Truth is always born as heresy,
and dies as prejudice

Georg Wilhelm Friedrich Hegel

The purpose of the journal

Our goal is to provide scientists in Russia and around the world with modern ideas on existing interdisciplinary areas and, first of all, on the theory of complex systems in the era of knowledge synthesis.

Current issue

№1 (7) 2020


The evolution of the Earth’s rotational movement for millions years

Smulsky J. J.

There are the main points of the derivation of the differential equations of the Earth’s rotational motion. The periods of oscillation of the Earth’s axis are grounded by the angular momentum theorem. The constants of the equations, the initial conditions, and the theory of their computations are discussed. The results of integrating the equations over time intervals from 0.1 year to 1 million years are considered. The theory of solutions transformation to the mobile plane of the Earth’s orbit is considered for millions of years, and the solution results are presented at different time intervals from 100 years to 20 million years. The evolution of the Earth’s axis is analyzed. It is established that the Earth’s axis precesses with respect to a fixed direction in space, which differs from the direction of the precession of planetary orbits. Physical explanations of the received oscillations of the Earth’s axis from 14.68° to 32.68° are given. The oscillations of the Earth’s rotation period are shown. Evidence of the reliability of the solutions obtained is presented. The work is of interest to a wide range of researchers in the fields of astronomy, paleoclimate and geophysics.

Key words: differential equations, Earth rotation, precession, oscillations, evolution, periods, causes, Moon, Sun, planets.


Splitting of allowed states in a complex self-organized system. Part 3

Smirnov V. L.

The self-organizing system’s approaching evolutionary maturity is considered, which allows us to explain the characteristics of their orbits for the four planets of the solar system. The system does not possess any specifics of natural objects and is treated as part of a structure that has boundaries. The structure, in its turn, is represented as a set of relations on the numerical axis and is understood as a network of nodes (the allowed states) and relations between them. The system is formed on the basis of the deployment of a proto-structure, a two-component cyclically organized system of relations, which is treated as primary and is intended for a phased study of the evolution of natural systems. Evolution is understood as a deployment from stage to stage, taking into account the background. The proto-structure defines the spectrum of allowed states for n — the order parameter of the system, which subordinates two relative characteristics. As a result of the interaction, the elements of the specified spectrum are split into components and specialize.

Here the feed data are the insights resulting from the analysis of the previous evolution stage, where the splitting of ten n-nodes within one isolated proto-structure cycle is considered. We study four n-nodes, which, as a result of detailing, are represented using approximately 50 positions interacting on the numerical axis. These positions are placed at three levels of the hierarchy: the level of positions n, as well as their splits — the level of shifts n relative to the initial positions — the level of small changes. Inter-level connections and the level of shifts are considered in detail, the basis of which are the invariants formed at the previous stage of evolution. An analysis of structural scenarios indicates the key role of shifts at the last stage of evolution.

When applied, each element of the spectrum n is interpreted as the relative moment of momentum in the solar system, when it comes to circular motion. Otherwise, any element of the spectrum is split into components, each of them responsible for the distance it is in charge of. The evolutionary maturity of planetary distances and periods of revolution for Jupiter, Saturn, Uranus, and Neptune is discussed. The stability criterion of the final positions n is considered.

On average, the model positions of perihelion, aphelion, major and minor semi-axes correspond to the observed distances within 5*10-5%. For the first time from structural positions, it is shown why the orbits of the planets differ so little from circular ones. Model circulation periods on average correspond to those observed within 5*10-2%.

Key words: evolution, structure, evolution maturity, order parameter, planet orbits, planet orbital periods.


Humanity as a system. Part 1

Torvich V. V.

For an in-depth understanding of the processes underlying the development of mankind as a whole, an approach is proposed in which the opportunities for actions of people and humanity are included in the consideration. The social structures, as well as the impact of mankind on the environment, are excluded from consideration. In the works known to me, this approach is practically absent. The purpose of this study is to develop criteria for the search for components or groups of components of such a system and identify their list. The other purpose is to consider the dynamics of development over time of a system consisting of these groups of components. The search criteria for components or groups of components that may constitute such a system are described. The list of groups of components is given, which, in particular, includes “Man-made materials”, “Mass transport”, etc. The totality of groups of components determines the range of opportunities for the actions of people and humanity as a whole. An analysis was made of the change in time of the proposed set of groups of components. It has been established that the range of these opportunities expands over time and that this expansion is realized with acceleration.

During the search per proposed criteria information was used from various areas of knowledge. Those areas are associated with the development of technologies, means of communication, social activity, globalization, and cognitive abilities.

Key words: complex systems, humankind, history of mankind, opportunities for human actions, development.