© A.P.Levich

Temporology is a science of the future. At present there is no such a discipline in any list of academic, educational or applied disciplines. Temporology, or time research, is understood as an interdisciplinary branch of general systems theory, which deals with causes, forms and measurements of the World's dynamical variability.

Time is an existential factor. Human interest in time is inseparably linked with the unacceptance of the perishable nature and shortness of one's personal being. An interest in the enigma of the appearance and disappearance of our own individual consciousness in the World revives in each generation and faces the absence of generally accepted scientific solutions.

Time is a resource that is almost unmastered by man and humanity. Desirable goals, still inaccessible by modern technologies, are: active longevity; methods of slowing down or accelerating the course of one's individual time (for instance, to avoid frustration or to gain a full scale of positive emotions, to act efficiently in critical situations, to improve achievements in sports, etc.); changing specific lifetime; maturing acceleration for plants and animals of human usage; desynchronization of parasitary and infectious organisms' life cycles; duration control of individual and public development stages (maturing, education, formation replacement etc.).

Time is a resource that determines the type of a civilization (its productivity, demographic indices, communication rate, outstripping strategies in competition and fight, etc.).

Time is an engineering problem: it is necessary to come to an understanding whether or not there exists a scientific prohibition of the dreamed time travels; it is necessary to comprehend and build into applied technologies the link between time and energy which exists in the fundamental theories (e.g., if the World time is inhomogeneous, then there should exist energy sources and/or drains).

Lastly, comprehension of time is a necessary component of the development of science itself. Description of the World dynamics is one of the basic functions of scientific knowledge. The goal of a developed dynamical theory is to discover the variability laws of the fragment of reality under study. In exact sciences, this law is called an "equation of motion". In essence, an equation of motion is a description of variability of the object under study with the aid of a variability reference, i.e., a clock. Therefore, a success in finding an equation of motion can depend to a large extent on the notion of time used by the researcher and on the accepted method of its measurement. Moreover, knowledge of adequate variability laws is a pledge of success in scientific forecasting (if one knows the "equations of motion", one can say that he "calculates" the future rather than forecasts it).

The causes of the emergence of changes and creation of the new in the World ("the nature of time") is the greatest enigma of science. Its solution will possibly lead to an understanding of the essence of many world phenomena. Thus, by the opinion of G. Cuvier (1817), "Life represents a more or less complex vortex whose direction is constant and which always captures molecules which possess certain properties; however, it is permanently entered and left by individual molecules in such a way that the shape of a living body is more significant for it than the substance. As long as this motion exists, the body where it takes place is alive... When the motion stops once and for all, the body dies", i.e., the biological time is not an extension of the building of life but this building itself.

Time is, in modern knowledge, an initial and undefinable notion. Its usage rests on the researcher's intuition, on his unreflected professional experience, on his elements of extra-scientific, often subconscious ideas about the World. But a hope for a possible instrumental introduction of a unified notion of time is also justified: clocks used to measure it may be absolutely different by nature or by the properties of time they create (Levich, 1995).

To make time an object of a consistent study, it is necessary to derive it from undefinable concepts of the conceptual basis of science. To do so, it is necessary to replace the image of time with some other fundamental axioms. This will turn the "axioms" of time to "theorems". In other words, a scientific discussion of the ideas and views of time will be possible.

In the present basement of knowledge, the concept of time is closely mixed with other initial concepts, such as space, matter, interaction, charges, energy, development, life, consciousness and many others. It is therefore impossible to replace the "bricks of time" separately from other elements of the conceptual basis of natural science: its rather vast area is subject to revision. We are actually dealing with the construction of a new "picture of the World" that should become a basis for building new dynamical theories.

For understanding the nature of time, we are apparently missing some new essences able to replace the concept of time in the conceptual basis of science. Our success in the comprehension of time is modest because moving forward to such a success involves an enormous layer of paradigmal views hidden by the vague formulation of a "picture of the World". Creation of a new picture of the World becomes a compulsory stage in bringing the initial concepts of science to an agreement in the professional work of a natural science theorist. However, the way from a non-contradictory picture of the World through a formal theory to reality is, as a rule, as long as life. Moreover, it is the life of several generations of researchers who do not serve the conjuncture and are not afraid of "Beothians' cries".

Since, at the present stage, a basic problem in studying time is to create its explicit model, I would like to give one of possible examples, the "metabolic time" construction (Levich, 1995; 2003). ("Metabole", according to Aristoteles (1981), is understood as alteration or motion in the widest meaning of these words.)

One suggests a hypothesis that there exist "generating flows" in the World – natural processes which create the World's variability and whose properties may be identified or put into correspondence with the properties usually ascribed to the time phenomenon.

The hypothesis of generating flows is not new in both philosophy and physics. Willingly, one may find a consonance to the hypothesis in I. Newton's views where "time is flowing by itself and by its very nature" (Newton, 1687). This hypothesis is pronounced quite explicitly in N. Kozyrev's works (On the Way..., 1996), which have introduced the term "time flow", and time is considered as a physical phenomenon.

Now I would like to present the postulates of the metabolic approach to the description of a substantial nature of time:

• All natural systems are hierarchic.
• At each level of the hierarchic structure of a system there occurs compulsory substitution of its elements - the master process.
• At the depth levels of the system structure there exist flows which are external with respect to the system and which generate the master process. All systems are open with respect to generating flows. In particular, our Universe turns out to be an open system.
• The substance of the generating flows is not a substrate represented by fermionic particles, atoms, molecules or other complexes of particles possessing charges and taking part in interactions. The charges responsible for the interaction of objects are sources or sinks of generating flows in our World. (A clear image of the charges is a spring, a fountain or a jet, "spouting" in the substantial "reservoir".) The dynamic characteristics of the generating flows in sources and sinks form the properties of particles - charges and the mechanism of their interaction. Thus the substance of the generating flows is not "heavy" matter, but creates this matter. The substance does not take part in the interactions known by now, but provides a realization of these interactions. In other words, the material nature and the interacting ability have a different status of being for generating flows as compared with "heavy" matter.
• The whole set of elements of generating flows forms space, or the environment of the system.
• The motion of a system in its space (metabolic motion) is carried out not by "moving aside" the ambient elements, but by their replacement in the system, namely, by "entering" some "points" of space into the system while others are "leaving" it. (A clear image of metabolic motion is the movement of an image on the screen of a kinescope, or of symbols in a "running line" advertisement.)
• The generating flow "entry" into the system may be identified with the course of time in the system, i.e., the generating flows are natural references of time.

Let us briefly formulate some consequences of the metabolic approach.

• The time phenomenon in our World is a consequence of the openness of the Universe and all its subsystems with respect to substantial generating flows.
• The establishment phenomenon can be described and parameterized by storage or decrease of the generating flow substance in the system.
• Metabolic motion is a special case of the course of time; both consist in substitution of environmental substance in the system under consideration.
• The notion of a generating flow unifies the following concepts: particles of "heavy" matter as singularities of the flow; space as a substantial medium; time and motion as processes of element substitution in the systems; particle interactions as manifestations of dynamical characteristics of the flow.
• Different "generations" of elements of the generating flow substance form a set of neighborhoods of particles which are sources in space, thus creating the notion of "proximity" of its points, its topology and metric.
• The substance of generating flows is, on the one hand, omnipresent and omni-penetrating in our World, but, on the other, it does not interact in a usual way with "heavy" matter and is therefore invisible for usual instruments.
• Since the generating flow substance does not take part in the usual interactions and, while "penetrating through" objects, does not cause such usual effects for motion in a medium as torsion and resistance, it is not the ether of the 19th century. In the conceptual basis of natural science, the notions closest to this substance are the field or physical vacuum.
• The generating flows belonging to different levels of matter structure create in a unified way different charges, interactions, spaces and times, maybe irreducible to each other. Along with the charges of physical interactions, one may consider living organisms and the phenomenon of psyche as specific charges.
• The time created by the generating flows turns out to be reversible or irreversible to the same extent and in the same sense as are reversible or irreversible the flows themselves.

In the framework of the metabolic approach, the variability of a system is formalized as replacement of its elements at different levels of its hierarchic structure. It is suggested to measure the variability by counting the number of replaced elements. In this way one introduces a "metabolic clock" – a natural object, in which replacement of elements is taken as a uniform variability reference (Levich, 1995).

The metabolic parametrization of variability can be only utilized for systems described by sets without structure. Meanwhile, theoretical natural science always describes objects by modelling them as structured sets. In particular, even systems created by several generating flows cannot be represented as hierarchies of structureless sets.

The language of category theory and the method of functor comparison of structures (Levich, 1982, 2000) allows one to pass from the metabolic parametrization of system time to an entropy parametrization, making it possible:

• To suggest a rigorous approach to comparison of system states by their "degree of structuredness".
• To formulate an extremum principle according to which the natural dynamics of a system tends to increase its degree of structuredness (the maximum structure realization principle).
• To find an exact method of putting into correspondence to each system state a value of a certain numerical function which monotonically increases with increasing degree of structuredness of system states.
• To show that this numerical function may be interpreted as a generalized entropy of the system which may be identified with the traditional entropy calculation results for particular cases of the system description.
• To use the maximum structure realization principle as a ground for a maximum entropy principle.
• To measure entropy time in terms of the number of transformations admitted by the system structure.

In the above-mentioned extremum principles, one means a conditional extremum determined by the "resources" of the generating flow substance available to the system. It is the additional resource conditions that distinguish the suggested extremum principle from the Second Law of thermodynamics. The requirement of a conditionless maximum of entropy leads to a homogeneous distribution which is interpreted as "thermal death" and chaos. The same requirement of entropy growth applied to open systems under restricted available resources leads to sharp distinction of systems, their development and self-organization.

I would like to note that the entropy and metabolic parametrizations of time are monotonic with respect to each other, whereas the maximum entropy principle is equivalent to the principle of minimum generating flow resource "consumption" by a system (see analogues of the Boltzmann and Gibbs theorems in the paper by Levich and Fursova, 2002).

How can the suggested metabolic approach, implying the existence of substantial generating flows, help one in achieving the goals outlined at the beginning of these notes? One can point out two ways of socializing the substantial ideas. The most direct way is an operational manifestation, i.e., a reproducible measurement of some characteristics of substantial flows. On this way, we are rather in a position of the "frog dancing master" Galvani than in that of owners of Faraday's frame, also well-known nowadays.

One should note that the experimental discovery of objects from depth levels of the structure of matter does not only depend on the intellectual effort of individual researchers, but, to a great extent, on the "summa technologiae" achieved by the whole civilization. Another, speculative method is to "contrive hypotheses": on the basis of new essences just introduced, to carry out a consecutive theoretical construction of a non-contradictory picture of the World, to explain known effects, to formulate predictions of new effects in experimentally accessible areas and to try to solve the topical problems of natural science in the framework of substantial approaches. In particular, one of the achievable results might be a demonstration (with the aid of the metabolic or entropy parametrization of time) of derivation, rather than taking as a postulate, of the already known fundamental "equations of motion" of physics in areas where such equations exist (e.g., the Newton, Maxwell, Schroedinger, Dirac, Einstein equations etc.) and manifestation of such equations in areas of natural science where fundamental equations have not yet been guessed, thus once again confirming the well-known thesis that there is nothing as practical as a good theory.

The work has been supported by the Russian Humanitarian Research Foundation Grant No. 03-03-00040a.

1. Aristoteles. Works in 4 volumes. V.3. Physics. // M.: Nauka. 1981. (Comment 9 to Chapter 11 of Book 4.) In Russian.
2. Cuvier G. Le regne animal distribue d'apres son organisation. // Paris. 1817. (Pp. 12-13.). In French.
3. Levich A.P. Sets theory, the language of category theory and their application in theoretical biology. // M.: Moscow University Press. 1982. 190 pp. In Russian.
4. Levich A.P. Entropy as a measure of structuredness of complex systems. // In: Proceedings of the Seminar "Time, Chaos and Mathematical Problems". M.: Institute for Mathematical Studies of Complex Systems of Moscow State University. 2000. 2nd issue. Pp. 163-176. In Russian.
5. Levich A.P. and Fursova P.V. Problems and theorems of variational modelling in the ecology of communities. Fundamental and Applied Mathematics. 2002. No. 4. Pp. 1035-1045.
6. Levich A.P. Time as viriability of natural systems: ways of quantitative description of changes and creation of changes by substantial flows // In: On the Way to Understanding the Time Phenomenon: The Constructions of Time in Natural Science. Part 1. Interdisciplinary Time Studies. Singapore, New Jersey, London, Hong Kong: World Scientific. 1995. 201 pp.
7. Levich A.P. Paradigms of natural science and substantial temporology // In: The Nature on Time: Geometry, Physics and Perception. Boston, Dortrecht, London: Kluwer Academic Publishers. 2003. Pp. 427-435.
8. Newton J.S. Philosophiae Naturalis Principia Mathematica. // London. 1687.
9. On the Way to Understanding the Time Phenomenon: the Constructions of Time in Natural Science. Part 2. The "Active" Properties of Time According to N.A. Kozyrev / Ed. A.P. Levich / Singapore, New Jersey, London, Hong Kong: World Scientific. 1996. 220 pp.