A summary to a new book which is now edited by me for publication
"Harmony of the Universe"
A new paradigm of knowledge is stated. This paradigm defines harmony as a general decree of nature, as a law of an organic Whole. The outcomes of long-term examination and facts obtained in the latest time are presented. The book consists of three large sections covering the logic, mathematical, and experimental principles of harmony.
In section "The Logic Principles of Harmony"::
1. Exact definition of harmony as paradoxical identity of opposites is stated for the first time on the basis of axiomatic construction of the theory of harmony, and also as a corollary to the relativity theory and Planck constant. The harmony in this framework has not a physical, but intrinsic sense. The given definition of harmony exposes interrelation of categories “particular” and “general”, or that of parts and whole.
2. A new kind of generalization (qualitative, or intrinsic) as a basis for mathematical laws of harmony is established for the first time.
3. It is proved that the world is harmony; the harmony is primary, and it generates the substance.
4. The newly formulated law of harmony does not contradict the known laws of natural sciences; on the contrary, it represents the essence, interior mechanism of these laws, which is demonstrated on examples.
5. The following propositions are established:
1) the laws of harmony have no physical, chemical, biological or any of other particular sense of concrete sciences. Their sense is intrinsic;
2) the laws of harmony are universal, they cannot be explained by any known (i.e. particular) laws.
6. For the first time a general law of perception - in particular, perception of new art styles and new scientific ideas - is stated.
In section "The Mathematical Principles of Harmony":
1. The mathematical sense of qualitative generalization is stated.
2. Kant and Einstein about space and time.
3. It is proved that harmony is the essence of space and time and consequently cannot be described in the space-time coordinates. So we are forced to return to an ancient Pythagorean paradigm, which sense is enriched during three-millennia development of knowledge.
4. Three numerical laws of harmony, obtained by the author, are stated. They define:
I - the qualitative (intrinsic) symmetry;
II - the violated symmetry;
III - the golden section.
The first two laws are originally formulated by the author, whereas the concept of the golden section has gained here a new diversiform content.
These laws are conceived on the basis of two mathematic principles, additivity and multiplicativity, complemented with those of symmetry and mean proportional (arithmetical, geometrical, harmonic).
Law I (the qualitative symmetry) relates to symmetry in strict modern sense; it defines a mathematical group. A general formula of transformations is derived. Deduction of new numerical series is set forth on the basis of Laws IIиIII.
The numerical laws are obtained speculatively, leaning on philosophical judgment of the problem. For this reason, their experimental confirmation is of extreme importance. The offered new paradigm of knowledge integrates the ancient (Pythagorean) and Galilean paradigms.
In section "The Experimental Principles of Harmony",
a wide panorama of new experimental facts obtained by the author is offered in support of his theory. These facts are uncommon to an extent that some of them may be qualified as discoveries. They are found out with the help of the qualitative symmetry, which suggests fundamentality and heuristicity of the latter.
Below are listed some examples:
1. For the first time, a natural acoustic scale (known in music as the pure pitch), which represents frequency ratios as musical intervals (the prime, second, third, fourth...), is deduced from laws I and II. The even-tempered scale, accepted in music, is based on the same laws.
2. For the first time, the linkage between the tempered scale and golden section is revealed (with the help of qualitative symmetry); this proves that all three laws of harmony constitute the base of the tempered scale.
3. A fundamental fact found out with the help of qualitative symmetry is stated for the first time: a musical scale (the pure pitch) is present in arrangement of elements in Mendeleev’s Table. This fact suggests the existence of a final element with number 118.
4. Harmony in the disposition of planetary orbits. For the first time are found out and demonstrated: (1) the order in disposition of planets according to Law I; (2) correspondence of the ratios of solar distances of planets to numerical series generated by Laws II and III. An amazing precision of agreement (up to 5 or 6 decimal places); (3) a mysterious fact: seven octaves are found in the disposition of planets. Let's imagine the keyboard of a grand piano. It contains seven octaves. If the Sun is located in the right extremity, Pluto will appear at the left-hand end. Other planets will occupy the octaves, the Earth and Mars will settle down in two adjoining semioctaves, approximately symmetrical to each other.
5. The harmony also is found and demonstrated in mass spectrum of fundamental particles, in biology, genetics, physics, mathematics, and other fields.
6. The harmony is shown in structure of musical compositions of Bach, Mozart, Beethoven, Skryabin, Prokofyev, Shostakovich... 85 % of the obtained numerical values belong to numerical series of the laws of harmony with an amazing exactitude of agreement.
Among the demonstrated paradoxical correspondences, there are: Mozart and genetics, Appassionata and Solar system, Mozart and universal constants (concordance of numbers amounts to 6 significant digits), and also: music, birth rate and fundamental particles, symmetry and disharmony, optical illusions and perfection of our eyes, to name but a few.
All indicated facts and numerical correspondences, including those in music, are found out by me for the first time with the help of qualitative symmetry.
There is one more part in the book, "PROBLEMS AND CONJECTURES", where the riddles of some important numbers, the problems of disharmony (incurable illnesses, environmental disorder), new energetics, and future civilization are considered in terms of the laws of harmony.
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