Kirill V. Simakov

  

GEOCHRONOLOGY, GEOCHRONOMETRY and the PROBLEM of MEASUREMENT of the GEOLOGICAL TIME

  Abstract

Author studies two essentially different viewpoints of the essence of the time category, which have been formed by now. The first approach is the best represented by substantial conception of time, according to which, presents itself just as an external indicator and a measure of quantitative differences between systems and processes, which are unequal by their matter-energetic properties. According to the second approach under relative-genetical conception of the real time-duration by Stenon and Vernadsky, time is a universal and immanent of both qualitative and quantitative characters of all manifestations of reality. It is essentially important, that these two conceptions hold the properties of time radically different, and this makes it objectively necessary to use different logic-mathematical approach to its measuring within the framework of each of these two conceptions, i.e. classical analysis in the substantial conceptions and a set theory in the relative-genetical conception.

At present we can distinguish between two geological disciplines dealing with the problem of time on the basis of specific time conceptions, i.e. a geochronology underline by the paleobiospheric time theory and a geochronometry based on the isotopic (radioactivity) time theory. A fundamental difference between them is that the course of the paleobiospheric time has been ruled by some global factors, whereas the flow of radioactivity time is determined by local and distantly placed, non-interrelated events, which have giving impetus to specific radiological clocks that is connected with the systems of mineral- and rock-levels of organization.

A rehabilitation of the value of the event approach to determination of chronostratigraphic boundaries excludes a possible isotope dating of their age positions by virtue of weighted average readings of distantly placed radiological clocks. The procedure of their tracing is based on a retrosynchronization of the global event records, but not on an identification of the isotopic (not absolute!) time moments, as according to the principle of the absolutely precise measurement. A transfer to an event-based definition of chronostratigraphic boundaries requires a serious change in methodological grounds of both procedures of their establishing and tracing. Both the establishing of boundaries between the conceptual paleobiospheric time units and their world-wide tracing require a system of non-trivial conventions. These conventions are objectively necessary due to an ecotone-like character of chronostratigraphic boundaries, and to the law of a metachronous development of heterogenous paleosystems and processes. These conventions are radically differ from trivial and banal agreements making ad hoc in usual practice: in this case not we prescribe such conventions to the Nature, but the Nature itself dictates them to us.

A cardinal difference between physical and paleobiospheric times is that they are mutually irreducible to each other. Consequently, it is impossible to use, for measuring the paleobiospheric time, neither the idea of a numerical continuum nor the whole logical-mathematical apparatus of classical analysis based on it. Construction of a countable" metrics of conceptual paleobiospheric time, corresponding by Stivens classification to a scale of intervals, can only be possible by virtue of the logical-mathematical apparatus of set theory. This approach will basically allow us to establish the relations of equivalence and strict order between the chronoindicators, which represent an irreversible character of the evolution of heterogeneous paleosystems, the models of which are taken as the basis for metrics for different intervals of the geological history. Implementation of this idea primarily depends on developing and reaching an agreement about the taxonomy of paleosystems, which will act as the basis for construction of a model of the universal (embracing the whole history of the Earths crust) conceptual paleobiospheric time.

The theory of paleobiospheric time, that has been created, give geosciences from many pseudo-problems related to the procedure of identification of the geological (s.l.) and physical (everyday, common) time notions. This theory offers a methodologically valid approach to solve the problem of chronostratigraphic/geochronological boundaries and also allows us to establish the principles of developing a measuring scale (a metrics) for the conceptual paleobiospheric time.

Table of Contents

INTRODUCTION...........................................................................................................................................................2

1. General notes (2).

MYTHS and REALITIES.............................................................................................................................................3

2. Origin of the substantial and attributive conceptions (3)

3. Separation of the conception of the absolute, relative, and relative-genetical time (5).

4. Vernadskys revolution in meaning of time (5)

5. Modern development of the Vernadskys theory (6)

ILLUSION and COLLISIONS........................................................................................7

6. General notes (7).

Geochronology (8)

7. The landmark in development of the representation on the properties of real paleobiospheric time (8).

8. The contradictoriness of the modern theoretical statements of chronostratigraphy (10).

9. The general properties of real paleobiospheric time (11).

The verbal and conventional components in boundaries determination (12)

10. The problem of chronostratigraphic boundaries (12)

11. Proposals on determination of the Phanerozoic chronostratigraphic/geochronological boundaries by paleontological technique (14).

Geochronometry (16)

12. From Moses to Rutherford (16).

13. Errors in methodological grounds of geochronometry (17).

14. Two trends of practical application of radioactivity backdatings (18).

15. Interrelation of qualitative and quantitative assessments of temporal properties and relations of geological phenomena (18).

16. Conclusions (20).

The PROBLEM of MEASUREMENT of the GEOLOGICAL (s.l.) TIME..................................................21

17. General notes (21).

18. The problems of creation of the model and the metrics of paleobiospheric time (22).

19 The methodological consequences of the tempodesinentia law (23).

20. A basic approach to the solution of the geological time measuring problem (24).

21. Conclusion (26).

REFERENCES .................................................................................................................................................26

 

INTRODUCTION

What, then, is time? If no one not

asks me I know what it is. But if I

wish to explain it to him who asks, I

do not know, I am baffled.

St. Augustine

1. Notions of time, space, motion, and substance fall into a number of fundamental philosophical categories. They are also the source conceptions underlying all natural sciences, from which sequential natural-scientific pictures of the universe arise. The notion of time seems self-evident, even trivial, and in ordinary life is identified with a clock. However, 1,500 years after Augustine the Blessed, Reichenbach conceded that the problem of defining the essence of time continues to put man's reason in deadlock.

Geology is usually classified as a so-called descriptive discipline, as opposed to a precise science. One of the reasons for such a separation of disciplines is the impossibility of using strict mathematical formulas in descriptive sciences to express regular behavior of studied objects in time and space. Not to argue in detail the problems associated with classification or discrimination sciences, I will point out the following.

(1) Introduction of the conception of time into the descriptive discipline of geognosy, turned it into the historical science of geology. However, the pioneers of geology did not address themselves to the questions concerning specific features of geological time as distinct from physical (absolute, relative, or common) time. To them the biblical time, the time of everyday experience, and geological time, all seemed identical. Yet, geology was gradually and unobtrusively accumulating empirical data and preparing the theoretical underpinning for formulating decisions about the notion of geological (paleobiospheric) time and its specific properties and structure. At the beginning of the 20th century, Vernadsky (, 2000) formulated a new theory of real time, as duration (length), based upon generalization of empirical data from physics, geochemistry, biology, and geology. However, it had little substantial effect on the development of a new conceptual picture of the geological kingdom to this day geological theory and practice rely upon notions of time that are independent of any external substance.

(2) Geology deals with a diverse class of natural systems compared to those in the study of physics, especially mechanics. First of all, most geologists do not study dynamic operating on our eyes but static systems. Secondly, static systems represent protocols of development of a previously functioning system. They are the systems, which were open (badly closed), self-organizing, and heterogeneous matter-energy natural systems bounded by the results of processes that were in composite interplay with each other. And thirdly, the validity of the final conclusions of geological study of genetical, geohistorical and other constructions does not lend itself to experimental verification because quasidynamic models, which are retrospectively reconstructed on the basis of the information contained in static systems, are connected with the latter by the relationships of one-to-multiple meaningful correspondence.

(3) The birth and subsequent development of geology as a special historical science is indissolubly connected with the usage of the notion of time. However, few geologists have reflected over its contents. Additionally, in geology, the notion of time is radically distinct from that of Newton, which early was generally adopted not only in all other natural sciences, but in philosophy as well. The identification of the notion of geological time with the notion of common (= physical) time and the acceptance of the substantial conception of time prevailing in physics as a methodological basis of geology, were and are now the major reason for a particular theoretical decline not only in chronostratigraphy (more precise geochronology), but also in the modern discipline of geochronometry, which are responsible for analysis of both definition of spatial-temporal properties and relations of geological phenomena.

Perhaps, one of the most obvious examples of the absence of attention to the methodological foundation of our science can be seen in generally accepted expressions of geological time or geological age . They are applied to temporal properties of miscellaneous phenomena of geohistorical process which are obtained with the help of various clocks, and which represent structure and properties of the own time of radically different matter-energy natural paleosystems and their included processes. Krut' (, 1973, 1978), speaking about geological (s.l.) time in general, stressed the necessity to recognize it as an integrative, complex notion. It integrates notions about structure and properties of the own time of different paleosystems. These paleosystems differ from each other not only by their matter-energy nature, but they also fall into different levels of organization of the Earths matter (ranging from atomic to planetary), which are connected with each other by a composite system of forward and backward interplays. Strictly speaking, the notion of proper geological (s.s.) time should be restricted exclusively to the time, which represents specificity of endogenous processes only. Parallel to it, it is necessary to distinguish at least between paleobiospheric, paleobiologic, isotopic and paleomagnetic time. They accordingly reflect features of interplay processes of endo- and exogenic factors, organic evolution, radioactive decay of elements, and variation of magnetic fields of the Earth. A model of any of these process can serve as a basis for constructing the corresponding metrics of conceptual time. Any of these model in principle can be used for an evaluation of temporal properties and relations of all other phenomena of geological history. However, due to the specific matter-energy nature of these processes, models and metrics based on each of them, surely will be unequal by their structure. Therefore, their practical application will inevitably result in a different estimation of the temporal properties of the same happenings and events, registered in the geological record.

The reader will constantly encounter the opposition of conceptions, on the one hand, of real time, and on the other of absolute and relative (sensu Newton) time. Thus, before discussing the general topic of this article, it is useful to briefly explore the discrepancy between Newtons substantial conception and the conception of a real time-length of Vernadsky.

MYTHS and REALITIES

Absolute, true, and mathematica

time, of itself, and from its own

nature, flows equably without

relation to anything external and

by another name is called duration.

I. Newton

The notion of time is one of the general

scientific empirical generalization...

Time is one of main exhibitings of sub-

stance, inseparable from it its contents

V.I. Vernadsky

2. The origin of the idea of time as an overall property or attribute of reality, enclosing man, began with the birth of civilization. From the start, it developed in two fundamentally different directions. One direction was connected with generalization of the sequential or intensive order of sensations. The other is connected with measuring time.

The first direction concerns the generalization of information, receivable in the intensive order of sensations, about properties of the actual world. On the one hand, it consists of continuous, periodically iterating external processes (replacement of day and night, climatic seasons etc.),which led to the idea about appropriate time cyclicity expressed, on the one side in the Gerbanites conception of Annus Magnus and, on the other in the extreme by Nemesius' conception of the Great Year of Stoics.

According to Lyell, the Gerbanites taught as follows:

After every period of thirty-six thousand four hundred and twenty years, there were produced a pair of every species of animal, both male and female, from whom animals might be propagated and inhabit this lower world. But when a circulation of the heavenly orbs was completed, which is finished in that space of years, other genera and species of animals are propagated, as also of plants and other things, and the first order is destroyed, and so is goes on for ever and ever (Quoted from: Lyell, 1853. P. 23).

Later on, at the end of the 17th century this version of Annus Magnum was explored by Burnet and the idea of the periodical renovation of the organic world was adopted in the 19th century by proponents of the Catastrophic school. Contrary to the latter, the Stoics idea of Great Year was developed in a very strange manner by Lyell who, like Nemesius, believed in perpetual repetitions of the same living beings in the same seasons of each Great Year.

The Stoics say that when the planet return, at certain fixed period of time, to the same relative positions which they had at the beginning, when the kosmos was first constituted, this produces the conflagration and destruction of everything which exists. Then again the kosmos is restores anew in a precisely similar arrangement as before. The stars again move in their orbits, each performing its revolution in the same former period, without variation.

Socrates and Plato and each individual man will live again, with the same friends and fellow-citizens. They will go the same experiences and the same activities. Every city and village and field will be restored, just as it was. And this restoration of the universe takes place not once, but over and over again indeed to all eternity without end. Those of the gods who are not subject to destruction, having observed the course of one period, know from this everything is going to happen in all subsequent periods. For there will never be any new thing other than that which has been before down to minutest detail

(Quoted from: Whitrow, 1973. P. 15).

On the other hand, this information is from the transitoriness, finiteness of existence, and irreversibility of changes of natural (physical) phenomena, including human life forming the basic notion about the arrow of time. This is clearly expressed in metaphors of the flow or the course of time, which A. Grunbaum believes to reflect the continuity of psychological sensations experienced by each individual person.

The other direction taken by early ideas of time measuring time is more exact and tended, even at the beginning of civilization, to quantitatively assess and compare parameters of temporal properties and relations of natural phenomena. In this framework the notion of time was as something external to and substantially independent upon all other realities. And around this background of a uniform and continuous flow, all peripeteias of daily life revolve. Time, from this point of view, appears as a universal parameter, which allows us to express and compare in a uniform system based on the of measure of discrepancy between all happenings of the world enclosing us. I emphasize that it was within this framework of the substantial conception, that the idea of usage of the system of hierarchically subordinate natural metrics for measuring time was put forward for the first time. Periodically repeating processes rotation of the Earth around its axis (day), orbit of the Moon around of the Earth (lunar month), and the revolution of the Earth around the Sun (year) were accepted as the basis for this system.

I would like to point out two important moments in the development of the conception of time. Firstly, within the framework of the first trend, the notion of time was based on the generalization of information about invariant properties of reality, and in the second trend, time played the role of an informant about discrepancies in features exhibited in natural phenomena. Secondly, both conceptions of time are based on the intensive order of sensations about happenings and events of the actual world or, alternatively, on the generalization of information about dynamic and kinematic properties of natural (physical) processes.

During the initial developmental stage of essential notions about categories of time, nobody paid attention to the fact that there is a vast spectrum of another natural phenomena. The information available on these phenomena does not allow us to deduce conclusions about time, either as to its universal property, or as a continuously streaming substance; during the life of not only an individual person, but also in the existence of all mankind, they remain invariable, static. It is as if they form a background, or substratum for all natural happenings and events, and for civilization as well. The information on these phenomena was generated in the consciousness of man, on the basis of an extensive order of sensations, which testified to a spatial and material (genetical) heterogeneity of an actuality, surrounding man. The comprehension that time was connected with these happenings of the actual world, demanded generalization at a higher intellectual level than generalization of sensual perceptions of phenomena experienced in immediate sensations. At this very time Aristotle had already no doubts about that these, static by their nature, phenomena relate to time. He pointed to alterations in physical-geographical situations of separate regions, experienced by his contemporaries and captured in legend. The intuitive representation that time is a universal attribute of not only dynamic phenomena, but also of static phenomena of reality, was underlined by the principle of an actualism, which allowed us to compare the result of something proceeding here and now, to static objects arisen at one time. The truth that nobody attempted to understand, what is the invariancy of dynamic and static systems, and what is the discrepancy of time, intrinsic to them.

In any event, the original notion of time, as a universal property of any (both dynamic, and static) phenomena of the actual world, formed, on the one hand, on the basis of generalization of the information, which entered in the intensive order of sensations, and on the other on the basis of its comparison with the information, gained by the extensive order. Or else, the attributic conception of time, which has arisen in Hellenic epoch had, in modern terms, the informational nature and represented the first attempt of generalization of invariant aspects of the information about a reality, enclosing the man.

3. Attributic and substantial conceptions peacefully coexisted till the second half of the 17th century, which becoming critical in understanding of nature of a category of time. To this period the design of those three main conceptions of time refers, and the competition between them continues till now: substantial, relative and relative-genetical. It is considered, that Newtons famous tract Mathematical principles of natural philosophy, published in 1687 had a crucial value in forming modern, both scientific and philosophical, ideas about nature of time. It was followed by a well-known dispute between Leibnitz and Clarke, that designated a legible difference between substantial and relative conceptions. However, just few readers paid attention to Stenos dissertation Concerning a solid body enclosed by process of nature within a solid, published in 1669, in which he laid up a foundation for not only methodology of all modern geology, but also special relative-genetical conception of time (, 1994, 1995; Simakov, 1995).

As it is known, Newton legibly differentiated between absolute and relative time. The former, alongside with absolute space, was, in his opinion, exhibiting a spiritual beginning of the world, the place of itself and all existings; it was considered by Newton as independent from anything external, flowing past evenly substance. The second was considered as an external measure of the former and represented its model possessing the same properties uniformity, homogeneity, continuity, and isotropy. As a matter of fact, having framed the myth about existence of some absolute time, Newton, firstly, simultaneously entered into science idea about a conceptual time, and secondly, assigned both absolute, and relative (= conceptual) time property of instruments, measuring it. Thus, as Vernadsky (, 2000) underlined, Newton removed a real time (as universal property of any phenomena) from a sphere of scientific concerns: henceforth the time has turned into passionless external parameter, permitting to build a computed picture of the universe. It is of fundamental importance, that in the Newton's conceptual picture of the mechanistic universe the laws, operating in it, did not depend on a direction of the flow (streaming) of time. Consequently, he attached to time one more universal property reversibility. In effect, due to this a methodological corner-stone of all Newtons conceptual picture of the universe was the principle of uniformitarianism, asserting independence of the laws of mechanics on space and time. As Vernadsky emphasized, this principle eliminate from a sphere of scientific concerns a history with all collection of its irreversible processes, developing in different vectors.

It is prime importance, that, having assigned to time properties of a continuity, homogeneity, uniformity, and isotropy, Newton was able to make an analogy between temporary, numeric, and geometrical continua. In its turn, it allowed him to utilize, for measuring time, all logic-mathematical apparatus of classic analysis, the postulate about possibility of absolute precise measurements and position, according to which reaching equal results demands identical time-spans.

I shall accentuate, that the idea, put forward by Newton, about a conceptual time and its properties was, certainly, rather useful and necessary: it enabled him to make an assessment and comparison of quantitative parameters of temporal properties and relations of all phenomena of a reality in a uniform frame of reference. It is quite clear, that the principle of imperativity should be utilized for constructing model and metrics of any kind of a conceptual time (, 1996). In other words, if we do not attach to its natural initial measures properties of uniformity, continuity and homogeneity, it will be impossible to justify equivalence of one-ranking measures of a scale. However, as A. Eddington pointed out, it does not mean, that similar properties have the real time, which represents universal attribute of all exhibitings of the world, surrounding us.

The authority of Newton was so high, that the idea, put forward by him, about time as an exclusively external parameter of any phenomena of a reality, survived till now. As Vernadsky pointed out, even a formal change of the substantial conception on relative one, generated at the beginning of 20th century by A. Einstein, has not influenced it: the time, in treatment of Einstein, remained the same unstructured, isotropic external measure of all phenomena of the world, enclosing us. Einsteins conception radically changed only the notion about a simultaneity and procedure of its determination, but has not affected in any way the point of view about properties of the time itself. I shall accentuate, that those conclusions, which follow from relational treatment of a category time, till now have had only philosophical value, but not a pragmatic one.

4. Vernadsky (, 2000) approached the analysis of a problem of time from fundamentally diverse grounds at the beginning of our century. He considered time not as a universal external parameter, but as an invariant of the alterations (development) of all phenomena of the actual world. Having extended the data of physics, chemistry, biology, cosmology, geology, history, Vernadsky, on the one hand, specified peculiar features of exhibiting of own time, bound with different by their matter-energy nature systems and processes. On the other hand, he demonstrated, that all of them and, therefore, real time, have, first of all, the property of anisotropy and cyclic-irreversible structure. The quasiperiodic processes provide a mobile-balanced state of any material system and relative homogeneity of the transitoriness, corresponding to it. The irreversibility is expressed in different polarity of developmental vectors of unequal, by their matter-energy nature, systems. As A.A. Silin showned, it now becomes clear, that a general irreversibility of time is instituted by two inversely directional and compensatory mutually processes: by scattering free energy and accumulating the information (, 1994).

Other invariant property of any natural process, from Vernadskys point of view, is the continuous-discontinuous structure of their development. It is conditioned by a jump-like change of quasi-stable states of the corresponding material systems. It is important to point out the following moments. Firstly, as H. Bergson (1911) pointed out, these alterations have no character of timeless transferrings, and have particular transitoriness; later on, it received experimental corroboration in discrepancies of temporary parameters of strong, gentle and electromagnetic interactions. Secondly, such critical moments in development of material systems (called by I. Prigogin the points of bifurcation) are connected with their choice of one of potentially possible for them paths of further development. A cardinal discrepancy between the happenings, representing quasistable states of systems at separate stages of their development, and events, separating them, institute one more universal property of a real time its heterogeneity (, 1996).

Further, Vernadsky specified indissoluble connection of space and time. He pointed out, that with the flow of a real time the state of real space varies also, that is expressed in change of a symmetry of material systems in a course of their development. As Yu.S. Urmanzev demonstrated, during evolution (in particular, of biological systems) there is a transformation of not only symmetry, but also of the geometry of space (, 1971).

Thus, key difference of Vernadskys real time, both from Newtons absolute, and relative time, is, that it represents not only (and not at all so much) quantitative, but to a greater extent a qualitative reference of all phenomena of the world, enclosing us. The physics (more exact, the physical chemistry) approached this understanding of the essence of time only in the second half of our century due to development of synergy. It allowed Prigogin to enter the notion of a so-called second time.

It is necessary to point out, that the model of any process, bound with heterogeneous (by their matter-energy nature) systems, can form the basis for constructing the metrics of a kind suitable to it, of a conceptual time. As A. Grnbaum demonstrated, from here it follows, that basically there can be a set (multitude) of the mathematically incompatible metrics of a conceptual time. Utilizing each of them for measuring temporal properties and relations of all others phenomena of a reality, we shall gain quantitatively non-comparable results. The given position has no practical value in daily life. It is necessary only to remember, that the ordinary practice uses the metrics of physical time, which represents specificity of individual time of closed systems in a quasistable mobile-balanced state. However, it plays a key role in constructing and practical usage of the metrics of a conceptual time, basing on model of evolution of open systems (, 1998).

5. The further development of Vernadskys ideas (, 1994, 1995; Simakov, 1995, 1997) results in the conclusion about necessity of a legible demarcation between two reciprocally supplementary conceptions of a category of time: dynamic, which is an invariant of processes immediately accepted in the intensive order of sensations, and static, which represents materialized results, to be exact traces, or protocols both proceeding in our sight, and having a place in more or less distant past processes, the information on which arrives in the extensive order of sensations. It is important, that a transfer from dynamic to static time is characterized not only by qualitative change of the temporal information, but also by its condensation. The latter is due to the loss of all its dynamic components, and a considerable proportion of material ones. S.V. Meyen (, 1989) termed this universal phenomenon as the law of tempodesinentia. According to this law, the static time has the protocolary, statistically-probabilistic nature. I shall emphasize in this connection two moments as follows.

First, the irrevocably lost part of the information can only be retrospectively renovated on basis of principles of actualism and uniformitarianism (in its modern treatment); it is always connected to the saved part of the information by the relations of one-to-multimeaningful correspondence. Second, the law of tempodesinentia, as a matter of fact, is similar to the second law of thermodynamics; thus the complete information receivable as a result of expenditure of energy, appears to be an intermediate product originating only here and now and step-by-step losing contents with transferring deeper and deeper into past time.

The unity of time as a universal attribute of both dynamic and static phenomena of the actual world is finally instituted by systemic organization of these and those. From this point of view, the real time represents, on the one hand, an invariant aspect of structure of material systems and processes, which reflects the general order of their organization (the alongside position, succession, inclusion), and on the other it is a universal basis to compare and differentiate between them that is conditioned by the unity of transformation laws of all system-organized phenomena of a reality. Or else, the real time is both the property, and relation, and means of alteration and/or delimitation of any one phenomena of the actual world. From these grounds the real dynamic time is an invariant aspect of structure and mechanisms of implementation of processes, and the real static time is an invariant aspect of structure and criteria of demarcation of material systems (, 1994, 1997).

It is of basic importance, that universal properties of both dynamic and static time are an anisotropy, heterogeneity and continuous-discontinuos, cyclic-irreversible structure. These properties of a real time, as Vernadsky emphasized, demand for a cardinal change in the methodological approach to a procedure of measuring real time. And it is true so, as they eliminate possibility of conducting analogy between time, and numeric, and geometrical continua. And it, in turn, makes it impossible to use for measuring a real time-length of the logic-mathematical apparatus of classic analysis. I shall accentuate in this connection, that the given limitation have not any practical value for elaboration of the methodology and measuring technique of dynamic time. Meanwhile, due to the law of tempodesinentia which, figuratively speaking, flashes these properties of real static time, measuring the latter can be based only on the theory of sets (multitudes). The key impossibility of application, as a methodological ground, of the theory of measuring geological time by the virtue of the logic-mathematical apparatus of classic analysis also predetermined unsuccessfulness of all earlier made attempts to make a quantitative assessment of temporal properties and relations of phenomena of geological history (, 1997a, 1998, 1999).

So, as it is seen from this short review, by now two fundamentally different ideas about essence of a category of time have been developed. The first one is the best expressed by the substantial conception stating independence of time on any phenomena of the actual world. Within the framework of this conception the time represents itself as an external parameter permitting to produce a quantitative assessment of temporal properties and relations of all exhibitings of a reality in the uniform system of measures. In other words, in a natural-scientific picture of the universe time, from the point of view of this (however, as Vernadsky underlined, the relative also) conception, it appears only as an external parameter and measure of quantitative discrepancies between unequal, by their matter-energy nature, systems and processes.

According to the second notion developed within the framework of the relative-genetical conception of a real time-length of Steno Vernadsky, the time appears as an invariant aspect of structure and properties of all natural (physical) phenomena independent on their matter-energy nature and level of organization. Within the framework of this conception the time in a natural-scientific picture of the universe is the universal, immanent characteristic of both qualitative and quantitative specificity of any one of exhibitings of a reality.

It is of fundamental importance that, accordung to these two conceptions, the time has radically different properties. And it dictates an objective necessity for usage, within the framework of each of them, different, by their logic-mathematical contents, approaches to its measuring: classic analysis in the substantial (and relative) conceptions, and set theory in relative-genetical ones.

 

ILLUSION and COLLISIONS

Time is what happens when nothing else does

Richard Feynman

Time is nothing but change... change is measure of time, not time the measure of change

Julian Barbour

6. As it was shown (Simakov, 2001), in the geology, as a matter of fact, there were and till now are utilized two conceptions of time: the substantial and relative-genetical. Therefore, there is a sense once again to apply to analysis of a problem of what from them can and should be a methodological ground of the theoretic-cognitive apparatus for not only stratigraphy, but also geology as a whole. As it is known, initially in geology, the idea of time was developing in two main trends. The first was connected with eliciting a chronological succession of those phenomena of formation history of the modern appearance of our planet, the protocols of which were saved in the geological record. The second was related to evaluation of a general duration of existence of the Earth. As a final result of the first trend studies the International Stratigraphic Scale (ISS), and, based on it, the geochronological scale was elaborated, and of the second trend studies a so-called numerical (radiochronological) scale of geological time. By the present moment, it is possible to talk about isolation in geology, as a matter of fact, of the two independent disciplines, which are engaged in analysis of time, and special conceptions, based on it: geochronology, which is founded on the theory of a paleobiospheric (geological s.l.) time, and geochronometry, which is based on the theory of a radioactivity (isotopic) time. The key discrepancy between these theories is, that the geological history, from the point of view of the theory of paleobiospheric time, is a clock, and from stands of the theory of radioactivity it has a clock (, 1993).

Unfortunately, as a methodological ground of all modern geology, Newtons substantial conception of time has been officially accepted. It, on the one hand, impedes a legible differentiation between the theories of paleobiospheric and radioactivity time. On the other hand, it brings to an essential tangle (if not to say confusion) in a solution of both theoretical, and especially practical problems, which concern not only construction of the metrics of conceptual paleobiospheric and radioactivity time, but also their mutual relationship, and also a definition of temporal properties and relations of phenomena of a geological history. In order to answer, on the one hand, a question about the interrelation of the theories of paleobiospheric and radioactivity time, and of lawfulness of usage of the substantial conception in geology on the other, it is useful to summarize briefly the analyzed before data (, 1996, 1999; Simakov, 1993, 1994a,b, 2001).

Geochronology

There is only one kind of time. I have no patience with the claim that organic evolution measures one kind of time and radioactive disintegration another. We may speak of relative age and absolute age, but they are relative or absolute with respect to one and the same kind of time

H.D. Hedberg

A reverberation of time in geology are the material documents of its history: replacing a formation of rocks, remains of organic life, tectonic structures etc.... The primacy in stratigraphy by virtue of specificity of constructing geological time belongs to material bearers of this time stratigraphic subdivisions and information, contained in them... Any properties of a time can not be revealed besides physical documents of geology, besides development of a material substance

B.S. Sokolov

7. The origin of the theory of paleobiospheric time is associated with several names, most particularly Steno, who established the methodological foundations of geology and formulated the basis of the relative-genetical conception of time, and Hooke, who framed the first scientific theory of the development of the Earth. Stenos key contribution is that, having encountered static systems, he defined their temporal properties and relations using not a spatial movement of self-identical bodies, but an alteration of a qualitative state of systems fixed in space. Figuratively speaking, if G. Galilee and Newton spatialized time, Steno materialized (genetized) time by connecting time with spatially-geometrical relations of genetically different paleosystems and with qualitative-state changes of the same system. In other words, whereas time was proposed by Newton to be some universal quantitative parameter, time for Steno was the qualitative index that characterized sequential transformations of paleo-systems. Time, from Stenos viewpoint, gained the properties of those retrospectively reconstructed processes and their protocols that were the phenomena of the geological record natural homogeneous bodies and their spatial relationships. From this perspective, time had an informative or negentropic nature and personified the properties, relationships, and criteria for differentiating geosystems.

Without dwelling upon a detailed presentation of the conceptual history that led to the development of the theory of paleobiospheric time, I shall briefly review the main highlights. The investigations of both Steno and Hooke detected the main properties of a real paleobiospheric time. These ideas were expressed in information that spoke to the character of the process as preserved in the geological record. This quality was characterized by an anisotropy and by a cyclical-irreversible, continuous-discontinuous structure. However, the conclusions of the founders of modern geology were rather more like ingenious guesses than empirical generalizations, as neither Steno, nor Hooke had sufficient empirical data to support their ideas. Such data, however, were obtained by the end of the 19th century, and only then was the sagacity of these original thinkers confirmed. However, the significance of their conclusions for the theory of paleobiospheric time has not received a worthy evaluation until now.

It should be pointed out that at the end of the 17th and during the first half of the 18th century Hooke, followed by de Maillet and Buffon anticipated the formulation of the second law of thermodynamics. Using different approaches, they justified the major difference between paleobiospheric time and common (physical) time; namely, its irreversibility, which is conditioned by a gradual attrition of energy and accountable for changes in the state of inert components of the biosphere. The irreversibility of the development of a biogenic constituent of the biosphere and the unilinear trend towards a more complex level of organization in living matter was apparent since the middle of the 18th century, owing to investigations by Fchsel, Giraud-Soulavie and other adherents of the Neptunian theory. Thanks to Smith, who first introduced a biostratigraphic method in the beginning of the 19th century, and followers of the Catastrophism school, this inverse directivity of evolution in both inert and living matter was empirically demonstrated. The data obtained in their studies were generalized by Bronn and then applied by Darwin in his elaboration of the Selectionistic theory of evolution. In other words, the fundamental differences between a real paleobiospheric time and the Newtonian absolute time its anisotropy and irreversibility were already empirically justified by the middle of the 19th century. This allowed for the final affirmation that geological (s.l.) time was a qualitative description of sequentially changing states of the paleobiosphere, which were replaced under the influence of some universal factors.

By the middle of the 18th century, Lehman, Fchsel and Werner introduced the notion of natural geohistorical subdivisions (i.e., formations) and the system of hierarchical stratigraphic subdivisions and associated geochronological (using modern terminology) units. Studies by followers of the Catastrophist school had by the middle of the 19th century already underscored another essential singularity of stratigraphic subdivisions. Subdivisions had an event nature of their boundaries; in other words, units expressed themselves in a material basis of natural (initial) measures of paleobiospheric time. Thus the heterogeneity of real paleobiospheric time and its continuous-discontinuous structure were demonstrated.

At the end of the 18th century, Hutton advanced and further developed the idea, initially proposed by Hooke, that geological processes are cyclical. This proposal was proven by Lavoisier from empirical data collected from Tertiary deposits of the Parisian basin. However, the thought, already pronounced by Steno, about the cyclic-irreversible character of the geohistorical process, received the status of an empirical generalization only by the end of the 19th century due to investigations by Renevier, Rutot, Chamberlin, and colleagues. These early explorers emphasized that in the development of a paleobiosphere, a cyclical component is connected with the periodicity of geological processes, and a irreversible component is connected with the evolution of living matter. Some time later, Amalitzky, Sobolev, and Schindewolf established that cyclicity was also characteristic of development within the organic world.

In the 1830s, Lyell postulated that the geological record was incomplete and the paleontological record was inadequate. His proposal was supported later by Darwin and demonstrated in the 20th century by Barrell and Efremov. They both also commented on the protocolary, statistically-probability nature of geological information. I shall accentuate that from the notion about the incompleteness of the geological record there followed a logically inevitable conclusion about a key non-reduction of the concepts of geological (s.l., i.e. paleobiospheric) and physical time. I shall elaborate below on the consequences of such a conclusion. At the same time, we owe to Lyell, Spencer, Darwin, and Huxley the reaffirmation that in geology it is possible to utilize a certain external scale, independent of documents of geological record, and therefore, utilize the conception of absolute time (sensu Newton).

By the middle of the 19th century, geological researches were expanded beyond Western Europe to Russia, North America, India and other regions. The results of these studies clearly showed the discrepancies in the composition, temporal scope, and character of boundaries of regional stratigraphic subdivisions. These data were testament to the metachronous development of separate regions or, more precisely, of the regional paleoecosystems. The correlation of local depositional successions required some type of external instrument or universal reference system that included the entire history of the formation of the Earths crust. In other words, geology had developed to the point of needing its own chronological scale, to be distinct from a generally accepted one. More precisely, the earth sciences needed a model and metric for understanding and applying paleobiospheric time similar to that applied in the physical sciences. The problem of constructing common, international stratigraphic and geochronological scales was central to the first eight of the International Geological Congress (IGC) sessions. The final version of this scale was officially accepted and confirmed at the 8th IGC session (Paris, 1900). When assessing the ISS, it is necessary to take into consideration the following circumstances.

Work on the elaboration of the ISS occurred during a period when the Selectionistic doctrine, which was based on the conception of continual constitution and development of substance, was dominating. Perhaps Leibnitz best expressed its tenets in the maxima, Nature does not make leaps. This was a period of rigid confrontation between the theory of evolution, which stated a conditional character and artificiality of any classification, and Catastrophism, which held to the natural character of taxonomic subdivisions and their boundaries. The creators of the ISS, who were overwhelmingly paleontologists and supporters of Darwinian theory, borrowed from biology the principle of an artificiality and conventionality of universal stratigraphic subdivisions. However, in their ardor and in disagreement with the Catastrophists they threw out with the proverbial bath water of creationism the baby of the event nature of stratigraphic boundaries. The ISS creators also borrowed the biological principle of a priority, according to which a temporal scope and position of boundaries of universal stratigraphic subdivisions were instituted by earlier condition, irrespective of their individual characteristics (i.e., structural, lithogenetical, paleontological). Thus, the ISS originally was dispossessed of the main property of any measuring device a communal ground for apportionment of natural (or initial) measures. Instead, the geologists assigned to themselves the right to designate universal stratigraphic subdivisions (and geochronological units corresponding to them) using the same terms (e.g., group/era, system/period, series/epochs, stage/age), despite major differences in the content and/or scope of these subdivisions. These divisions were related to each other only by relationships of to be more, than, or to be included in. On the whole the ISS classification by Stivens (, 1960) falls somewhere intermediate between scales of naming and scales of ordering.

It is vital to note that the 8th IGC session (Paris, 1900) assumed as a source of the ISS not stratigraphic subdivisions but geochronological units (i.e., era, period, epoch, age). This approach was rationalized by stating that the incompleteness of the geological record dictated that the stratigraphic subdivisions ostensibly should incorporate only that time represented by the rocks. In contrast, geochronological units included not only the materialized in rock, but also the so-called dark time that corresponded to interruptions in deposition. Thus, the idea about the existence of absolute time was officially sanctioned in geology, and Newtons substantial conception was identified with relative (common, or physical) time.

The idea about a possible usage in geology of the substantial conception of time received further reinforcement of the International Subcommittee on Stratigraphic Classification. This Subcommittee was organized at the 19th IGC session (Algeria, 1952) specifically for the preparation of the International Stratigraphic Code (ISG), which has had already two versions (ISG-1, 1976; ISG-2, 1994). Unlike the initial conception of the ISS, the priority in the ISG variants returned not to geochronological units, but to chronostratigraphic subdivisions (the material basis of the geochronological units). The adherence of the ISG to the substantial theory of time was most clearly exhibited in the conception of so-called points of global chronostratigraphic boundaries (GSSP). Such boundaries are ostensibly associated with conterminous and particular instants of absolute" time. Radiometric dating has been attempted to define precise ages (expressed in years) of these boundaries thereby placing them in their correct chronostratigraphic position (ISCh, 2000).

Numerous eternal contradictions are connected with the geological usage of notion absolute time, including concerns about the isochroneity-diachroneity of stratigraphic boundaries, of temporal slipping or temporal transgressions, facies, etc. We owe the origin of these paradoxes to Lyell, Spencer and Darwin. Darwin, having encountered the problem of a retrosynchronization, sacrificed the conception of a geological simultaneity" in favor of the possibility of using absolute time as a frame of reference in geology. Forty years later, Einstein encountered a similar problem, but followed an opposite interpretive path. He refused to acknowledge an absolute frame of reference, having sacrificed it to the benefit of absolute (more exact the metric) simultaneity (Simalov, 2001). The controversies and dilemmas inherited from uniformitarianism and selectionism have continued for more than 150 years. Their solution basically is impossible within the framework of the substantial conception of time. This fact alone should have forced geologists to refuse the prevailing point of view and to make basic changes concerning the essence of the conception of geological (s.l.) time.

8. Here I shall stop and mark off next point. First of all, the contradictoriness of the theoretical viewpoints of the ISG-makers is obvious even from the comparison of the definitions of basic for this conception notions a chronostratigraphic subdivision and geochronological units. Indeed, on the one side chronostratigraphic subdivisions are a material (substantial) ground for geochronological units corresponding to them (ISG-2, 1994. P. 9-11. P. 77). The logical consequences from this statement are: 1) that the properties of the geological time must and are determined by the properties that are characteristic of chronostratigraphic subdivisions, and 2) that a geochronological scale which is isomorphous to the chronostratigraphic one is, in fact, its conceptual model. From this it follows inevitably (a) that the geochronology is a discipline that deals with the problems connected with conceptual geological (s.l. = paleobiospheric) time, and (b) that the chronostratigraphy is a discipline that concerns the problems bounded with real geological time, i.e., their properties fixed in the geological record.

But on the other side, all authors of the ISG and Guidelines are absolutely convinced in that (1) boundaries of chronostratigraphic subdivisions coincide with unique instants of time and represent isochronous time-planes which encircle the globe as enclosed hyper-surfaces, (2) that a magnitude of a chronostratigraphic subdivisions is determined by the interval of time between two (coincided with the lower and upper boundaries) designated instants of time, and (3) that the precise fixation of the age position of chronostratigraphic boundaries (and, therefore, the temporal scope of the chronostratigraphic subdivisions) could and must be established by the isotopic data (ISCh, 2000).

From these standpoints it follows that besides real geological time (represented by geological record) and conceptual geological time (which reverberate in the abstract form properties of information about geohistorical process) exist some external time which seems independent of any material characters of geological phenomena: it is the intangible property, and in this sense it is absolute. Isochronous time-planes of this absolute time which encounter the chronostratigraphic subdivisions, in opinion of the leaders of the ICS, cut all geological bodies like Razors Edges and are absolutely independent of any kinds of real stratigraphic boundaries (ISG-2, 1994. P. 92).

Second, it is very surprising and strange, but in all recommendations of the ICS we could not find a clear and unambiguous definition of the term boundary neither chronostratigraphic, nor geochronological. ICS has only presented a carefully elaborated (and very useful) procedures for determination of certain chronostratigraphic boundaries. In fact, there has been created a paradoxical situation: now we know how to determine but not what to determine. Maybe the fact that the leaders of the ICS have not defined the meaning of the term boundary could be easily explained since this terms seems to be so self-obvious that no special explanation is required. I shall remind that Einstein who analyzed the meaning of the notion of simultaneity was the first one revealing the insidiousness of such a pseudo-obvious concept. We seem to have the same situation, when we start to think about and analyze the essence of the notion of boundary.

Indeed, when thinking about the term chronostratigraphic boundary (more precisely geochronological boundary) most of us automatically imagine, first of all, an arrow-like time-coordinate marked by points separating successive units, and, secondly, planes which conjugated with these points and encircle the globe. The first imagination is realized in the ICS recommendation in the conception of the GSSP which are fixed in the limitotypes by a Golden Spike . The second imagination is represented by the statement of independence of boundary time-levels of any kind of real stratigraphic boundaries owing to they could be compared with Razors Edges . Let me shortly try to analyze whether images of Golden Spikes and Razors Edges are adequate to real chronostratigraphic boundaries or not.

(1) Elaborating the systemic approach of Wallisers (1984. P. 241) definition of the notion natural boundary, I shall emphasize that any real chronostratigraphic boundary is a protocol of a global event. This event marked in the geological record by alteration of biotic or/and abiotic components, composing a certain system (i.e., chronostratigraphic subdivision), its number, and/or relationships between them which are characteristic of succeeding systems (i.e., chronostratigraphic subdivisions). Because of short-range principle of interactions between all biotic and abiotic processes in the biosphere each real chronostratigraphic boundary is represented in the geological record by some stratigraphic interval and, therefore, has ecotone-like nature.

(2) It seems that we must to be clearly aware of what kind of boundaries we represent on our stratigraphic schemes and geological maps; that is do we mirror in them a real (i.e. ecotone-like) or conceptual (i.e. representing our Golden Spikes and Razors Edges image)? In other words the question is: do we reverberate by different colors, separated by lines, chronostratigraphic subdivisions or geochronological units on our maps? It seems that because our stratigraphic schemes and geological maps are the conceptual models of a reality, therefore, we use in them units of not real but of conceptual geological time. Thus, images of Golden Spikes and Razors Edges could be very reasonably applied for representation of geochronological units which are units of conceptual geological (paleobiospheric) time but not of chronostratigraphic subdivisions which correspond to units of real geological time. This difference between chronostratigraphic subdivisions and the scale, on the one side, and geochronological units and the scale, on the other side, we should constantly bear in the mind because the former represent the material, substantial basis for the second. The ISS represents the structure and properties of real paleobiospheric time, whereas geochronological scale is based on the ISS model of conceptual paleobiospheric time, which express our abstract vision.

(3) It should be emphasized that in fact modern chronostratigraphic subdivisions and geochronological units are not units in proper sense of this term (i.e., initial measures) of a real and conceptual geological (paleobiospheric) time, respectively. As it was shown above, due to different criteria for the initial establishing certain subdivisions of the ISS, it represents the model of the biography of the Earth crust. The ISS delineates not equable intervals of a real paleobiospheric time, but unequal spans corresponding to separate stages of self-developing paleobiosphere only. In these circumstances, the chronostratigraphic subdivisions and adequate to them geochronological units could be regarded only as prototypes of initial measures of a real and conceptual geological (paleobiospheric) time, respectively. But for simplifying the text below I will use the term initial measures instead of prototypes of initial measures and point out which kind of units I mean in each case.

9. In our critical analysis and revision of existing notions of time in geology and of the construction of the theory of paleobiospheric time, we must consider the relative-genetical conception of Steno Vernadsky. Of equal importance are the empirical generalizations about the nature of geological information, its impact on the geological record, and the universal, invariant properties and structure of the geohistorical process, the specific features of which condition knowledge of real paleobiospheric time. Thus, it is necessary to differentiate clearly between the notions of real and conceptual paleobiospheric time. The former falls into a category of static time. It represents an invariant aspect of integrated results of interplay of different paleosystems and processes that have been captured in the Earths crust. In modern practice it is represented by the ISS. The second notion is a retrospectively reconstructed quasidynamic model of the development of a given paleosystem. The model is selected according to specific criteria. It helps us to delimit the basis for constructing an instrument (i.e., scale, metrics) that will be used to estimate (i.e., to measure) temporal properties and relationships of all phenomena of geological history (, 1994). Certainly, constructing the metrics and applications for a conceptual paleobiospheric time model to which in our practice correspond geochronological scale must be based on those properties that have real paleobiospheric time.

The following cardinal tenets of real paleobiospheric time constitute the general methodological approach for constructing the necessary metrics. First of all it is the protocolary, statistically-probability nature of any geological information, which is conditioned by the law of tempodesinentia (, 1989). There are two key consequences of this law of tempodesinentia.

The first of these implications is that real paleobiospheric time can not be likened to a numeric or geometrical continuum. Consequently, while time being measurable, it is impossible to utilize the logic-mathematical apparatus of classical analysis that is the basis for measuring ordinary (i.e., physical) time. Thus geology is deprived of application of one of the original positions in chronometry, according to which identical intervals are demanded to achieve identical results. Paleobiospheric time first appeared as a qualitative description of geological phenomena but subsequently there is need to add a quantitative determinacy to its temporal properties and relations. This quantification necessitated engaging the special branch of modern mathematics, namely the theory of sets (multitudes) (, 1997, 1998, 1999; Simakov, 2001).

The second implication drawn from the law of tempodesinentia is the absence of a one-to-one correspondence between static systems and their retrospectively reconstructed quasidynamic models. Using the same static information different quasidynamic models of the same paleosystem can be constructed. The correctness of any model can not be verified experimentally. The most vivid example of such one-to-multiple meaning correspondence between static paleosystems and their quasidynamic models are the numerous evolutionary conceptions and phylogenetical reconstructions. These evolutionary schemes are based on the same paleontological data, but each explanation emphasizes different empirical data, deterministic conceptions, and phyletic criteria (, 1996, 1999).

Another fundamental feature of real paleobiospheric time is its cyclical-irreversible, continuous-discontinuous structure. The flow of paleobiospheric time is represented in the geological record by three types of chronoindicators: 1) chronophantomes, which represent traces of quasiperiodic processes describing mobile-balanced states of paleosystems at separate stages of their development; 2) chronostops, which are indices both of stage-by-stage irreversible evolution of the same paleosystem and sequential origins of paleosystems (and paleobiosphere as whole); and 3) chronoseparators, which score events, causing alterations in states of paleosystems during their own development and/or the replacement of certain paleosystems by another ones.

As the natural (initial) measures of real paleobiospheric time, protocols exist for those unique happenings, which fix a stage-by-stage cyclical-irreversible development of a paleobiosphere and are limited by the protocols of global events. The so-called primary or finite causes for explaining these world-wide rearrangements were used to interpret vastly different phenomena (e.g., from a regular lowering of global sea-levels to the impacts of cosmic bodies). Deterministic conceptions, unequal in their contents, were typically utilized. Since the end of the 19th century, global paleobiosphere perturbations were connected with a rather restricted set of so-called secondary or concrete causes (e.g., world-wide transgressions and regressions, episodes of folding etc.).

The verbal and conventional components in bondaries determination

10. The event character of natural boundaries of the initial measures of real paleobiospheric time (i.e., chronostratigraphic subdivisions) implies their causal connections with the operation of any factor that exercised their influences over the entire surface of the planet. Now there are just a few who doubt, that, independent of nature of such global disasters, their influence both on separate, natural apportionments of the paleobiosphere and on different paleosystems was carried out through a composite system of interactions (see, for example, Walliser, 1996). These interactions generally obeyed principles both of a short-range interaction and those of Le Chatelier Brown, which were described in the law of metachronous development of paleosystems (, 1997). To use the analogy proposed by Lane (1906) at the beginning of the 20th century, the natural boundaries of initial subdivisions of real paleobiospheric time are compared with the approach of the new day, which comes in at different instants of the Greenwich time in Magadan, Novosibirisk, Moscow, London, New York, and Los-Angeles. Moreover, the first rays of rising dawning sun do not simultaneously reach the windows of the upper level of the Empire State Building and the Wall Street bridge. Ager (1993) used a figurative expression, saying that global events proceeded by a principle of a moved writing finger. In other words events have some rate of propagation. The important conclusions from these thoughts radically contradicted the conception of standardization of chronostratigraphic boundaries, which were accepted in the ISG and which were based on Newtons substantial theory of time.

The judgment by the GSSP to ostensibly fix the coincidence of an event with the particular moment of some absolute time, which in turn institutes a precise age position of a boundary, is basically incorrect. Such a point represents only a nomenclature measurement-standard (i.e., some symbol) of a real (i.e., chronostratigraphic) boundary and fixed the position of a boundary between units of conceptual geological time (i.e., geochronological units). Supposing that the scale of an absolute time actually exists, it is possible that this point-boundary, selected for its special stratigraphic characteristics, specifies only the moment of an event occurrence restricted to a given concrete place (a limitotype) and has no more relevance than this. To return to the analogy mentioned above, same instant as measured by Greenwich time is actually midnight in Alaska and midday in Moscow. Accordingly, the attempts to determine ages for the GSSP through radiometric techniques and the usage of these age-data to trace any given chronostratigraphic boundary lack scientific sense. Such efforts are reduced to identifying the different-placed protocols of the same global factor as it influences heterogeneous paleosystems at different stages of their individual development. As Ager (1993) has emphasized, for geology retrosynchronization is a correlation of the protocols of global events, instead of a correlation of the protocols of local events with the instants of a mythical universal absolute time. To oversimplify, one might say that the midday (midnight) event in Alaska corresponds to an analogous event in New York, Paris, Moscow, Novosibirsk and Magadan, but not to the readings of a clock found on the Greenwich meridian or in one of these cities (which may be regarded as stratotype-locality).

The event character of natural chronostratigraphic boundaries implies that a fundamental procedural change is necessary for both standardizing and tracing boundaries of a conceptual paleobiospheric time units (i.e., geochronological units). Because any event is not a timeless act, standardization ideally should require the use of the stratotype for a boundary. This limitotype should be a section in which a complete protocol of an event is represented, including its initiation, culmination, and finite phases. However, it is improbable that such sections exist, given the incompleteness of the geological record. A modification of this ideal would be the use of a limitotype where only the fullest section of that stratoecotone is selected and the adjacent chronostratigraphic subdivisions, which are the material basis for initial measures of a real paleobiospheric time, are clearly evident. The protocols of alterations in the state of different paleosystems should also be represented in this section. Protocols drawn from such a section would permit the further tracing of any boundary of conceptual (instead of a real!) paleobiospheric time, beyond the limits of a stratotypical region, thereby allowing their use as parachronological markers.

As to following the chronostratigraphic (more exactly geochronological) boundaries, the existing practice is reduced to tracing the phenomenon that is accepted as an official basis of the given boundary in the limitotype. As it will be shown below, tracing the boundaries of the Phanerozoic subdivisions involves establishing everywhere the first occurrence of guide-species within those zones, the lower boundary of which coincides in the limitotypes with the boundaries of chronostratigraphic subdivisions of a higher rank (i.e., stages, series, systems). Such a procedure is underlain by the substantial conception of time and is based on false statements. On the one hand, this supposition about a coincidence, between the given phenomenon and the unique moment of an absolute time. On the other hand, this is supposition about the usefulness of an orthochronological datum-marker of a boundary for identifying a unique instant, adequate to it, so long until it begins obviously to intersect a temporary level corresponding to it. The truth is that neither Hedberg (ISG-1, 1976), nor Salvador (ISG-2, 1994) specified the objective criteria that form the basis for the affirmation of a coincidence with or deflection from an isochronic hypersurface, which as they believe, surrounds the entire globe. Actually by admitting the event character of natural boundaries, their tracing is a retrosynchronization of protocols of those different-placed events, which are a consequence of some global factor affecting heterogeneous paleosystems.

The event nature of boundaries of initial measures of a real paleobiospheric time (i.e., chronostratigraphic subdivisions) is an important principle that also institutes the contents of those operational laws and rules, on which both a procedure for constructing and a practical application of a model and metrics of a conceptual paleobiospheric time can and should be based. In this respect, the most essential element is the objective necessity for introducing, both in its construction and practical usage, a model and metrics of a conceptual paleobiospheric time of the system of nontrivial conventions. These conventions are radically distinct from the banal and trivial agreements that underlay the current definitions of concrete boundaries (e.g., , 1997a, Simakov, 1984, 1994).

The first of these conventions concerns a choice of that privileged quasidynamic model, which will represent itself as the basis for the metrics of conceptual paleobiospheric time. As for the geological record, there are no protocols for the development of any process, the model of which could be introduced as grounds for metrics applicable throughout the complete history of the planet. Quasidynamic models of the evolution of different systems and processes for different periods of geological history should be selected for the standard clock.

The second of these conventions is required to accept a universal criterion for fixing the nomenclature measurement-standards of natural-event boundaries between adjacent, initial subdivisions of real paleobiospheric time. I emphasize that simultaneous with the installation of orthochronological datum-markers for each concrete boundary, there also should be instituted a set of parachronological markers, These markers can aid in siting boundary outside a stratotype region, following the principle of Meyen (, 1989; , 1986, 1997a etc.)

The necessity for introducing the third convention is connected with a procedure of tracing boundaries by the realization of a metric (instead of a topological) retrosynchronization. In brief, this convention permits the position of a boundary to be established outside the region of the limitotype with the first occurrence of any of its officially prescribed parachronological marker.

I shall emphasize once again that at present state of knowledge the conclusions that follow from the theory of paleobiospheric time, and the one most relevant from a practical point of view, is the immediate necessity of changing the concept of limitotype. The points of global boundaries, which are only the nomenclature measurement standards of real boundaries, should not be etalonized, but rather primary importance should be given to the stratoecotones, which divide the adjacent initial subdivisions in real paleobiospheric time and which represent the protocols of global events. Only in such a way will it be possible to achieve a satisfactory resolution to the problem of both determining and tracing boundaries of a conceptual (instead of real!) paleobiospheric time.

11. The above explained general theoretical considerations about a standardizing and tracing chronostratigraphic (more correct, as stated above, geochronological) boundaries could be clarified by an example of boundaries of the Phanerozoic, for which the ICS recommended to utilize paleobiological technique. By this reason one can say that the geochronological scale of the Phanerozoic reflects the evolutionary stages of the organic world, or more precisely, that of certain orthochronological groups, and it can be regarded as an evolutionary model of these groups. In other words, the development of the orthochronological groups performs the function of a standard clocks for Phanerozoic time-span and their evolutionary peculiarities determine the specific character of elaboration and practical appliance of the geochronological scale.

It is obvious that recognition of chronostratigraphic subdivisions identified on a paleontological ground is only possible on basis of the fact that any group of fossil organisms was predominated by taxa with various archetypes during certain time-spans. Changes of archetypes of any taxon and/or appearance of taxa with new archetypes are the events which has been recorded in the course (flow) of paleobiological time in the geological history. Chronostratigraphic boundaries should be marked by these events.

Although archetype representatives of various faunal groups are transformed in different ways, in any case, chronostratigraphic boundaries recognized in terms of paleobiological data are evidently not represented by clear-cut well-defined lines and connected with them planes, but they occupy certain stratigraphic intervals so-called transitional beds, zones, stages etc. Analyzing the regularities of biosphere development, Krasilov (, 1970) suggested to name such transitional intervals in between successive subdivisions as stratoecotones (by analogy with ecotones a spatial transition between adjacent ecosystems). Concerning the development of individual faunal groups and lineages, a stratigraphic interval characterized by an alteration of taxa with various archetypes could be termed phyloecotone (more correctly phylotone Simakov, 1994), and temporal equivalents both of stratoecotone and phylotone could be designated as chronotone (a common term which could be applied for the definition of temporality of any physical interactions including gentle, strong, and electromagnetic).

As it is known, the existence of such transitional stratigraphic intervals serves as an objective prerequisite for long-term debates: on the one hand, as to whether those should be included into younger or older chronostratigraphic subdivisions, or recognized as independent ones, and on the other hand, which criteria (the first appearance or wide distribution of representatives of taxa with new archetypes, or disappearance of last representatives of a taxa with ancient archetypes) should really be used for determination of chronostratigraphic boundaries (more precise a location of their nomenclature standard, which symbolizes positions of geochronological boundaries).

Analyzing these debates I should like to underline two points.

Firstly, in both question the competing suggestions aim at the same object, i.e., to schematize the evident really existing in nature phenomena by representing them, according to our common understanding of boundaries, as clear-cut well-defined points, lines, and planes. In other words, when elaborating a model of conceptual paleobiological time (i.e., geochronological scale based on paleontological data) we are inclined, as stated above, to replace a natural phenomena (i.e., phylotones) by a conceptual images of Golden Spikes and Razors Edges , which are customary and, therefore, convenient for practical appliance.

Secondly, as Schindewolf (1928) first demonstrated, the alterations of archety-pes in different groups of fossil organisms at the same boundary-interval proceeded not simultaneously, but in a cascade-like manner. The latter is consequence of the law of metachronous development of various faunal groups, phyla, and lineages. In other words, each orthochronological group is acting as an individual clock counting off a specific conceptual paleobiological time characterized by its own pulse or pace. Therefore, accepting the evolution of different groups as a basis for elaborating of chronostratigraphic scale and determination of chronostratigraphic boundaries we inevitably get a set of geochronological scales each of which will differ from all other by its structure, a position of boundaries between successive units, and ranges (magnitude) of units themselves. In this situation it is very reasonable to follow the recommendations of the ICS and to choose for fixation of a nomenclature standard of a concrete chronostratigraphic boundary (i.e., position of a geochronological boundary), a single orthochronological group the representatives of which are characteristic of adjacent chronostratigraphic subdivisions. Here it is necessary to underline the following circumstances.

Because the ISS based on paleontological data is a global counting system, only records of events within a chosen orthochronological group that reflect the influence of globally acting factors, i.e., affecting the development of other groups of organisms, should be taken for defining chronostratigraphic boundaries. By this reason, the practical application of a selected chronostratigraphic boundary is entirely dependent on the scale of adopted event. If it is a macroevent (such, for example, as the appearance of genera with a new archetype within a separate lineage of an orthochronological group), with corresponding transformations (not necessarily of identical scale) in other (parachronological) groups, then we can be optimistic as to its practicality. Conversely, the selection of a microevent (such, for example, as the first appearance or disappearance of even zonal guide-species), which does not correspond to alteration in some other groups, cannot be used as a suitable datum-mark.

The objective necessity of taking a evolutionary macroevents as a chronostratigraphic boundaries is dictated by the dualistic nature of the notion of simultaneity. This implies identification of both properties and relations between side-by-side developed natural phenomena. Regarding chronostratigraphic boundaries, we may say that simultaneity as a property manifests itself as coincidence (i.e., including in the same stratigraphic interval or level) of events in different faunal groups. From this standpoint protocols of all events in a development of all parachronological groups, which are fixed inside the stratigraphic interval corresponding to a macroevent (i.e. phylotone) in evolution of the selected orthochronological group, are objectively (topologically) simultaneous with each other and with a formally recognized nomenclature standard or datum-mark of a chronostratigraphic boundary (i.e., geochronological boundary). Due to that phylotones in the generic evolution usually encompass wider stratigraphic diapasons than at species-level development, it is clear that the former can include more protocols of events in parachronological groups, than the latter.

Therefore, (1) chronostratigraphic boundaries should not be marked by events reflecting alterations at the species level, but only by protocols of transformations within the archetypes at least of the genera rank; (2) all protocols of any event in parachronological groups, which are fixed inside the stratigraphic interval of phylotone of the orthochronological group, selected as a chronostratigraphic boundary, are topologically simultaneous and should be regarded as parachronological markers of corresponding geochronological boundary. But sometimes a phylotone of an orthochronological group may have within it protocols of not only single but of several events in development of one and the same parachronological group (e.g. Simakov, 1984). In this situation it is necessary to decide upon a convenient basis the protocol of which concrete event should be used as the parachronological marker of a given geochronological boundary. Thus, it is already at the stage of determination of parachronological markers that we have to achieve a common agreement about the choice of the protocol of certain event amongst the protocols of topologically simultaneous events. And by definition, we will consider these to be simultaneous in a metric sense with the orthochronological datum-mark of a given geochronological boundary.

Thus, accepting recommendations of the ICS for fixing the position of chronostratigraphic boundaries with the help of Golden Spikes we should we aware of the fact that by this procedure the boundaries between units of conceptual paleobiological time, i.e., geochronological units, are materialized. I would like to emphasize once more that the necessity for a nomenclature standard of chronostratigraphic boundaries, which symbolize geochronological boundaries is predetermined by a contradiction between our traditional notion of boundaries as clear-cut well-defined lines and the ecotone-like nature of real chronostratigraphic boundaries. It should be also pointed out, that proposed above procedure of standardization, which obviously differs much from that recommended by ICS, allows us not only to fix the orthochronological datum-mark of a certain geochronological boundary, but objectively determines a set of its parachronological markers which could and should be used in world-wide tracing of given boundary.

Now after clarifying the essence of the procedure for establishment of datum-mark and parachronological markers of geochronological boundaries we are ready to analyze the prerequisites connected with the realization of the second divine nature of chronostratigraphic (more correctly geochronological) boundaries, i.e., an imagined Razors Edge. Before we tackle this problem, it is necessary to clarify what is meant under expression tracing chronostratigraphic (as stated above, more precise geochronological) boundaries, which could be interpreted in two ways.

First of all, it can imply tracing an orthochronological datum-mark for concrete boundary; second, it entails eliciting (all over the surface of the globe) the traces of results of operation of that globally acting factor which affected the development of the organic world, and determined that replacement and/or origin of taxa with new archetypes within the orthochronological group which is chosen as a datum-mark for a concrete boundary in its stratotype.

Nowadays, geologists tracing chronostratigraphic (geochronological) boundaries are usually guided by the principle put forward by Schindewolf (1928). He proposed using orthochronological faunal groups not only for fixing a paleobiological datum-mark (i.e., origination or first appearance of guide-species of certain faunal zone) within a boundary stratotype but also for determining its (i.e., boundary) position in any other section throughout the globe. This method is based upon the axiomatic supposition that the distribution of representatives of an orthochronological group is independent of the environment. Meanwhile, comparison between stratigraphic ranges of representatives of various orthochronological groups in different localities shows that spatial-temporal distribution of any fossil is determined by the law of ecological control (Simakov, 1984, 1994; , 1986). This law can be formulated as follows: the occurrence, range, and disappearance of species of any (benthonic, planctonic, neketonic) kind were controlled everywhere by favorable for their habitation environmental conditions. Consequently, outside a given boundary stratotype, fossils belonging to an orthochronological group are not necessarily preferable to an those of any other parachronological group for determination of a position of a boundary in certain section. Moreover, if we follow the recommendations of the ICS (which are based on the Schindewolfs principle) and use orthochronological datum-marks (i.e., zonal guide-species) for world-wide identification of a positions of a geochronological boundaries only, then we shall be able only to establish the first occurrence of these species in space and time, which is locally or regionally influenced by the law of ecological control. Obviously, by this reason we will not be able to realize the image of Razors Edges.

Therefore, the expression of tracing the chronostratigraphic (geochronological) boundary can be treated only as an identification of the effects resulting from one and the same factor influencing a development of different faunal groups. In other words, the materialization of the Razors Edge image of a geochronological boundary is reduced to a procedure of retrosynchronization. It provides for usage of the Meyens principle of chronologically interchangeable indications. As such indications parachronological markers mentioned above, which are fixed in the boundary stratotype, should be used because they by definition represent the protocols of topologically simultaneous with the orthochronological datum-mark events in the development of parachronological groups.

An agreement about parachronological markers is a prerequisite for tracing geochronological boundaries all over the globe. But it is insufficient to formulate a general operative principle and rules permitting materialization of Razors Edge image of geochronological boundary. This is due to the fact that the same parachronological markers do not coincide in their stratigraphic succession and, sometimes, even appear in different order of succession in various localities because of the influence of the law of ecological control. Thus, if we try to trace a geochronological boundary by means of parachronological markers we will meet in each locality with some spatial-temporal (stratigraphic) interval containing a number of protocols of topologically simultaneous but stratigraphicaly differently placed events. And because all parachronological markers are by definition simultaneous with each other and with orthochronological datum-mark we do not have objective criteria to choose one of them for the recognition of the exact position of geochronological boundary in each case. Therefore, it follows that we must achieve the general agreement according to which beyond the stratotypical region geochronological boundary must be situated at the level of the first occurrence of any of the officially accepted its orthochronological or parachronological marker. Only in this case we shall be able to ensure methodologically correct materialization of the geochronological boundaries as images of Razors Edges .

Thus, fixing of geochronological boundaries on the time-arrow (the materialization of an image of Golden Spikes) and their global tracing (the realization of an image of Razors Edges) require at least three agreements (conventions), if we agree with that chronostratigraphic boundaries are of a natural-event character and are marked by the turning points in the development of the organic world and, particularly, its orthochronological faunal groups.

Objectively, the need for these conventions is dictated, firstly, by ecotone-like character of the natural chronostratigraphic boundaries, secondly, by the law of metachronous development of different groups, phyla, and lineages of organisms, and, thirdly, by the law of ecological control. By these reasons, mentioned conventions have nontrivial nature and drastically differ from those banal and trivial agreement which in existence practice are concluded ad hoc for each concrete boundary (for example, estimating a weight of some characteristics used to trace the boundaries). If we wish to continue using the concept of geochronological boundaries as clear-cut well-defined limits (which is useful and convenient for us in practice), on the one side, and if we wish to reach stability of our determination and to avoid a subjectivity of decisions about boundaries-positions, then we must involve these nontrivial conventions in the theoretical-cognitive apparatus of stratigraphy. Otherwise in our practice we will continue to contradict, on the one hand, the revealed principles of the organic world development as it is recorded in the geological history, and on the other hand, the empirically established ecotone-like characters of natural boundaries. Figuratively speaking, under these conditions not we dictate these conventions to Nature, but in the contrary the Nature herself prescribes upon us these conventions.

Geochronometry

Geochronometric units are units established through the direct division of geological time, expressed in years. Like geochronological units, geochronometric units are abstractions, i.e., they are not material units. Unlike geochronological units, geochronometric units are not based on the time span of designated chronostratigraphic units (stratotypes), but are simply time divisions of convenient magnitude for the purpose for which they are established... Their boundaries are arbitrarily chosen or agreed-upon ages in years.

North American Stratigraphic Code

Geochronometric units cannot be free of material referents and defining events. No some units can. Samples of some radioactive minerals and their decay products are, for example, material entities which may permit inference of two events a separated in time and consequently suited to designating an interval of time. The fact that the interval between them can be expressed in years should not obscure the fact that, like any interval of time, it is defined by events

D. Kitts

12. The creators of geology, Steno and Hooke, were not concerned with the question of duration of geological history. According to prevailing in the 17th century ideas that the Earth was built simultaneously with people and specially for prosperity of mankind, they were quite content with the age of our planet of 6000 years as declared in the Sacred Scriptures. The problem of defining duration of geohistorical processes was put off until the middle of the 18th century, when Buffon risked extending the temporal range of Earths existence to 75,000 years, which was met with swords and daggers by the church. At the end of the same century, Hutton theoretically justified the depth or abyss of geological time, offering the conception of geohistorical development founded on a principle of indefinitely iterating cycles of upheaval and subsidence.

The question of the endurance of geological history arose sharp at the beginning of the 19th century in connection with the introduction of the biostratigraphic method. The practice of this method testified to an infinite turn of breeds of extinct organisms, the existence of which could not be accounted for within the time boundaries prescribed by the Sacred Scriptures. Step-by-step antagonism accrued between empirically established scientific generalizations and church tenets. Simultaneously, a spontaneous construction of a paleobiospheric time scale from the middle of the 19th to the beginning of the 20th century was undertaken by both geologists, who proceeded from upon their own empirical data, and physicists, who built their calculations upon strict theoretical laws. Repeated attempts were made to determine the age of the Earth in measures of ordinary time years.

So, the conflict between science and church, in many respects, explains the fact that the so-called absolute geochronology (geochronometry) roughly formulated in the 20th century, inherited from medieval theologists the habit to express results in years.

Changes in the beginning of the 20th century were marked not only by acceptance of the ISS at the 8th IGC session (Paris, 1900), but also by a discovery by Bacquerel of the phenomenon of radioactive decay. This phenomenon was utilized by Rutherford for age determination of rocks, and this significantly extended the scope of the notion of duration of the geohistorical process. However, it is noteworthy that, both in constructing the ISS and elaborating the grounds for an absolute geochronometry, methodological errors were originally incorporated and thus conditioned the preference of its creators for Newtons substantial conception of time.

13. From the very beginning there was a lack of a legible demarcation between paleobiospheric and radiological time. Each represents specificity of processes, bound by cardinally different organizational levels of Earths matter planetary and atomic, respectively. Moreover, usage of measures of ordinary time for the expression of duration of radioactive element half-life decay reinforced the illusion in the minds of geologists, on the one hand, of the existence of some absolute time, and on the other, of the possibility of application of a uniform system of measures for measuring both ordinary (physical), and radiological time. But, some important points were ignored by radiologists.

In radiological time, using for example the cesium standard, years in modern chronometry are the measures of an individual time of dynamic systems of the closed type that are in a mobile-balanced state, whereas, a radiological clock falls into the category of open systems, which record the irreversible changes of the state. It is principally important, that the scale of ordinary time based on chronophantomes reflects only one aspect of the existence of timekeeping systems their quasistable state. For measuring physical time, both the idea of a continuum, and a whole logic-mathematical apparatus of classic analysis, based upon it, are quite applicable. This also includes a postulate about absolute precise measurement. At the same time, neither the idea of a continuum, nor a logic-mathematical apparatus of classic analysis, can form the basis for measuring radiological time, due to the following reasons (, 1998, 1999).

First, the primary incompleteness and fragmentariness of the geological record eliminates the possibility of constructing a continuum of radioactivity backdatings, which fix only the moments of starting up of a concrete radiological clock. This is convincingly testified to, as pointed out by Semikhatov (, 1991), by considerable gaps in the general database between separate arrays of more or less compactly disposed readings of radiological age. Such gaps and clusters uniquely attest to the original quantumness of processes originating and triggering concrete radiological clocks. From this point of view, radiological time, as well as paleobiospheric time, is continuous-discontinuous.

Second, as Lennuiet (, 1970) has shown, the disintegration of radioactive elements is a probability process, the endurance of natural initial measures (half-lives) changes within some limits of a range of a probability. And according to Born (, 1963), it means that in practical measurement of radiological time, it is basically impossible to utilize such a relevant component of classic analysis as a postulate about absolute precise measurement.

The methodical miscalculations not only in constructing a geochronometric scale, but also in practical usage of radiological backdatings, are also indissolubly connected with the idea about a continuality of radiological time.

Both in constructing the ISS and a geochronometric scale (more precisely the metrics of a conceptual radiological time), all rules generally accepted in physics and principles of constructing metric scales were upset. As it is known, the basis of all of them is the system of hierarchically subordinate natural (initial) measures, which in radiology are the half-lives of radioactive elements.

14. From the beginning, the construction of a geochronometric scale proceeded in two trends, which were in no way bound by their usage.

On the one hand, the attempts to construct a geochronometric scale by co-ordination of radioactivity backdatings with boundaries of subdivisions of the ISS have been and still are undertaken (ISCh, 2000). The development of studies in this trend can ostensibly lead to a precise (expressed in years) definition of the temporal position of boundaries and, therefore, of the temporal scope of subdivisions of the ISS (more precise, geochronological units). The ultimate goal of these investigations is the construction of a scale (more precisely, a calendar), similar to the one set by a standard clock according to the Greenwich meridian. However, the following essential elements were skipped.

First of all, an overwhelming majority of radioactivity backdatings of ISS subdivision boundaries are obtained from deposits that are rather poorly characterized paleontologically, and in any case are very rarely obtained from those sections selected as limitotypes of the corresponding boundaries. As it has been pointed out by Naydin, even in the situation when radioactivity data actually characterize some stratoecotone, it remains completely vague as to which (initial, culmination or final) phase of a global event triggering of a concrete radiological clock in this or that region, it is connected (, 1998).

Further, in definition of the radioactivity age of boundaries of adjacent subdivisions of the ISS, the method of averaging available backdatings is applied. Meanwhile, their inaccuracy for different intervals of the ISS ranges from 20 to 100 million years ( ., 1985). In a number of cases the age position of boundaries is determined by an interpolation and/or extrapolation of the available, rather low-fidelity, radiological data. Thus, for definition of the averaged age of boundaries, the data are gathered from as many different sites as possible, which are frequently rather remote from each other and usually differ sharply in their geological history. The proposition to utilize such weighted-mean values for determination of the position of boundaries of the ISS subdivisions and their global tracing is equivalent to analysis of weighted-mean temperatures of patients for an evaluation of the state of average sickness rate in hospitals throughout the world. The boundaries of the ISS subdivisions (as the prototypes of unit boundaries of the metrics of paleobiospheric time) represent the protocols of response of metachronously developed paleoecosystems to some global events. Under such conditions, a simultaneous switching on local radiological clocks related to differently-located paleoecosystem, can only be a result of an accidental coincidence of those events. They are causally not interrelated as, for example, a volcanic eruption in East Siberia and deposition of glauconite in South America. In this case, if at some time the technical opportunities allow us to gain a radioactivity date of the same boundary global event that took place in the above mentioned regions, it will allow us only to make an estimation of parameters of metachroneity of their development and nothing more. A good illustration of this can be seen in data of Malinovsky about a west-to-east migration of forming granite phases and metamorphism in the Northern hemisphere for the last 200 million years (, 1982).

Another trend in constructing a geochronometric scale that became especially popular during the last decade, is based upon a so-called principle of arbitrary and conditional division of a temporal continuum into units, which are suitable for practical usage as a scale (NASC, 1983; ISG-2, 1994; Remane et al., 1996; etc.). This idea has neither any scientific, nor any general reasonable substantiation. On the one hand, this method skips the empirically demonstrated statistical-probabilistic, protocolary nature of the geological record that eliminates the possibility of digitization of chronoindicators captured in geological record (including moments of triggering of radiological clocks). Therefore it is impossible (and illegitimate) to draw an analogy between these and numeric or geometrical continuum. Even if we allow for the substantial conception about the existence of absolute (independent from material substance) time to be true, and even if we agree with the statement of Hedberg (ISG-1, 1976) and Salvador (ISG-2, 1994) that this absolute time represents a certain intangible property, which also has the property of a continuum even then, the use of the principle of conditional splitting a time interval is as well improper. This principle skips a generally accepted method in physics of constructing measuring scales for magnitudes that allows for mediated measuring only (and from the point of view of the substantial conception, time is just such a magnitude).

15. As it follows from all this mentioned above, none of the currently developed trends in radiometric geochronometry have a rigorous methodological substantiation. Therefore a reasonable question to ask is, what is the role of radioactivity backdatings for a solution of those problems that we encounter in geohistorical reconstruction? To answer this question, it is necessary to take into consideration the following circumstances.

At the beginning of the development of geochronometry, its adherents were especially delighted by the statement about the complete independence of the course of a radiological clock on conditions of its existence. Now it becomes more and more apparent that non-disturbed readings of radiological clocks are rather an exception to the general rule. Their independence of the course of events at a biospheric organizational level of the Earths matter is the main obstacle to practical usage of radiological backdatings. It also highlights a fundamental problem of the mutual relation of both qualitative and quantitative assessments of temporal properties and relations of phenomena of the geological record. In connection with the latter problem, first of all, there arises the following question whether the quantitative representations of time in geology play the same role, as in physics, or can (and should) they be utilized for diverse purposes?

Having agreed to express half-life duration of radioactive elements in measures of ordinary (conceptual physical) time, the creators of an absolute geochronometry apparently had an opportunity to utilize in geology the t parameter, generally accepted in precise sciences. However, none of them (with the exception of Vernadsky) were puzzled by the question of what sense the application of this parameter has in geology?. It is well known that the t parameter is used in fundamental equations of classical mechanics, relativity theory, and quantum mechanics, and allows us to describe such properties as speed, acceleration, and duration. Thus, the formulation of physical laws is indifferent to the sign with which the t parameter is used in the equations. Physicists are not interested in when this or that event occurred, or what its age is, because modern physic has as its basis the principle of uniformity. According to the latter, the actions of any physical law are independent on space and time. In the formulas of physical laws the discrepancy between past and future is ignored. Vice-versa, geologists are primarily interested in the question of age time of an accomplishment or of phenomena of geological history. It may seem that having an opportunity to use the t parameter, geology would gain a mighty tool for definition of the same parameters of geological happenings and events as physicists are interested in. However, this has not taken place and the blame falls on the matter-energy nature of radiological clocks.

The readings of a radiological clock once it is switched on (ideally in the absence of failures of flow in their individual time), do not correspond in any way to peripeteias of development of the paleoecosystem to which it appeared to be originally bound. So, a radiological clock, which is built in the products of a volcanic eruption, do not further respond to the subsequent deposition of terrigenous and carbonaceous strata, nor to post-depositional uplift or erosion, etc. Readings of a radiological clock fix the time of their triggering and nothing more. Thus, it allows us to answer only one question (not of any interest to physics) when this concrete event in the history of a given local paleoecosystem took place. The radiological clock does not provide for any information on the duration of alterations in the state of the clock-containing paleoecosystem following this event, which result from its cyclic-irreversible development. Moreover, from readings of a radiological clock it is impossible even to determine the endurance of the quasistable state of the system that caused their starting up. Therefore, a radiological clock cannot be used for the calculation of either the speed or duration of processes in an event bound by a given concrete paleoecosystem. And this is the key difference between a radiological clock and the clock used by physicists for registration of temporal parameters of phenomena.

From time to time there are controversies in the geological literature that concern an assessment of the role of geochronological and geochronometric scales for the solution of practical problems arising before explorers of Earth history. First of all, these questions concern both a highly detailed division of supracrustal deposits and split-hair accuracy of correlation. One of the main benefits of the ISS subdivisions, the minuteness of its units, is usually inaccessible for geochronometry. The adherents of a geochronometric scale usually appeal to the greater accuracy of correlation that is underlain by the principle of an absolute precise measurement. However, from the above viewpoints it is clear that both the controversies, and the attempts at a reconciliation between geochronological and geochronometric scales, are senseless. Each of them should represent a model and metrics of conceptual time of different levels of organization of the Earths matter.

In their controversies, the proponents of a traditional geochronology and geochronometry fail to take in consideration a very important factor the content of the information receivable for their use. Operating under the notions of a geochronological scale (i.e. the Devonian or the Cretaceous age) we receive information not only about the relative (i.e. earlier later) age of particular phenomena, but also information about the qualitative features of the corresponding time-span its organic world, climate, etc. Whereas, an expression such as the age is 10 Ma, yields only the information that a local event happened 10 million years back that is all. For a better understanding of what has taken place, we need additional geological information, which concerns the qualitative features of the geosystem with which this local clock is connected.

Assessments of age of the same geological object, which are based upon the usage of both a paleobiospheric and a radiological clock, are not only reciprocally complementary, but are also connected with each other by the principle of uncertainty. On the one hand, for the same geological object it is impossible to receive simultaneously information on its qualitative features (its association to a specific ISSs subdivision) and quantitative parameters (the radiological age). On the other hand, the definition of radiological age of any object cannot warrant its reference to a concrete subdivision of the ISS. For example, we cannot state that a radiological clock in deposits at the bottom of Siphonodella sulcata zone switched on in China 361 million years back (Yang-Jie-dong et al., 1988), point to a Late Devonian age. Whereas a clock, which was started in Western Europe 353 million years back (Claoue-Long et al., 1993), testifies to an Early Carboniferous age. According to a geochronological scale, the deposits from these regions are of the same age. According to a geochronometric scale, the deposits in China fall into the Late Devonian, and in Western Europe they fall into the Early Carboniferous, because by the scale of Harland the boundary between Devonian and Carboniferous is fixed at 360 million years ( ., 1985) and in the last version of International Stratigraphic Chart it is estimated as 354 or 355 Ma (ISCh, 2000).

It is quite apparent that radiological data have great heuristic value for estimating the general endurance of geological processes the fact that it demonstrated that our planet appeared not 6000 years back, but at least about 4.5 billion years, has a great cognitive value. However, to raise the capability of radiological backdatings to practical use in geological studies, it is necessary, first of all, to construct regional geochronometric scales. The coordination between radiological backdatings and paleontologically documented sections of boundary deposits in concrete paleoecosystems of a regional level of organization, will allow us to outline an interrelation between the boundaries of the ISS subdivisions (established for the Phanerozoic by paleontological data) and their radiological age. On the one hand, the generalization of these data can give us some information on parameters of the transitoriness of global paleobiospheric rearrangements. On the other hand, it will allow us to elucidate the question of metachronous development of individual paleoecosystems and to approximate the rate of propagation of signals of specific global events.

16. Thus, geochronological and geochronometric scales reflect (or should reflect) the structure and properties of two types of static time paleobiospheric and radiological, which are connected with planetary and atomic levels of organization of the Earths matter, respectively. A key discrepancy between them consists in that the course of paleobiospheric time was regulated by general factors of global value, whereas the flow of radioactivity time is instituted by local, causally independent, geographically different events, which switched on a concrete radiological clock.

The age definitions of concrete geological objects, which are represented in terms of both scales of paleobiospheric and radiological time, are connected by the relationships of complementarity and uncertainty. Using the radioactivity age, as defined, for the improvement of a temporal position of the geological object in the terms of the ISS subdivisions, is improper.

Other basic discrepancies between paleobiospheric and radiological time are that paleobiospheric time is represented by information about sequential, cross-cutting, and side-by-side events and happenings of the past, which proceeded under influence of planetary-universal factors, whereas radiological time carries the information, on the one side, only about events triggering a local radiological clock that is connected with the systems of mineral and rock levels of organization and, on the other side, about the temporality of their existence (if their flow of individual time is uninterrupted).

The resurrection (or rehabilitation) of an event-approach for determination chronostratigraphic boundaries eliminates the possibility of dating their age-position with a weighted-mean reading of differently-located radiological clocks. The tracing of chronostratigraphic (more exact, geochronological) boundaries involving correlation of protocols that are the response of metachronously developed, differently-ranked paleoecosystems to the same operating global factor. Reconstruction or retrosynchronization of geological history is based on the identification of protocols of events, as underlain by the principles of Huxley and Meyen, but not on the identification of the instants of radiological (instead of absolute!) time, which is underlain by a principle of absolute precise measurement.

Construction of a geochronometric scale (more precise metrics) that reflects the structure and properties of radiological time, demands severe methodological study. It is necessary to allow for the empirically demonstrated incompleteness of geological record, which eliminates the possibility to use for its construction the idea of a continuum. Therefore, in construction of a geochronometric scale, it is also impossible to use the logic-mathematical apparatus of classic analysis, or the principle of arbitrary subdividing and averaging of temporal units.

The proposed theory of paleobiospheric time allows us to avoid many pseudo-problems that are innately connected with conceptions of identity of geological (s.l.) and physical (ordinary) time and that also are expressed in the eternal dichotomies of isochroneity diachroneity, the naturality artificiality of boundaries, etc. Only within the framework of this theory is it possible to offer a methodologically correct approach to a solution of the problem of chronostratigraphic/geochronological boundaries or more specifically to the problem of retrosynchronization. Lastly, this theory enables us to envision a clear path for construction a quantitative scale (or metrics) of conceptual paleobiospheric time. Next chapter is devoted to the consideration of a basic methodological approach for a solution of this problem.

 

The PROBLEM of MEASUREMENT of the GEOLOGICAL (s.l.) TIME

It is utterly beyond our power to measure the changes of things by time.

Quite the contrary, time is an abstraction, at which we arrive by means of the

changes of things: made because we are not restricted to any one definite measure,

all being interconnected

Ernst Mach

17. The readers may remember that the idea of constructing a geological chronograph arose at that very time when geologists became persuaded of impossibility of an unconditioned and universal use of Stenos criterion of coevality of geological phenomena (the same means coeval). Results obtained from new regional studies demonstrated differences in the compositional characteristics, formation environments, bed occurrences and other features that were used to establish local stratigraphic subdivisions. Moreover, paleontological evidence testified to a non-coeval emergence of the local stratons in different places. However, there was a need for a universal grid of coordinates, which would allow to orderly arrange regional-specific phenomena according to a time sequence, and to represent in general the developmental history of the modern Earths surface. The solution was found to be a composite stratigraphic column that was used as a factual basis for a universal (international) stratigraphic scale and a geochronological scale isomorphic with it.

I would also like to remind the readers that the ISS was developed at a time when there was a complete predominance of evolutionary doctrine. This conception had as its methodological corner-stone the postulation of a non-interrupted and continuous character of the development process. Leibnitzs maxim that Nature does not make leaps seemed to have been completely confirmed by both evolutionary and field theories of the Universe which were dominant at the end of the 19th century. In addition, this idea was supported by geological evidence of gradual transitions between contiguous stratons, which were previously thought to have well-defined boundaries. All these factors resulted in an illusive idea of the ISS founders about a possible creation of a composite stratigraphic column that would adequately represent the complete geological record. From a methodological point of view, this notion meant that the ISS either voluntarily or involuntarily was assigned the property of a continuum isomorphic with the continuum of past historical time.

It is of prime importance that the ISS founders were well aware of both an incompleteness of the geological record and inadequacy of the paleontological record. However, they believed it to be just an unfortunate circumstance preventing them from an empirical corroboration, first of all, of the hypothesized non-interrupted continuity of evolution in the organic world. They considered the discoveries of scarce transitional forms to be, on the one hand, a factual substantiation of evolutionary theory, and, on the other hand, evidence of an occasional but not regular occurrence of hiatuses.

Consequently, the idea of a one-to-one (isomorphic) correspondence between the geological record, with all its obvious and concealed interruptions, and the temporal continuum was deeply rooting in geology. This idea is best expressed in the demand made by the adherents of different ISS conceptions; mainly that the ISS must include the entire record of the history of the Earths crust and be free from mutual overlaps and breaks. It remains a mystery: how it may be possible to construct a composite stratigraphic column free from breaks, considering an incompleteness to be a fundamental characteristic of the geological record. The same unexplained mystery is the demand to exclude mutual overlaps from the ISS, since it suggests some independent and external, with respect to the phenomena of the geological record, criterion of their identification.

The delusion of ostensibly existing isomorphic relationships between the geological record and the time continuum has resulted in the following: (1) the conception of unit stratotypes, which is assumed to be the only means to determine the basic property of chronostratigraphic subdivisions, i.e., their time-span; and (2) the above-mentioned arguments about the amount of time lost by the geological record and how these dark times refer to the duration of one or another zonal unit.

In this connection, I would like to remind the readers of the following. As new areas were covered by regional geological studies, it became clear by the middle of the 19th century that the bulbous stratosphere model, which had been offered by Steno and supported by the Neptunians, had failed. The Catastrophists method of discriminating between stratigraphic subdivisions by the events separating them also was rejected for ideological reasons. However, geology was in a strong need for a universal (world-wide) grid of coordinates, which would possess the same bulbous (onion-like) structure. This grid, being superimposed over the entire diversity of local geological situations, would allow different-placed phenomena to be ordered by their temporal succession. Proceeding from the viewpoint of an artificial character of any unit, from a belief in isomorphic relationships between the geological record and the time continuum, and from the idea of an occasional appearance of breaks in the geological record, the ISS founders began to determine the size of stratigraphic subdivisions not in terms of their separating events but in terms of the time intervals confined to their boundaries. One important point to remember is that these boundaries were established according to the principle of priority. Given these reasons, it is clear why chronological units and not stratigraphic subdivisions were declared to be the basic ones at the 8th IGC Session (Paris, 1900).

It is remarkable that the ISS received its final formulation at the very time when the quantum-field conception of a physical world, which was underlain by the idea of a continuous-discontinuous nature of substance and motion, was developing. In fact, geology was even ahead of physics in approaching this idea, as indicated by Chamberlin's attempt in the 1890s to take the transgressive-regressive or diastrophic cycles as a basis for the ISS. Indeed, all different versions of the ISS that have been developing through the 20th century are closely connected with this quantum-field image of the Universe. Nevertheless, this fact has in no way influenced the idea of relationships between the geological record and the time continuum, nor the methods of determining the size of chronostratigraphic subdivisions.

In the last fifteen or twenty years, the event approach to determining the chronostratigraphic boundaries has been reanimated and rehabilitated, and the situation has somewhat changed now. However, the importance of such an approach both for defining and tracing the boundaries and the construction of the ISS itself, as a substantial basis for the model and metrics of the conceptual paleobiospheric time, needs a more profound understanding.

18. With respect to the problem of the measurement of geological (s.l.) time, I shall accentuate the following. First of all, it is quite obvious that the crucial possibility constructing of a model that would serve as the material basis for the metrics of conceptual paleobiospheric time, is constrained by the fact that the geological record preserves only the traces of the existence and changing states of heterogeneous (by their matter-energy nature) paleosystems and related processes. This traces includes the magnetic field reversals and radioactive decay, the evolution of the organic world and alterations in paleoecosystems, transgressions and regressions, tectonic movements and magmatism, etc. An examination of the general structure of geological chronicles clearly illustrates three basic classes or categories of natural phenomena any of which can act as a chronoindicator (, 1994).

When constructing a clock that could measure off geological time, we basically cannot use the principle of a metronome as a source for measuring physical (dynamic) time. We must be aware of the empirically established impossibility of globally tracing protocols of any steadily recurrent geological (biospheral) process (the identical states of which are treated as natural initial measures of time and its elementary measured subdivisions). That will predetermine a main feature of natural initial measures of real geological (s.l.) time - their uniqueness. The originality and individuality of protocols of these sequential states of cyclic-irreversible and continuously-discontinuously developed paleosystems and processes, specifies a key measurability of a real geological time on the one hand, and a cardinal difference from the procedures for measurement static and dynamic time, on the other. In constructing a model and metrics of conceptual paleobiospheric time, it is basically possible to utilize only two categories of chronoindicators.

The first category includes the protocols of happenings that fix, both the fact of existence of a particular paleosystems from the moment of its origin to its disappearance or regeneration, and the stage-by-stage (phase-like) character of their self-contained qualitative transformation and conservation of a mobile-balanced state at each stage. Generally, in the development of all systems, regardless of their matter-energy nature, it is possible to pick out three main qualitative stages, corresponding to their origin, quasistable state, and transformation. Such chronostops are represented by natural geological bodies possessing a particular archetype, i.e. an invariable composition, amount and relations of primary components of that particular paleosystem, the traces of existence and development of which are accepted as a basis for subdividing the Earths crust (, 1997a, 1998).

The second category is represented by protocols of events, which indicate an alteration in the state of a paleosystem during its individual development, and replacement of some paleosystems by others. In the geological record these chronoseparators are established by changes in archetypes of chronostops, which are divided by the chronoseparators. They can be expressed by one of the 15 universal types of system transformations, which can affect the composition, number (quantitative parameters), and relation between the primary components of the corresponding paleosystems (, 1994, 1997a, 1998, etc.). It is critically important, that the chronoseparators do not represent protocols of instantaneous events. And vice-versa, they have a particular transitoriness, the parameters of which depend on the matter-energy nature of paleosystems. Generally, the structure of any event allows for identification of its beginning, culmination and termination (, 1998).

Finding a solution for the problem of measuring real paleobiospheric time is primarily related to a choice of such a privileged process, the model of which can be used to create a metrics of conceptual paleobiospheric time. As I have noted repeatedly (, 1997, etc.), another key point is that the geological record does not contain traces of any process, from the entire history of the Earths crust, which could be used as an acceptable model for the basis of metrics that would be applicable for the definition of temporal properties and relations of all other geological phenomena during the complete history of the paleobiosphere. It follows, that in constructing the metrics of conceptual paleobiospheric time we shall be objectively forced to use as its basis, quasidynamic models of processes that are unequal by their genetical (matter-energy) nature, for different segments of geological history. Or else, for different historic periods of the biosphere, we must use clocks of different construction that run on unequal rhythmics. I want to emphasize that this concerns both Precambrian and Phanerozoic history, since by even accepting a biochronological standard, we are objectively compelled to employ as the standard clock, models of development of different orthochronological fossil groups for each Phanerozoic time-span. Such an objectively existing situation (I point it out once again) gives rise to a whole set of both procedural problems (concerning a choice of privileged processes proper for individual intervals of paleobiosphere development, not to be specifically examined in this article) and methodological ones.

If we accept the modern ISS as a starting point for constructing a model of conceptual paleobiospheric time, then, naturally, we shall recognize its chronostratigraphic subdivisions as the chronostops. In this case as the chronoseparators should be considered the chronostratigraphic boundaries. The position of lower and upper boundaries of chronostratigraphic subdivision determines the time-span corresponding to it the geochronological unit. A traditional use of the ISS as an instrument for interregional and world-wide correlations is aimed at establishing a coevality of differently-placed phenomena, by means of their comparison with the stratotypes of corresponding chronostratigraphic subdivisions. Until recently, tracing the boundaries (i.e. a retrosynchronization of the protocols of regional events) has been regarded as being just of a subordinate value. The negating results of this are as follows.

The stratotypes of all chronostratigraphic subdivisions are regional by their character. This means that they are the protocols of local phenomena, the limits of which are determined by local events. In addition to this, an incompleteness of the geological record results in a stratotype perhaps representing just a part of event, which may correspond to its beginning, culmination or end. Furthemore, such an event itself may or may not be a consequence of any world-wide factor. It is possible to confirm a world-wide value of the protocol of the event chosen as a boundary only by virtue of its retrosynchronization with the protocols of other events; i.e., by its tracing beyond the limits of the stratotype area.

Thus, establishing and tracing the protocols of world-wide events become especially important in the development of the paleobiospheric time model. In this connection, I would like to point to the following.

First, assembling a composite stratigraphic column, which acts as a material basis for real paleobiospheric time, implies a necessary use of the models of heterogeneous processes, as the standard clocks for individual intervals of geological history. Consequently, it will require a conjuction of events, which differ by their nature and mark the developmental stages of heterogeneous paleosystems. Also, an inevitable use of differently designed standard clocks for the Archean, Proterozoic, Phanerozoic, and Quaternary will raise the question about the world-wide nature of the events, which are used to calibrate the corresponding intervals of the conceptual paleobiospheric time scale. As is well-known (, 1991, 1993), a possible use of an event-based approach to distinguish between the chronostratigraphic subdivisions of the Precambrian is doubtful.

Second, regardless of which developmental model can be taken as a basis for metrics of conceptual paleobiospheric time of a given interval of geological history, tracing its unit boundaries will need a retrosynchronization of the protocols of events, which are related to heterogeneous paleosystems. In consideration of (1) modern ideas about the interrelationships between heterogeneous factors, and, (2) the law of metachronous development of regional geosystems, it becomes obvious that a retrosynchronization of the protocols of differently placed heterogeneous events can proceed only on the basis of Meyens principle, which allows the establishment of their topologically coeval character (, 1997. C. 106).

19. I want to further point out that all attempts undertaken until now to develop quantitative assessments of temporal parameters of geological phenomena, have been doomed to failure because they proceeded from the false assumption that geological (paleobiospheric) and physical (common) time are identical. Thus, such common properties as continuity, uniformity, and isotropy, were assigned to both of them. What was not considered was that common and real paleobiospheric time fall into two principally different categories dynamic and static, respectively and that the transformation of the first into the second obeys the fundamental law of tempodesinentia. Apparently, it is impossible to evade this law and its consequences when arguing the methodological problems in constructing the metrics of conceptual paleobiospheric time.

As it has been demonstrated previously, the first and the most important consequence of tempodesinentia is the protocolary (statistical-probabilistic) character of all data represented in the geological record. This record contains the chronicles of countless and undetermined intervals of lost (dark) time. As it has been already mentioned, this fact makes it quite useless to create a break-free material basis for a scale of geological time that is interpreted as an equivalent of physical time. Proceeding from these circumstances, we can make the following conclusions.

First of all, the statistical-probabilistic nature of geological information essentially eliminates the use of a major postulate of classical logic-mathematical analysis, upon which the procedure of measuring physical time is based, and according to which under equal conditions, identical results of the same process are reached for equal time-spans.

Furthermore, the protocolary nature of geological information does not allow making an analogy between a numeric (and geometrical) continuum and real geological time. It follows, therefore, that it neither allows for the reduction of real geological time to physical time, nor for an application of the logic-mathematical apparatus of classic analysis that is based on the idea of a continuum, and which is used for measuring physical time.

Finally, a key feature of the geologicalal record is the discretization of its constituent natural geological bodies at all levels of organization from separate strata, divided by bedded surfaces, up to stratigraphic subdivisions of any rank, whose boundaries are represented by protocols of global events. I want to accentuate that the question is not about the interruptions (breaks) or unconformities, but about protocols of events that marked boundaries of all subdivisions and have a particular transitoriness expressed in the geologicalal record by some stratigraphic intervals such as so-called transitional layers, stratoecotones or buffer zones.

So, the general conclusion from analysis of the consequences of the law of tempodesinentia for the development of the general methodological approach to measuring real paleobiospheric time, is that it cannot in princiole be reduced to physical time, and also that in constructing the metrics of conceptual paleobiospheric time it is basically impossible to use the logic-mathematical apparatus of classic analysis.

This conclusion is natural and inevitable. Real paleobiospheric time differs in principle from absolute (sensu Newton) time (which is modeled in terms of the conceptual physical time) not only because each belongs to a different category (static and dynamic, correspondingly), but also because they represent the temporal properties of systems that follow cardinally differing laws. Paleobiospheric time is characteristic of evolving, open, non-stationary, and self-organizing systems, whereas physical time is characteristic of closed, stationary systems characterized by their own reversible processes.

This conclusion, however, does not cover the whole significance of the tempodesinentia law for solving the problem of measuring real paleobiospheric time. The point is that a tempodesinentia causes a complete loss of the kinematic component of information, which can be recovered with some extent of reliability, only by virtue of actual observations. In addition, a validity of such retrospective reconstructions is impeded by wide-spread depths and curses of convergence (, 1996). This convergence results in a lack of one-to-one correspondence between the static information and quasi-dynamic models based on it. A striking example of such one-to-multiple relationship is found in the above-mentioned evolutionary hypotheses underlain by the same empirical paleontological data.

A one-to-multiple correspondence between the static and quasi-dynamic models, which is objectively possible, specifies one more methodological peculiarity of the measurement of real paleobiospheric time. When physical time is measured, there may be many mathematically incompatible metricss due to different processes used as the basis for the model (, 1969). In geology, different metrics may be underlain, in principle, by a static model of the same paleosystem.

From here it follows that for constructing a quasi-dynamic model of the process that is selected as a basis for the metrics of conceptual paleobiospheric time, as well as in any other historical reconstruction, it is necessary to use the method of multiple working hypotheses (Chamberlin, 1897; , 1989). We may hope that the use of this method will allow us, by virtue of successive approximation, to ultimately construct (although probably not very soon) relatively adequate quasi-dynamic models of the processes that will be selected as the basis for the metrics of conceptual paleobiospheric time for individual intervals of geological history.

20. Since it is impossible in principle to use the logical-mathematical apparatus of classic analysis to solve the problem of measuring paleobiospheric time, then it would be reasonable to address another area of modern mathematics, i.e. set theory. Unlike classic analysis, set theory operates not with quantitative but with qualitative notions (, , 1974). Proposing this way of solving the problem of measuring real paleobiospheric time, I proceed from the following considerations (, 1997, 1998).

As is well-known, the first stage in the construction of any metrics of time is the development of a system of hierarchically subordinate initial (natural) measures. To make a choice of the basic principles for developing such a system, it should be remembered that any paleosystem, a cyclical-irreversible and continuous-discontinuous evolution of which is represented in the geological record, is an open one. Therefore, the system of universal taxonomic categories of natural measures of paleobiospheric time can have, as their basis, only the protocols of irreversible and qualitative changes of those paleosystems, the developmental models of which are taken as the basis for the metrics of conceptual paleobiospheric time. These include two sets of protocols. The first consists of the protocols of complete periods of existence (from origin to transformation or disappearance) of privileged paleosystems. The second set is hierarchically subordinate to the first and includes the protocols of stages of development, which generally signify the emergence (origination), a quasi-stable state, and the transformation of these paleosystems.

When constructing the metrics of conceptual paleobiospheric time, we are objectively forced to use quasidynamic models of genetically different paleosystems for different periods of geological history. So far, corroboration of the equivalence of natural measures that correspond to stages and periods of their irreversible evolution, have been a fundamental problem. But by selecting a quasidynamic developmental model for any genetically particular paleosystem as a basis for a frame of reference of conceptual paleobiospheric time, and by accepting the protocols of stages and periods of its development for initial measures, we thus intentionally isolate some closed set of objects (natural geological bodies). In other words, we pick out some set by the indication of the characteristic property, which only the members of the set and only they have (, , 1974. C. 118). Accordingly, we obtain the important possibility of establishing an equivalent relation for this set (, 1971).

To enter these relations, it is necessary to lay out a general definition of the notion of a member (element), which would allow us to establish the presence or absence, for each concrete natural geological body, properties that are essential and adequate for understanding the twofold relations of reflexivity, symmetry, and transitivity. Before discussing the establishment of an equivalence of natural geological bodies, which are members (elements) of a temporal structure, and have relations of inclusion and succession, I propose the following definition of the notion of a member (element): a concrete natural geological body that is the protocol of a qualitatively specific stage and/or, of a complete period of development of a paleosystem (from origin to destruction or transformation), the model of which falls into a particular level of a hierarchical organization of that genetical type of paleosystems, a continuous-discontinuous, cyclic-irreversible evolution of which is selected as a base for constructing a frame of reference of conceptual paleobiospheric time (, 1997a, 1998; Simakov, 2001).

This definition clearly contains the idea of a hierarchical subordination and a different scale of the set elements. This idea is the basis for measuring paleobiospheric time. In other words, by assigning such properties as representing the protocol of a developmental stage of a particular paleosystem and representing the protocol of a period of existence of a particular paleosystem to the elements of a closed set (i.e., natural geological bodies) we recognize a system of hierarchically subordinate classes of equivalence in a given set. These classes serve as a basis for the system of natural initial measures of conceptual paleobiospheric time (like a year, lunar month or day). By this means, the relationships of a strict order in each set are established (, 1971).

Making a structural extension of quasi-dynamic models of genetically different paleosystems, which are taken as the basis of the metrics of conceptual paleobiospheric time for successive intervals of the geological history, we also receive a number of corresponding sets. It is important that the elements of any such set are the protocols of the periods and stages of a cyclic-irreversible and continuous-discontinuous development of paleosystems, which are taken as a basis of the metrics of conceptual paleobiospheric time. From here it follows that these sets are themselves equivalent. Indeed, in accordance with set theory, we may regard, as equivalent, the protocols of both stages and periods of development of paleosystems of the same scale, and, as well, the protocols of a transitoriness of qualitatively different and successive paleosystems from any interval of the arrow of time.

In these circumstances the procedure for measuring conceptual paleobiospheric time will be reduced, in practice, to counting the elementary initial measures. These measures will be represented by a class of equivalence of the protocols of the developmental stages of particular paleosystems. These protocols should occupy the hierarchically lowest level among paleosystems of those genetic types that form the basis for constructing a model of conceptual paleobiospheric time. In this case, it is possible to quantitatively determine specific initial measures at higher hierarchical levels, and ultimately, to quantitatively characterize the laws of development of privileged genetical types of paleosystems. A so obtained metrics, which represents a system of hierarchically subordinate natural initial measures of conceptual paleobiospheric time, can not be supplemented with artificial units (like an hour, minute, and second). According to the classification of Stivens (, 1960), this metrics will belong to the category of scales of intervals. Therefore, it will not be of high resolution for assessing the temporal properties and relationships of any other geological phenomena.

The proposed definition of an element, generally speaking, allows us to establish a single system of hierarchically subordinate classes of equivalence for quasi-dynamic models of evolution of heterogeneous paleosystem, which successively replaced each other in the history of the Earth. Additionlly, it is very important that, according to set theory, not only the protocols of identical developmental stages of heterogeneous systems (corresponding to their origination, a mobile-stable state, and transformation), but the protocols of any stage also will be equivalent. This fact is particularly important, because the geological record has often preserved the protocols of not all but just some stages of a complete period of existence of some paleosystems. In this connection we should recall the scarce findings of transitional forms or initial representatives of an overwhelming majority of taxa.

However, the identification of the protocols of developmental stages of genetically different paleosystems will be correct only if it deals with the paleosystems, which have the same position in the hierarchy of taxa (i.e., if they are at the same level of organization) of corresponding genetical types of paleosystems. So, the general opportunity for constructing the model and metrics of the universal (embracing the entire geological history) conceptual paleobiospheric time directly depends upon developing and reaching a mutual agreement about the taxonomy of heterogeneous paleosystems (, 1997a, 1998).

21. In summary, the ISS is used at present as a grid of coordinates to temporally arrange the phenomena recorded in geological chronicles and represents by itself a model of the biospheres biography that is heterogeneous in its various intervals. For example, during Precambrian it represents a continuous-discontinuous and cyclic-irreversible evolution of tectono-magmatical processes; for Phanerozoic it represents different aspects of biotic development. Since the basic subdivisions through all intervals of the modern ISS are established on the basis of different criteria, it is therefore obvious that its structure reflects the flow of a local paleobiospheric time. Thus, it can not perform the functions of an external, with reference to geological phenomena, time-counting instrument (a metrics).

A specific character of the problem of constructing a metrics of conceptual paleobiospheric time is primarily determined by the statistically-probabilistic (protocolary) nature of geological information. This peculiarity excludes in principle the opportunity for drawing analogies between the numerical, geometric, and temporal continua. Consequently, geology excludes both the use of physical time metrics and methodological principles of its construction.

From here, the second peculiarity follows. It is impossible in principle to use, for constructing the metrics of conceptual paleobiospheric time, the protocols of cyclical processes, which serve as a basis for constructing the metrics of physical time. As the initial natural measures of conceptual paleobiospheric time, there can be used only the protocols of irreversible qualitative alterations of paleosystems, the developmental models of which are taken as the basis of such a time metricss.

The third peculiarity is that, as the basis of metrics for different intervals of the geological history, we must use, due to objective reasons, the quasi-dynamic models of the development of heterogeneous paleosystems. which differ by their matter-energetic nature.

A cardinal difference between physical and paleobiospheric times is that they are mutually irreducible to each other. Consequently, it is impossible to use, for measuring the paleobiospheric time, neither the idea of a numerical continuum nor the whole logical-mathematical apparatus of classical analysis based on it. Construction of a countable metrics of conceptual paleobiospheric time, corresponding by Stivens classification to a scale of intervals, can only be possible by virtue of the logical-mathematical apparatus of set theory. This approach will basically allow us to establish the relations of equivalence and strict order between the chronoindicators, which represent an irreversible character of the evolution of heterogeneous paleosystems, the models of which are taken as the basis for metrics for different intervals of the geological history. Implementation of this idea primarily depends on developing and reaching an agreement about the taxonomy of paleosystems, which will act as the basis for construction of a model of the universal (embracing the whole history of the Earths crust) conceptual paleobiospheric time.

As it has been demonstrated by a comparative study of methodological aspects of the development and use of the metrics of conceptual dynamic and static (paleobiospheric, as well) time (, 1998), the non-trivial conventions, that we have to introduce due to objectively existing reasons at different steps of development and practical use of corresponding conceptual time metrics, are of key importance in both cases. Such conventions in principle differ both from trivial agreements ad hoc, which are widely used in modern stratigraphy and from pragmatic directives for a model-aimed approach. It is obvious because not we prescribe them to the Nature, but the Nature itself dictates these conventions to us because of the time static character and a systemic organization of studied entities.

Finally, I would like to emphasize that constructing a metrics of conceptual paleobiospheric time will be the task for future generations of stratigraphers. However, even if such a countable scale of conceptual paleobiospheric time is constructed, it will hardly be able to replace the existing ISS. Such a scale (metrics) will just provide for a quantitative definiteness of temporal properties and relationships of those phenomena of the paleobiospheric history, which have been recorded in the biography of the Earths crust that is represented in the ISS.

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