
Dr. Leo Semashko Mathematics of Harmony and Global Harmonious Social Revolution very early 21^{st} Dear Harmony Creators! Let me to state opinion on ingenious Prof. Alexey Stakhov’s article (http://www.mi.sanu.ac.yu/vismath/sg/stakhov2008/index.htm) devoted to mathematics of harmony, which he kindly sent to us as the new coauthor of the World Harmony/Peace Academy (WHPA) project: http://www.peacefromharmony.org/?cat=en_c&key=277. About Prof. Stakhov look in more details at: http://www.peacefromharmony.org/?cat=en_c&key=330. As humanitarist, I never thought and did not suspect that mathematics is imperfect and requires the basic additions. I thought, that it is exception from Heisenberg’s principle of subsidiarity. Alexey Stakhov excellent proved and imperfection of mathematics, and necessity of its addition. He shown development of qualitatively new mathematics: mathematics of harmony by almost 40 years experience. He entered his experience in a history of mathematics, which began 2500 back by Pythagoras, Plato and Euclid. He ensured to mathematics of harmony the historical basis. He ensured also scientific basis, having illustrated, that all nature is subordinated to harmony laws, hence, requires mathematics of harmony, for which the traditional analytical mathematics is only special case. Mathematics of harmony is mathematics of the future, it is mathematics of the mature, instead of initial, stage of natural sciences and society. This mathematics opens an exit to the new kinds of energy which is qualitatively distinct from mechanical, electromagnetic and nuclear. It opens exit to the new information technologies. Therefore it opens exit to the new, harmonious, worldview, to new, harmonious, ways of social production and to new, harmonious, markets ensuring prosperity for all nations. Prof. Alexey Stakhov’s mathematics of harmony is revolution not only in mathematics, but also in natural sciences. Therefore I count, that his discovery and contribution deserve top world recognition, including Nobel Prize. I shall recommend to our Harmony Association to put forward his works on mathematics of harmony on this Prize of the next year. Participation of such outstanding scientist as Professor Stakhov in our World Harmony/Peace Academy, in which the Mathematics of Harmony Department will be created by one of first, considerably raises scientific and economic value of this Academy and its appeal for world community. Harmony Academy and mathematics of harmony mutually supplement, strengthen and enrich each other. They promote a mutual recognition and development. The Harmony Academy based on social harmony of four spheres of society and the human, unfolded in tetrasociology, expands a range of mathematics of harmony on area of social sciences, which are not covered yet by this mathematics. on the other hand, created by me in 1982 the infinite, appropriate to Prof. Edward Soroko’s law of structural harmony (1984), hierarchical system of sphere matrixes (matrixes of the sphere statistical indices), for opening and accounts of harmonious proportions of social spheres, finds in mathematics of harmony ADEQUATE mathematics. Therefore sphere social harmony and mathematics of harmony mutually strengthen each other, releasing each other from the appropriate lacunas or restrictions. The most important and surprising consists that mathematics of harmony completes a picture of the GLOBAL HARMONIOUS REVOLUTION of a beginning of the XXI century, which launch a HARMONIOUS INFORMATION CIVILIZATION in history of humankind. It is the HARMONIOUS SOCIAL REVOLUTION! The Harmonious Social Revolution (HSR) of a beginning of the 21^{st} century includes, at least, eight harmonious revolutions of knowledge and social life:
1.Mathematics of harmony unfolding a way for natural sciences harmony, 2.Laws of a deep (sphere) structure of social harmony unfolding a way for sociology of harmony or tetrasociology, 3.Harmonious peace culture (Prof. Ada Aharoni, 2000, and others) as revolution of traditional, military, peace culture, 4.Information international site and community "Peace from Harmony" (2005) as revolution in the communications, 5.Chinese transition from dictatorship of the proletariat to construction of a harmonious society (2006) as revolution in state policy, 6.Harmonious Era Calendar (2006) as revolution in chronology and in estimation of historical events, 7.Magna Carta of Harmony (2007) as revolution of worldview and vision of life, 8.World Harmony/Peace Academy (2008) as revolution in general (global) education. Certainly, the number of similar revolutions will grow continuously in this century. Now all these eight revolutions consciously are united by Global Harmony Association and WHPA. Similar comprehension and union are first in the world. They make HSR by the powerful scientific and social tendency. on place of the industrial scientific and technological revolution (STR) limited by the separate branches of natural sciences and engineering come the harmonious social revolution, covering all social spheres. Certainly, this revolution keeps the STR’s achievements but gives them a new, harmonious, social quality. As an industrial society evolves in an information society so and the STR evolves in the HSR, which opens the unprecedented prospects of harmonious development and knowledge (opening new energy, explanation of the paranormal phenomena etc.), and culture (harmony of science and religion, harmony of "two cultures", harmonious peace culture etc.), and society (harmonious state, technologies, production, markets, world order etc.), and separate human. The HSR achievements will allow each schoolboy from 1012 years to calculate the harmonious ways of development not only any state, city, enterprise, family but also harmonious development of his consciousness (mind and heart), body, will and character (spirit) at different stages of life and under different conditions. The World Academies and local schools of general harmonious education will ensure with necessary knowledge, technologies and skills each child on the Earth. They will exclude wars, violence and hunger. They will ensure the common good of the global harmonious peace, prosperity and sustainable development. Such I see a picture of consequences from synthesis of mathematics of harmony and sociology of harmony. To this synthesis the different scientists and different societies go independently from each other, that expresses general tendency of humankind to harmony, to its embodiment in a harmonious civilization. The greatest contribution to this synthesis is Professor Stakhov’s mathematics of harmony. Dr. Leo Semashko, President, Global Harmony Association, Founder of TetraSociology as the first science about social harmony 08/07/08 
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