No 1 (2022)

The article shows that when constructing a relational picture of the world based on binary pre-geometry, the principles of metaphysics play a key role. In particular, they manifest themselves in the metaphysical roles of integers. First of all, this refers to the numbers 2 and 3. The charges of elementary particles, their distributions by types, the values of their masses of hadrons and their other properties are determined through integers. Moreover, the discovered properties of hadron states determine the properties of atomic nuclei and the structure of the periodic table. It is noted that binary pregeometry is an approach to the description of physical reality, alternative to the currently generally accepted one within the framework of the field theory paradigm.

The basis of mathematics is set theory, to which almost all mathematical directions go back. However, the importance of category theory for mathematics as a whole is steadily increasing. If in set theory the determining role is played by the internal structure of the object under consideration, then in category theory an object is characterized by its connections with other objects. The article discusses the features of set-theoretic and category-theoretic approaches in mathematics.

The article shows that the model of the trinity principle in the holism methodology allows us to resolve the well-known contradiction of statistical mechanics and become a model for the development of an open system. We have described the open system by three functions of the distribution of coordinates, impulses and structure, that there is a previously unknown interaction between them, which leads to the excitation of new structural events. The model contains a three-essential invariant, an equation of symmetry of measures of chaos and order, and a recurrent equation describing accelerated development along three golden spirals.

Main points of the Einstein program for creating the consistent field formulation of particle physics are discussed. The basis of this program includes the representation of particles as clots of some material field satisfying nonlinear equations. It is shown how the stability criterion implies the characteristic features of the corresponding field model.

Mathematical cosmology is that branch of theoretical physics where some of the most intricate, complex, and deeply unresolved issues lie. Beginning with the Einstein static universe in 1917, in this brief paper we freely float above all major developments that shaped the field until today. We discuss highlights that are further documented in the authors’ recent survey ‘100 years of mathematical cosmology’ scheduled to appear in the Theme Issue ‘The Future of Mathematical Cosmology’. This Theme Issue is to be published in two parts by the Philosophical Transactions of the Royal Society A, and contain a number of important contributions by key researchers in the field.

A brief review of publications devoted to oscillatory phenomena in the solar system is given. Periods equal to or less than a daily one are considered. Possible resonant connections between different periods are analyzed in connection with the concept of A.M. Molchanov about the “maximum resonance” of the solar system.

The mass reaction of the ground-based complex systems (i. e. the ones with an internal structure that can stay in different inner states) (1) to total solar eclipse and (2) to Sun shielding by a tower located in the neighborhood of the observation is invited to consider. This reaction has revealed the basic factor of observed natural dynamics of mass - the Sun. These observations data were collected by a special geophysical monitoring which every ten seconds synchronously records mass of some definite geological systems (minerals/mineral aggregates), atmospheric electric field strength, and six physical characteristics of the observation conditions at three geographical points: Dubna, Nauchny (the Crimea), and Novosibirsk. Due to significance for modern experiments and technologies, a physical phenomenon associated with the role of the Sun in the mass dynamics is briefly discussed in conclusion.