Читать книгу Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science - Alexey Stakhov - Страница 19

V.P. Shestakov, the author of the book Harmony as an Aesthetic Category [10], notes the following:

“In the history of aesthetic teachings, various types of understanding of harmony were put forward. The very concept of “harmony” was used extremely broadly and multivalently. It denoted both the natural structure of Nature and the Cosmos, and the beauty of the physical and moral world of man and the principles of the structure of the work of art, and the laws of aesthetic perception.”

Shestakov singles out three basic understandings of Harmony that evolved in the process of development of science and aesthetics:

(1) Mathematical understanding of Harmony or mathematical Harmony. In this sense, harmony is understood as the equality or proportionality of the parts with each other and the part with the whole. In the Great Soviet Encyclopedia, we find the following definition of Harmony, which expresses the mathematical understanding of harmony:

“Harmony is the proportionality of parts and the whole, the fusion of various components of an object into a single organic whole. Harmony is the outer revealing of inner order and the measure of existence.”

(2) Aesthetic harmony. Unlike the mathematical understanding, the aesthetic understanding is no longer just quantitative, but qualitative, expressing the inner nature of things. The aesthetic Harmony is associated with aesthetic experiences, with aesthetic evaluation. This type of harmony is most clearly manifested in the perception of the beauty of Nature.

(3) Artistic harmony. This type of Harmony is associated with art. The artistic Harmony is the actualization of the principle of Harmony in the material of art itself.

The most important aspect that follows from the above reasonings is the following: Harmony is a universal concept that has relation not only to mathematics and science but also to fine arts.