Ideas and Mathematical Models about Symmetry, Dynamism, Anticipation

The antique study of geometric properties of symmetries continued by algebra with the group theory, and then with matrix calculus. The present paper illustrates new trends in the study of symmetry concept and its implication in explanation of the matter structure and of the evolutionary phenomena from nature. It is well known that in 2008 the Nobel Prize in Physics was awarded for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics. As an introduction to the necessity to study symmetryn ot for static states only, but also for dynamic systems, the paper presents the philosophical concept of the symmetry of senses in the profound matter. For the dynamical systems, the definition of the symmetry by anticipation and retardation belong to the author. Certain cases when the symmetrical evolution of two conjugate systems is broken are indicated in a mathematical model.