In this article the development of numerical method of qualitative analysis is continued within the borders of the theory of quantity-to-quality transitions. Philosophical criteria of objectivity of scientific theories are considered.

          In this work for the first time a mathematical analogue of the definition of "harmony" is developed using a numerical method of qualitative analysis and its specification is given, on the base of which the notion of "beauty" is formulated.

          On the base of the discovered law of bipolarity mathematically formalized relationships between component parts of a whole are determined, which depend on the type of evolution of the object's state - differential evolution or integral evolution.

          The numerical values of the coefficients of harmony are derived. As a result of this research, the reason of existence of such a global phenomenon of our world as the symmetry is established and its connection with the law of bipolarity is proved.

          An interval of invariance of a qualitative state of an object in relation to changes in its quantitative parameters is discovered.

          The borders of applicability of Newton mechanics to description of the world are determined; the reasons for the unique properties of the water molecule related to its unique structure as a "whole" are explained; the rationale for the ability to control nuclear fusion is given; the maximum possible number of points of attraction (strange attractors) for an arbitrary system is calculated; relativity of the upper border of D. I. Mendeleev’s periodical system of chemical elements is determined and objective necessity of transition to Mendeleev-Idlis' physicochemical table that would reflect the evolution of matter in the Universe is explained; the reason of appearance of magical numbers in the shell model of atomic nucleus is identified and the formula for the computation of the appropriate series of numbers is given.

          The work lays the methodological basis for linking the entirety of objects, events and phenomena of the world, based on different types of interactions, into a single whole. This paves the way for creation of an analytical synthesis theory of the Universe that would have no fundamental limitations in objective cognition of the entire totality of natural phenomena including those that cannot be currently explained by modern scientific methods of cognition of the world.

​

​