med fr om cells; the latter in tur n unite to for m populations; populations for m communities which in tur n can be consider ed as elements of the biospher e. That is a fr agment of the biological hierar chy. A ver sion of the geological hier ar chy: molecules, miner als, r ocks, sediments, terr ains. The geogr aphic hier ar chy: molecules, sediments, faces, landscapes, physical-geogr aphic distr icts, pr ovinces, zones, countr ies, continents, the dr y land, the geogr aphic shell (accor ding to I.A.Solntsev, fr om the book by I.I.Mikhailov (1985)). A sketch of the astr onomical hier ar chy: molecules, bodies, planet systems, star associations, galaxies... (All these examples ar e not r igor ous constr uctions, r ather, these ar e just illustr ations to enlighten the gener al consider ations.)

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The hierarchy structure of systems is not only a natural-scientific generalization but also one of the axiomatization methods within sets theory, making it possible to avoid logical contradictions which can appear from uncontrolled construction of objects from elements. Thus, if each element is ascribed to a certain type, then sets (natural objects) are formed from elements of the same type (Whitehead and Russel 1910; Frenkel and Bar-Hillel 1958). The types of objects are usually marked by natural numbers. It is significant that in the suggested axiomatics all the concepts acquire the character of types: in a rigorous presentation (Levich 1982) a specification of any construction (an object, an element, belonging, unification or intersection, time, space, etc.) must be followed by specification of a type. Only in an unformalized presentation, when the construction type is quite clear from the context, its identification is frequently omitted. When hierarchic systems are considered, the question commonly occurs on how far "up" and "down" the hierarchy levels are extended. It appears convenient for the author to hold on to the following position: the depth of a hierarchy is determined by the existence of operational ways to identify the elements of the "remote" levels. For any identification technology there exists a level of unidentified elements, the one to be taken for a boundary of a hierarchy (a relative one, since the available object Fig. 1. Hier ar chy of systems and the pyr amid of studying methods can change). time It is convenient to call the number of structure levels, which are taken into consideration, the depth of a system. The hierarchy principle requires that the elementary object of the theory, "a system", should be of necessity a hierarchic construction (Fig.1). The words "the set of elements of a system varies" will mean that either new elements appear (growth of a system), or that some of the elements are replaced by other copies of these (a stationary state of a system), or that some of the elements are lost (system degradation and destruction). T h e v a r i a b ili t y p r i n c i p l e : In all the natural systems there always exists the phenomenon of varying the constituent element set. Any variation of a system consists in variation of the set of elements at a level of certain depth in the hierarchy containing the system. I will call the system element variation phenomenon the general process of natural systems.
I would like to mention the gener al pr ocesses for objects belonging to the canonical example of biological hier ar chy. The gener al pr ocess in living cells is metabolism, the pr ocess of r eplacing molecules for ming the 2


cell. For multicellular organisms the gener al pr ocess is gr owth, dur ing which new cells appear and the existing ones ar e r eplaced or disappear. The number dynamics, summing up the bir ths and deaths of individuals, is the gener al pr ocess for a population. Species r eplacement, called succession, is a manifestation of the gener al pr ocess in ecological communities. The change of associations of species in the Ear th's biospher e is called the evolution pr ocess.

The hierarchy and variability principles make it possible to unify the variety of variability manifestations (quality, relation, connection changes, etc.): only the system element numbers are varied, or certain elements are replaced by others. Qualitative peculiarities of the variations are described in terms of different levels of system structure at which the elements are changed. Thus to describe the variability means to find the hierarchy levels at which the sets of pre-elements are changed. It should be noted that the term "variability" is often used in some context other than dynamical. One can speak of spatial (for instance, geographical) variability of biological or social objects. The term "variability" is also used to describe the diversity of objects in taxons of certain classifications (atoms in the chemical element system, butterflies in a collection). Choosing the position of historical method, one may try to reduce all the variability types to their appearance resulting from only dynamical evolutionary variability; however, in the framework of the present paper it is offered to discuss only manifestations of "pure" dynamic variability of natural objects. Along with the terms "element set variation" and "the general process", let us use their synonym "the course of time". Thus the postulate of existence of a "pre-time" is replaced by the postulate of the existence of the general process. Such a modification, without making clear the "nature" of time, is nevertheless useful since it defines the events operationally in terms of system element replacing. Measurement of time. The general process, unifying the variability, thus introduces the pre-time of natural systems. To introduce a parametric time, i.e., a representation of the variability process by numbers, it is necessary to make a methodological digression.
"In the descr iptions of the measur ement pr ocess, so essentially simple, one can notice a significant r eticence in many cour ses of mechanics and physics which have become classic. It was my task to establish mor e deter minacy in the pr oblem and, along with that, to show what a gr eat ar bitr ar iness is present in establishing a measur ement" (Fr iedmann 1965, p.16). Namely, if a r elation of or der is established on a set K of the pr oper ties of a cer tain fr agment of the r eality, then those pr oper ties ar e called intensities. If the r elation of "equal spacing" is defined for the intensities K1, K2 and K3, i.e., K1 is smaller than K2 as much as K2 is smaller than K3, then these intensities ar e called measur able. For example, the volumes of geometr ic bodies ar e measur able intensities, while the quality of students' knowledge is an unmeasur able one. The mapping A: K R of a class of pr oper ties K into a numer ical set R is called ar ithmetization of the pr oper ties K. A monotonic ar ithmetization of intensities is called an estimate. Examples: estimation of students' knowledge using five- or hundr ed-gr ade scales; juxtaposition of the corr esponding electr omagnetic wavelengths to the colour s of the solar light spectr um. Estimations of measur able intensities, satisfying the condition A(K2) - A(K1) = A(K3) - A(K2), ar e called measur ements. Any two arithmetizations, if they ar e measur ements, can differ ent fr om each other only linear ly, i.e., only zer o points or measur ement units can be differ ent. 3


Thus "any class of pr oper ties can be ar ithmetized; if these pr oper ties ar e made intensities (by our definition), then we can... estimate them by number s; finally, if the intensities ar e made (again by our definition) measur able intensities, then we can... measur e them; a measur ement will contain cer tain ar bitr ar iness, r emoved by establishing the zer o point and the measur ement unit" (Fr iedmann 1965, p.15).

Thus to make it possible to measure the variability it is necessary to have an agreement (an instruction, an imperative...) of which intensity differences are taken as equal. T h e im p e r a t i v i t y p r i n c i p l e : A standard object belonging to a certain level of system structure, is called a clock. Changes of the set of elements of the standard object by one element are considered to be equal and can be taken as the unit of time.
The necessity of such an agr eement is r ealized by natur al scientists (Milne 1948): A pr ior i we can take any dynamic phenomenon and use its development to define the time scale. However, a unifor m natur al scale does not exist, since we cannot say what is meant by the wor d "unifor m" with r espect to time; we cannot catch the pr esent minute and put it side by side with the next one. It is sometimes said that a unifor m time scale is defined by per iodic phenomena. However, allow me to ask a question: can anybody tell us that the two periods, following one another, ar e equal? In physics the r ole of a unifor mity agr eement is played by Newton' s fir st law: the time inter vals dur ing which a body, moving without inter action with other bodies, cover s equal distances, ar e called equal (Thompson and Tait 1890).

Let us introduce a few definitions to illustrate the ways of conceptual basis construction becoming evident after the imperativity principle is adopted. A t y p e i e v e n t x (a synonym: a time instant) for an object A of the type i + 1 is a replacement of the element x in the object A. We will also call an event the replaced element x itself. A s u b s t i t u t i o n a l c l o c k is a natural object whose element substitution is taken as a uniform variability standard.
The pr oper time (Vasilyev et al. 1974) or the pr oper age (Zotin and Alexeyeva 1984) of an organism can be defined fr om the counts of consumed oxygen molecules. The pr oper age of an organism can be measur ed by the number of newly for med cells; by wound healing ar ea (NoЭy 1936); by gr owth of specified organs of the body, e.g., the size of eye cr ystalline lens is consider ed to be one of the best biological age mar ker s for mammals (Shaher 1982); the number of separ ated cells of yeast, being their only stable age char acter istic, unlike any chr onological dating (Voitenko 1985). The scale of age stages of a plant (Chebur ayeva 1977): ger mination, juvenile, immatur e, young vegetative, young, matur e, old, subsenile, senile stages) is tr eated as a specific for m of ontogenetic time accounting, such that the inter vals between the neighbour ing age stages ar e taken to be equal (Ur anov 1975). The same is the case for the scale using the instants of pea alter nate leafs appear ance (Thor nwaite 1953). The dynamics of micr oalgae populations is well descr ibed in ter ms of consumed biogenic elements which ar e limiting factor s of community development (Levich 1980; Levich et al. 1986). The matur ity par ameter of an ecological community (a concept close to ecological age) is intr oduced by M.E.Vinogr adov and E.A.Shushkina (1983): the matur ity index is connected with the r atio of community destr uction (commonly measur ed by the amount of biogenic chemical elements leaving the community) with r espect to pr imar y pr oduction (pr opor tional to the amount of biogenic elements enter ing the community). In paleontology the analysis of large gr oups of organisms on the basis of measur ing the number 4


of taxons is quite common. One usually takes into account those char acter istics which r efer to a single str atigr aphic division, namely, the over all number of taxons and the number s of those appear ed and died out (Dmitr iev 1978).

A p r o p e r t im e i n t e r v a l o f d e p t h k between an event a of type k and another event b of type k for an arbitrary system of type i is, by definition, the number of type k elements which have been replaced in the system as a result of the general process. Thus the proper time of depth k for a type i system is measured by the clocks of the type i - k + 1 obtained by unification of type i - k + 1 elements belonging to the above system. If the concept of event simultaneity can be correctly introduced, then there is a possibility to measure not only the proper time of a system but also its time by an arbitrary clock. E x t e r n a l t im e ( t im e b y t h e c l o c k C ) . A time interval between the events a and b by the clock C is the proper time interval of the object C between the event x belonging to C and simultaneous with a and the event y belonging to C and simultaneous with b. T h e a g e T o f a n o b j ec t A according to some clock is the time elapsed by this clock between the events which have occurred in the object A and consisted in the appearance of an element d in A and its leaving A (d belongs to A).
The amount of oxygen consumed by an animal fr om its "fir st sigh" and "last br eath" can ser ve as its physiological age. If the Rubner r ule is valid (Zotin and Alexeyeva 1984), then this quantity is the same for all r epr esentatives of a single biological species. Mor eover, if one assumes that the oxygen consumption r ate for oxidation of a unit mass of food is constant, then the physiological age corr esponds to the amount of consumed food, i.e., one speaks of a cer tain substr ate-energetic pr oper time scale of an organism. The Rubner r ule is confir med by exper imental r esults obtained mostly on r odents, insects and unicellular s: food limitation leads to life pr olongation (McCay 1935; Bauer 1935).

T h e p r e s e n t o f a n o b j ec t . Given an object A of type i + k and its type i element d, I will call "the present of the level k for the object d with respect to the superobject A" the time interval (by some clock) between the events consisting of d entering A and d leaving A. The quantity T may be called "thickness of the present". I would like to note that the thickness of the present for an object d with respect to the superobject A is equal to the age of A measured by the element d. It is natural to call the events which took place before the object d entered the object A "the past with respect to the superobject A". Accordingly one can define "the future of the object d with respect to the superobject A". It is evident that the past, present and future of an object are relative since they depend entirely on the choice of the superobject A (that is, the higher level of the natural hierarchy and the representative A of that level which contains the object d). The multicomponent nature of the substitutional time has turned out to be essential
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for the introduction of the past, present and future. The multicomponent nature makes it possible to separate operationally the non-coinciding properties of time: the temporal sequence "past - present - future" for an object d is defined only with respect to its superobjects while the sequence "earlier - later" is determined by a clock of the same type as the subobjects of the object d. I would like to note that the ideas connected with the "thickness of the present" have been induced by the works of G.E.Mikhailovsky which are also presented in this book. Substitutional time and a substitutional object of the theory. In Latin the word "substitucio" means replacement. The clock construction operating with element replacements in systems, is called substitutional according to the tradition to use Latin terms in scientific texts. In the following we will also use a synonym of the word "substitutional", namely, the word "metabolic" of ancient Greek origin. The scientific tradition traced back to Heraclites and Aristoteles, which connects time with the perception and experiencing changes in the World. Aristoteles (1981, Comment 9 of Chapter 11 of Book 4) distinguished changes as movement in a broad sense ( ), as emergence and destruction (genesis kai phthora), as qualitative transformations (alloisis) and as mechanical motion (kinesis). The above variability axiomatics: the general process = generalized movement = the course of time - does not refer to a separate type of transformations and apparently corresponds to the term " ". By S.V.Meyen' s proposal, the described constrcu tion of time is called the metabolic time of natural systems (see also the term used in papers by Goodwin (1966), G.E.Mikhailovsky (1982) and Schmidt-Nielson (1987)). However, the word "metabolic" is to be understood in a much wider sense than just biochemical metabolism of living cells and organisms. Usually one imagines time as some cyclic process, or the one connected with repeated periods: alternation of day and night, oscillations of a pendulum and ticking of a clock, metronome rythme, ... Measurement of time in physics is always connected with periodic processes: rotation of the Earth, mechanical or electromagnetic oscillations. The suggested construction replaces "cyclic" clocks by "substitutional" ones, transferring the accent to processes, which are not necessarily periodic but can be nonstationary and evolutionary. However, the "cyclic" and "substitutional" process representation can be complementary to each other.
In quantum-mechanical field descr iption ther e exists a deep corr espondence between the r epresentations of phenomena in the language of fr equencies and that of par ticle r eplacements ("cr eation" and "annihilation"). It is involved in the second quantization method.

Metabolic time is a property of a elements of a certain structure level. The substitutional construction metabolic view of the World, or, more p of the theory does not resemble "points" ily an open one.

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system which is of necessity open with respect to of time creates an archetype of hierarchic and recisely, of natural systems: the elementary object or "states", it is a hierarchic object and necessar-

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To describe a metabolic object rigorously, new mathematical means are required. The hierarchic nature of an object can be described in terms of the armade construction (Levich 1982), which explicitly introduces into mathematics, apart from a tangle of the traditional algebraic, topological and order structures (Bourbaki 1963), a hierarchic algebraic structure (on the basis of the already mentioned theory of types). However, the setstheoretic foundations of mathematics are apparently insufficient for a formal description of a metabolic object: one needs a formalism for describing systems with appearing and disappearing elements (this circumstance was noticed by A.A.Sharov). Maybe that could be achieved if a softer form of extensionality were adopted but possibly more radical means are required to operate with "dynamic sets" instead of those with elements determined once and forever. A good implicit example of a "dynamic set" is a "metapopulation" of organisms, including, along with the individuals existing at the moment, their ancestors and potential descendants. One more feature of a formal description of a substitutional object is the necessity of rejecting Archimedes' axiom: no "mechanical addition" of pre-level elements can result in a consistent object of a given level. Thus the algebraic properties of the objects (universums) from different levels imply that those universums are related to each other as objects of nonstandard analysis (Robinson 1966).

1.2. Properties of substitutional time The multicomponent character. Proper times of different depths belonging to a system form a multicomponent quantity for which I would like to suggest the name "the pyramid of time" of a given system (Fig.1). The term "pyramid" looks rather awkward but the other term coming to mind, "the vector of time", would be mathematically inaccurate, since neither a coordinate frame is introduced, nor transformations under which the studied multicomponent quantity would behave as a vector.
The pr oper time t1 of depth 1 for a cell is measur ed by the number of molecules r eplaced in that cell. In a similar manner the time of an organism is measur ed by the number of r eplaced cells (NoЭy 1936; Shaher 1982). The time t1 for a population is measur ed by the bir th-death balance for the member s of the population (Abakumov 1969; Alexeyev 1975; Svir ezhev and Pasekov 1982). For a community t1 is the number of species changed in the succession. The biospher ic time t1 is counted by associations of living organisms, r eplacing each other, disappear ing and for ming again. An ecological community can be imagined as a unity of individuals belonging to all the species for ming the community; the balance of changes of the total number of individuals deter mines the value of the time t2 of depth 2 for the community. For an organism t2 is deter mined by the molecular flow thr ough the organism (Vasilyev et al. 1974). The biospher ic t2 is the number of r eplaced species (Dmitr iev 1978). To find solutions of many ecological pr oblems it is convenient to r epr esent a community as a pool of a cer tain biogenic chemical element limiting the development of organisms (e.g., car bon, nitr ogen or phosphor us). The sum of molecular number changes in the pool (in pr actice such quantities ar e estimated in ter ms of mass or concentr ation units) is the pr oper time of depth 3 for the community (e.g., for algocoenoses - Levich et al. 1986a) or 4 (for communities of multicellular organisms - Vinogr adov and Shushkina 1983).

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Usually one of the components is chosen for measuring time, nearly always the deepest one, close to the indistinguishability level and connected with physical processes (e.g., the electromagnetic scale corresponding to photon "replacements" in atoms). The imperativity principle allows one to choose a system belonging to any level of natural hierarchy as a reference clock.
The ideas that time is mor e than one-dimensional r epeatedly emerged in natur al science. "For life viewed fr om the geochemical standpoint, time is expr essed in thr ee differ ent pr ocesses: fir stly, the time of individual existence, secondly, the gener ation changing time, with the for m of life unchanged, and, thir dly, the evolutionar y time, i.e., that of changing for ms along with gener ations" (Ver nadsky 1988, p.231). "The existence of many time scales is without doubt the most significant aspect of life.... For instance, ther e exist the physical time (in equations of motion), the catalytic time (necessar y for descr ibing fer mentative r eactions), the time of cellular fission, the ecological succession time and, finally, the evolutionar y time..." (fr om G.Patti' s letter addr essed to C.H.Waddington. On the way..., 1970, pp.177-178). G.E.Mikhailovsky (1982) intr oduces the complex time of living organisms (see also G.E.Mikhailovsky' s chapter in this book). Its r eal par t is the ontogenetic time of an organism while the imaginar y one is deter mined by the stage of the self-r epr oduction pr ocesses. N.I.Moiseyeva (1980) insists that a thr eedimensional biological time should be intr oduced.

Non-uniformity of the course. The freedom of choosing reference objects time measurements allows one to ask the question, whether or not all the processes commensurable, i.e., can any of the existing processes serve as a reference for any o process? We are forced to answer negatively, since due to the imperativity principle

for are ther the

Fig. 2. The points a1, a2, ... ar e events consisting in system A element r eplacements; the points b1, b2, ... ar e events consisting in system B element r eplacements. If system A is taken for standar d, i. e., the time inter vals between its elements ar e r egar ded as equal, then element r eplacements in system B occur nonunifor mly, so that each next event happens after a bigger time inter val. If, on the contr ar y, system B is taken for standar d, then events in system A occur non-unifor mly: the inter vals between them decr ease.

time intervals, equal as measured by one clock, can turn out to be different as measured by another clock (a schematic example in Fig.2 illustrates the mutual non-uniformity of two time scales). The non-uniformity of metabolic time, as a consequence of the hierarchy and imperativity principles, is discovered only when several time scales are present. If a scale is unique, the course of time is uniform by the definition contained in the imperativity principle. For example: "The absolute, true, mathematical time as it is, by its very nature, without any relation to anything outside, flows uniformly and is also called duration. All the motions can accelerate or decelerate, while the flow of absolute time cannot change"
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(Newton 1687, translated from Russian ed.). A choice of a "sufficiently deep" component of the pyramid of time as a representative of the whole pyramid leads to adoption of a uniformity standard for cal time scales. The man-made instruments for measuring time, such as a burning with marks drawn along it, sand, water, pendulum, astronomical, atomic and clocks, are most equally mutually uniform.
Note that the physical pr ocesses aspir ing to be used a ephemer is time, the "second wor ld time" taking into account the Ear th, the tr opic year, r adiation of caesium atoms) r epr esent the ties fr om the standpoint of the moder n level of accur acy (Mar tyn

unique physicandle pulsar

s time standar ds (the r otating Ear th, the seasonal corr ections to the r otation of the clocks of significantly differ ent unifor miov 1961).

The choice of a clock is to a large extent a psychological problem: although very different natural processes can be suggested to play the role of standard clocks, the ones convenient for a man are preferred. I.e., those in agreement with the course of "time of the consciousness", which in turn is induced by the planetary conditions of human life. "As a matter of fact, the uniform motion concept already assumes the existence of time, while the expression "the stars are moving uniformly" means only that we call the stellar motion uniform. The uniformity of motion is an entirely relative concept: one can speak of one motion uniform with respect to the other, so that when we speak of a uniform motion, we mean motion uniform with respect to that of stars, or, though it sounds still more odiously, uniform with respect to the rotation of the Earth. Ascribing a specific, mystic sense to stellar time, one reveals the human unwillingness to understand the whole extent of the non-central, modest position of the planet where, as the fates decree, he has to live" (Friedmann 1965, p.13). The anthropomorphic selection of time scales is understandable but must not overshadow the possible application of time scales with different course uniformities in descripting various forms of generalized motion in various frames of reference. A change of standard objects and the corresponding scale change connected with uniformity change is not just a replacement of measurement units or that of a zero point: that is necessarily a nonlinear transformation, since linear ones would preserve the scale uniformity, so that equal intervals would have remained equal. Most of "proper" time scales in natural science are non-uniform with respect to astronomical time, which sometimes allows one to discover certain laws escaping one' s attention when the traditional physical time scales are used.
The scale connected with wound healing r ate (NoЭy 1936) tur ns out to be non-unifor m with respect to the chr onological age: a five-year -old child' s wound is healed ten times faster than that of a pre son of fifty. A nonlinear tr ansfor mation of planetar y time (Backman 1943) applied in a descr iption of gr owth cur ves for a br oad class of living organisms made it possible to discover the elementar y dur ations, "life quanta"; their density is unifor m in Backman' s "organic time" and is much gr eater at the fir st stages of development fr om the viewpoint of the or dinar y time scale (that is why it is so har d to catch them). E.Milne (1948) r emoved the postulate of congr uence between time inter vals shown by clocks of one type, namely, mechanical and atomic ones, and intr oduced the logar ithmic scale to measur e the cosmological time of the Univer se. The time tr ansfor mation eliminated the gr avitational inter action fr om the fundamental equations of motion and gr eatly simplified the descr iption of the non-stationar y univer se. 9


The hypothesis of logarithmic connections among time scales. Inasmuch as the time scales determined by standards of different levels are mutually non-uniform, the question arises as to what are the functional relations among different scales. Many scientists suggest that some specific times depend logarithmically on the common physical time. Among those there are the above cosmological time due to E.Milne (1948) and G.Backman' s (1943) "organic time" which parametrizes the variability of living organisms by quantitative characteristics of their growth. The size of an eye crystalline lens of a lamellidental rat Nesocia indica (as a biological age indicator) and its chronological age are logarithmically related (Shaher 1982). An attempt to use statistical methods in order to select the most adequate approximation for the dependence between the physiological age of rats, determined from 23 physiological characteristics, and their chronological age also led to the logarithmic function (Hofecker 1981). An origin of the logarithmic law discovered experimentally for some time scale connections is one of the problems in the description of multicomponent metabolic time non-uniformity. One of the attempts to solve that problem can be found in a paper by V.S.Fleischmann (1986). The specific nature of time scales. The times determined by standards belonging to different system structure levels and, the more so, to different natural hierarchies, are specific rather than universal.
Speaking of specific time, for instance, of physiological, ontogenetic or evolutionar y times, we mean that the fir st one is measur ed by the number of absor bed oxygen molecules, the second one by the number of newly for med cells of a gr owing organism while the thir d one by the number of taxons in the r econstr ucted biosher ic annals. The geological, biological, geogr aphic and other specific times ar e pr oper time pyr amids constr ucted in the corr esponding natur al hier ar chies.

The idea of universality of time originates fro