2.5. Base dependency of time of existence
of the object

V. I. Melnikov

In the equilibrium position of the environment and the object their states are equal and inverse , i.e. and there is no interaction between them.

Under , they are interacting

During interaction both the object and the environment change in equal amounts but with reverse signs.

When there is no interaction (equilibrium) or when there is an persistent interaction of the object and the environment without the exit of its state beyond the boundaries of the object’s existence, the object will also exist perpetually.

Any object of research by definition is a random part of the world possessing particular quantitative and qualitative characteristics contained inside the state of the object’s existence per se. Should these characteristics exist beyond the assumed object’s state boundaries, the object is transformed into the different object. In general, value of the range of existence is determined by some admissible states’ difference between its actual value and its nominal state. In accordance with the above-mentioned definition the notion of the object is to a significant extent conditional and depends on the type of task to be solved.

The equation of the object’s existence:

,

where C₀ – current state of the object, C_n – nominal state of the object, ΔC_n – possible (admissible) deviation of the object’s state within its existence limits; – range of the object’s existence.

Interaction time of the object and the environment necessary for its condition’s exit beyond the limits of existence is the time of the object’s existence.

This time can be retrieved from the differential equation of the object’s change of state when it is interacting with the environment:

(14)

where N_t – current power of interaction of the object and the environment depending on a set of factors and determined as state change value per unit of time; dtC – elementary unit of time.

After division of variables and integration we shall get

In a general case , where N₀ – initial value of interaction’s power (when t = 0); R – characteristics of a division zone (resistance to interaction value); П – nature of the object; B – type of interaction; У – interaction’s conditions.

Therefore

(15)

The above-mentioned relations can also be used in order to determine and research both objects in general and their particular indicators in particular. In the simplest physical and technical cases mass, temperature, chemical composition, energy, intensity, capacity, dimensions etc. serve as objects.

Numerous experimentally substantiated generally known and widely used calculated relations that are, per se, particular cases of relations (14) and (15) (see, e.g., Table 2, cl.3.2) are suggested for physical and technical applications in different spheres of natural science.

The research difficult biological, social, economical etc. systems’ calculation and determining of values and indicators and their parts contained in these relations is probably a matter of a distant future. It is possibly that these indicators will be elaborated on the basis of the above-mentioned methodology and corresponding experiments. The life itself though forces us to randomly formulate a great number of complicated, dubious multidimensional integral values. E.g., an integral human being’s states such as spirituality, culture, morals, health (see cl.2.8), happiness (see cl.2.7), religiousness from time immemorial, s (see cl.2.9), beauty, good and evil etc. existed and were used from time immemorial. Such an integrated approach for such objects leaves no alternative as it is quite obvious that element-based research of complicated objects and phenomena is meaningless. For example, study of moral principles of a human being on the basis of analysis of behavior of his/her elementary parts or even molecules is a preposterous and an impossible idea. Though the research of a notion of happiness using notions of value system leads to quite concrete results (cl.2.7).

Not all the objects of research are of a concrete material nature, though all of them possess their own area of origin and existence, reason and factor of development and preservation, terms and conditions and time of extinction. And, therefore, all of them can be researched and to some extent learnt in the object – environment system of coordinates.

The transformation types of these relations and concrete practical results brought for by such a general, it would even seem aimless, problem definition are given in the parts 2 and 3.