 Coauthors Rules: https://peacefromharmony.org/?cat=en_c&key=1224 Paragraph-1:https://peacefromharmony.org/?cat=en_c&key=1228 Paragraph-2:https://peacefromharmony.org/?cat=en_c&key=1236 Paragraph-3:https://peacefromharmony.org/?cat=en_c&key=1241 Paragraph-4: https://peacefromharmony.org/?cat=en_c&key=1242 Paragraph-5:https://peacefromharmony.org/?cat=en_c&key=1254 Paragraph-6:https://peacefromharmony.org/?cat=en_c&key=1256 -------------------------------- Peace Science Primer (PSP) Paragraph-7. Fractal structure of social spheres in the coordinate system of fourdimensional space/time Publication: In English: https://peacefromharmony.org/?cat=en_c&key=1257 In Russian: https://peacefromharmony.org/?cat=ru_c&key=1106
The growing complexity of detailing the eternal planetary spheres of social nature, obvious in the logic of our presentation, leads to the awareness of its necessary qualimetry, the adequate instrument of its measurement, in order to master the complexity of these spheres and their interconnection spheral laws. But on this path, a generalized and formal mastery of the mechanisms/methods of unification and interaction of these spheres in their structures is also necessary. The first mechanism here is the fractal method of interaction and organizational unification of the spheral structures. 1. Dynamic fractal structure of social spheres The fractal, tetradialectical nature of social spheres in their dynamics is another of their fundamental attributes that elude narrow, and therefore "blind" to the whole disciplinary thinking. The subject of spheres and their spherons, from which they produce their corresponding products, are and can be only the corresponding PIOT. Here, the immutable dynamic law of production of "like from like by means of dissimilar, additional resources" is in effect. This means that people can be produced (born and brought up) only from people with the help of appropriate additional resources. Information can be produced only from information with the help of appropriate additional resources. Organizations can be produced only from organizations with the help of appropriate additional resources. Things can be produced only from things with the help of appropriate additional resources. Resources/products of PIOT are not converted into each other, but exist and are produced only through others, including their parts in themselves according to the principle of Anaxagoras “all in all”, but in a spheral, constant version, and not in a literal, absurd sense, “all that is in all that is”. only adequate spheral components, as true, constant “homeomeries/seeds” of Anaxagoras, are included in all spheres that is presented in the model on Fig. 8. In the process of producing any product of the PIOT from any corresponding subject of the PIOT by means of all other necessary spheral resources, their qualities and properties are inevitably transferred to the final product of production, which includes them as an intermediary spheral component (property, attribute) that is illustrated by model-5. 
Fig. 8. Model-5. Interconnection of the PIOT resource-product spheres The interconnection and similarity of all other groups of social production and perpetual peace spheres are similarly illustrated. 2. Generalization of the fractal coupling method for social spheres The fractal similarity and mutual inclusion of the PIOT social spheres in a generalized dynamic format is not limited to their juxtaposition, but is their continuous vital interdependence, when each spheral element of the four cannot exist without all together as sufficient and vice versa. Here, the principle of Anaxagoras "ALL IN ALL" operates, but in spheral cross-cutting and universal variants, which are expressed as follows: "ALL IN FOUR", "FOUR IN ALL" and "FOUR IN FOUR". Their "iron mechanism" of inseparable continuous coupling on "live" of functional spheral resources of PIOT (as well as all others) in their fractal parts interdependence at all end-to-end levels is well illustrated by scheme No. 1 in Fig. 9. 
The principle of Anaxagoras in the wholeness of 16 eternal social spheres ensures their constant inseparability through the mutual penetration of their fractal structures in their single existential organization. Fractality, structural cohesion and similarity of the whole and parts is revealed in physics, mathematics and social structures by Benoit Mandelbrot, the fractal geometry creator, which we started discussing and applying in the GGHA since 2008 (https://peacefromharmony.org/?cat=en_c&key=343). This is the most complex, integral and nonlinear attribute of spheral components, ensuring the unity of all of them in synergy, i.e. in mutual reinforcement and strengthening of the viability of each and their entire structure as a whole. It constitutes their common natural source of the most effective, optimal and sustainable development, accessible only to holistic, spheral thinking, but inaccessible to fragmentary disciplinary thinking. Therefore, it remains terra incognita for thousands of years for all its modern "Godless Fake Science" according to the sarcastical, but not far from the truth definition of Mark Keenan, 2023 (https://peacefromharmony.org/?cat=en_c&key=1255). The fractal spheral structure and organization is identical for all 16 social spheres, which is used in the following paragraphs. However, scheme #1 in Fig. 9 reveals and defines the integral, fourdimensional fractality of all spheral components in their statics, abstracting from their changes dynamics. The introduction of the dynamic parameter of spheral fractals, and therefore the social spheres themselves, makes their picture holistic and at the same time extremely complex with many spheral constants and variables in the dialectic of at least two pairs of dialectical opposites: whole - parts and constants - variables. Without going into their philosophical and sociological theoretical depth, revealed in our generalizing monographs of 1999-2004 in Fig. 9, we will limit ourselves to their simplified operational presentation. Here it is necessary to emphasize one fundamentally important attribute of the tetradic dialectic of spheres (or spheral tetradialectics), which distinguishes it from the traditional, Hegelian dialectic. The spheral tetradialectics is the dialectic of “one contradiction in different relations”, preserving the formal logic laws, and therefore, the possibility of its digitalization. It is not the Hegelian dialectics of “one contradiction in the same relation”, which opposes this, the so-called “dialectical logic” to formal logic and denies it, rejecting along with it the possibility of digitalizationof the most complex dialectics of spheral contradictions. The multidimensional dialectics of formally logically consistent “different relations”, opening up the theoretical possibility of their digitalization, was developed by Moscow State University professors V.F. Asmus, the author of the textbook "Formal Logic" (1947) and I.S. Narsky, the author of numerous works on the relationship between formal and dialectical logic ("Dialectical Contradiction and the Logic of Cognition." Moscow, 1969) in the history of Western European philosophy. I had the honor to be the student of these outstanding scientists, but opposition professors during my studies in the graduate school of Moscow State University Philosophy Faculty, in 1967-1970 and after it until the end of their lives (see the special appendix with their responses to me). During my long scientific research work, I was completely convinced of the truth of their "different relations" dialectics, without which a scientific understanding of spheral thinking and its "Perpetual Peace Science" is impossible. 3. Spheral constants of statics and spheral variables of dynamics All social spheres are at the same time eternal structural constants of the society past, present and future and permanent variables in scale, content, quantity and quality in each "here and now", but in different relations. Misunderstanding of their inseparability in their earthly existence divided Plato and Aristotle. Plato proved the eternity of constants, all concepts by their divine origin, and Aristotle proved their earthly origin, in that he was right and that our realistic "Perpetual Peace Science" follows. The spheres, like any constants, laws of reality and thinking, exist only in the only way of their continuous historical change of all their parts, turning out to be a statistical crystallization and "dry residue" of the entire infinite multitude of their internal changes. The continuous changes of parts/partons of spheres is the only way of existence of spheres as eternal constants, which constitute stable, immanent boundaries, laws and structures of all their changes, i.e. their constants. Therefore, spheres are both constants as a whole and variables in parts, partons and fractals, i.e. in different, above-mentioned interconnected relationships of the whole and its parts. In our spheral macrosociology, their consideration is divided into its different parts "Statics" and "Dynamics", which was discussed above. But for their holistic, true understanding and practical use, their operational unity is necessary, which is realized in the "Perpetual Peace Science" and its Primer. The dialectical contradictoriness of spheral constants and variables lies in the fact that they are simultaneously constant (stable) and changeable, but always in different relationships and to different degrees, being inseparably interconnected. This is clearly expressed in scheme No. 2, Fig. 9, where each spheral resource of PIOT is designated simultaneously by fused uppercase and lowercase symbols, where uppercase symbols express the PIOT constancy and lowercase symbols - their variability. Figuratively speaking, the PIOT spheral constants, like others, are 90% stable and only 10% variable. At the same time, their spheral variables (parts, partons, fractals) are 10% stable and 90% variable. Of course, this measure is hypothetical, which for a real assessment requires long and professional research, which is inaccessible to the volunteer GGHA and will be available only to spheral scientific academies of the future. Such a link between spheral integral constants and their variable parts-fractals opens up a promising opportunity for their mutual and end-to-end qualimetry, measurement and mathematical calculation at all social levels from the individual and family to humanity as a whole with the help of various digital gadgets, including AI, which will be the subject of the following paragraphs. The dialectical duality "in different respects" of any planetary spheres was intuitively noticed and implicitly expressed by the ancient philosopher Heraclitus, nicknamed "the dark" for his mysterious contradictory aphorisms: "Hidden harmony is stronger than the obvious." "Secret harmony is better than the obvious." "Perfect harmony arises from diversity." "The "most beautiful harmony" arises from struggle." "There is nothing permanent except change," etc. (https://ru.citaty.net/avtory/geraklit-efesskii/). They are used and receive the following, "logically clear" interpretation in the spheral dialectics of different relations of the "Perpetual Peace Science": Hidden, secret harmony of integral eternal spheres of being is stronger and better than the transient, partial "explicit" harmony of their parts. From the diversity of an infinite number of parts, perfect and eternal harmony of integral spheres of being arises. From the temporary struggle of transient parts arises the perpetual peace most beautiful harmony of social and other spheres of being. There is nothing constant except the changes of countless parts of being integral spheres, generating the eternal constants of these spheres. Etc. Therefore, we have reason to recognize a complex of similar aphorisms of Heraclitus as the “SECOND LAW OF HERACLITUS” in the spheral thinking of the "Perpetual Peace Science" after his first law “Multiple knowledge (of parts) does not teach the mind (of the whole, of spheres)”. These laws are extremely instructive for all disciplinary “blind people” to understand the limitations and insufficiency of disciplinary thinking for the knowledge of the spheral, holistic reality of all Earth planetary natures. The unity and sufficient wholeness of all 16 social spheres with all their attributes and parameters are presented in scheme No. 3, Fig. 9, which expresses the constant spheral structure of the "Perpetual Peace Science" in all its end-to-end applications and uses, starting with an individual smartphone, which we wrote about in “Gandhica”, 2019 (pp. 78-83). But this transdisciplinary structure requires another image of integrity in the coordinates of social space and time of each of the four groups of these spheres. 4. Tetradimensional harmony and qualimetry of social spheres and their fractals Now, the spheral logic of our presentation has prepared and led to the solution of the integral question of the spheral fractals harmony measure of any PIOT social resource/product. This spheres harmony measure is generated by their objective logic of equal necessity and sufficiency of the society crosscutting spheres and constitutes the initial basis of all methods of their measurement and qualimetry. We have historically focused and limited ourselves for more than 40 years only to the universal statistical measurement and statistical qualimetry of all social spheres, all their constants and variables as the most accessible and universal method, existing since ancient times, but officially recognized about four centuries ago. Here the objective foundations of the statistical measurement of spheres and their fractals are briefly revealed. Previously, based on the ENSS social law, the PIOT eternity of four resources/products, determining all its social statics and dynamics in the integral social genome, was proven. Their objective tetradic structure objectively constitutes the tetradic way of differentiation, integration, spontaneous harmonization and organization, connection of all fractals/parts of all 16 social spheres without exception. Therefore, the objective measure of all spheral constants and variables, their organization, integration and harmonization as the most optimal general measure for them is tetrarity, or tetradimensionality. It is clearly illustrated by the tetrametric structure of all PIOT spheral fractals in scheme No. 1, Fig. 9. The PIOT tetradimensional objective structure defines society as a whole as their sum in statics: SOCIETY = P + I + O + T. The tetradimensional structure in dynamics, in the production of new PIOT products, necessarily requires and generates objective differentiation of each of them as a whole into four parts/fractals with a dimension of 4 x 41: P = P1 + P2 + P3 + P4 I = I1 + I2 + I3 + I4 O = 01 + O2 + O3 + O4 T = T1 + T2 + T3 + T4
This structure defines the fundamental law of the universal tetradimensional fractality of the PIOT resource spheres: any product from them requires a fractal complex of PIOT resources for its production, and each resource from them was also produced earlier as a product only by means of the corresponding complex of PIOT resources. We will call this law the LAW OF FOURFOLD FRACTAL RECURSION OF PIOT RESOURCES/PRODUCTS. Or, in short, this is the law of: "Fourfold Fractal Recursion" (FFR) of PIOT. It ensures an infinite similar fractalization of PIOT resources/products, their infinite multiplication and differentiation in both directions as a recursive infinite function of PIOT spheres in dynamics and their inseparable coupling/link in their historically infinite evolution. But, naturally, the recursion of PIOT spheres in practice is limited and stops at this or that step by a variety of reasons, the consideration of which we exclude due to their cumbersomeness. This law is expressed in the most elementary way by the basic matrix of fractals PIOT: 4 x 4, so it is easiest to call it "PIOT:4x4". (Note: The terminology of spheral thinking and the Perpetual Peace Science, due to its still unsettled nature, is open to further clarification and improvement.) For the production of 16 spheral components as products,a tetrametric structure of the corresponding resource fractals with a dimension of 4 x 42 is required, and so on ad infinitum according to the algorithm 4 x 4n, where ‘n’ is a series of natural numbers. This algorithm constitutes the first dimension of the social genome of humanity everywhere and always, accessible for calculation on spheral AI (further). This algorithm expresses the objective law of structuring, organization and harmonization of PIOT spheral fractals, realized in their spheral dynamics of the humanity continuous eternal production peacemaking cycle in its planetary sociogenesis. Therefore, it constitutes the objective foundation of statistical measurement and qualimetry of 16 social spheres in the "Perpetual Peace Science" (PPS), called "Spheral Global Statistics", abbreviated as GlobStat, which will be presented in the next paragraph. 5. Four groups of eternal social spheres as the coordinates of the fourdimensional space/time of perpetual peace and social production The structural analysis of the spheral dynamics, its attributes, constants and variables is finalized in the spheral coordinates system of the humanity fourdimensional social space/time for perpetual peace and social production in Fig. 10 below. This integral spheral representation of the humanity statics and dynamics of social production and perpetual peace in the structure of the fourdimensional social space and time complements their integral expression as a systemic social genome in the structural model of the PPS, presented in Fig. 1 at the Primer beginning. They are identical in content, but different in the form of presentation, complementing and deepening the understanding of the PPS spheral wholeness, its spheral thinking and knowledge. The figure below, in simplified form, was published on the cover of the book "Tetrasociology" 2002 is quite clear in itself, therefore it does not need additional comments, individual blocks of which will be detailed in the following paragraphs. The main mission of such drawings and structural models is to illustrate the unimaginable complexity of understanding human society as a whole and its perpetual peace, which is impossible without the corresponding, spheral AI (SAI); we lead our entire presentation in the Primer to understanding the need for an open structural code of this SAI. 
Fig. 10. The system of spheral coordinates of the fourdimensional space/time for perpetual peace and social production The proposed figure is a different holistic map of knowledge of the humanity social spheres for perpetual peace and social production in the system of fourdimensional social space/time compared to its first map, which expresses its 16 spheres outside the coordinates, explicated on this map. The numerous properties, details and planetary consequences from it are detailed in the books listed in Fig. 8. This completes the holistic scientific-theoretical vision of the planetary human community and its general, static and dynamic spheral laws and structures as constants of the PPS. The following paragraphs will be devoted to two main topics. Firstly, the construction of some of the main proprietary tools for mastering, using and applying the PPS, primarily its spheral statistics (GlobStat) and the Spheral Artificial Intelligence (SAI) of a planetary scale, the open theoretical code of which is presented in two PPS maps in Fig. 1 and 10. Secondly, the consideration of some of the most important solutions to the global problems of modern humanity: perpetual peace, social equality, including equality of women with men, fractal organization of social production and its management, spheral democracy, ecology and others. The paragraph text for discussion was prepared by: Leo Semashko https://peacefromharmony.org/?cat=en_c&key=253 23-03-25 --------------------------- RESPONSES Fractal structure of social spheres. Discussion on March 24. Dear peacemakers-coauthors, We are pleased to send you Paragraph-7 of our Peace Science Primer (PSP) “Fractal structure of social spheres” (6 pages) in an attachment in two languages, which is published here: https://peacefromharmony.org/?cat=ru_c&key=1106 https://peacefromharmony.org/?cat=en_c&key=1257 Its discussion and approval on March 24. With peace and love, Leo Semashko https://peacefromharmony.org/?cat=en_c&key=253 23-03-25 ----------------------------- Не профессионалу невозможно оценить достоинство сложного, специального параграфа. Очевидно, это от него и не требуется. Он, наверное, должен озадачиться одним вопросом: а что мне в нем нравится? Во-первых, я вижу упорное научное движение мысли автора к целостному пониманию мира, которое недоступно простому, разорванному мышлению людей и такой же разорванной на 75 тысяч дисциплинарной науки, как говорилось ранее. Во-вторых, я вижу и мне очень нравится столь же упорное стремление автора визуальными моделями сделать свои мысли доступными простым людям. По-моему, этих двух симпатичных стремлений достаточно, чтобы поддержать движение нашей науки мира по этому пути, которое непременно увенчается успехом. Это же не последняя попытка и редакция наших параграфов. Давайте думать и работать дальше над тем, что нам нравится и симпатично, не зацикливаясь на недоступных специальных деталях. Смысл не в них, а в конечной цели мира во всем мире на научной основе, к которому мы упорно стремимся 20 лет. С уважением, с пожеланием мира и здоровья, Вера Попович, Россия 24-03-25 --------------------
Dear Leo, I received your document and paragraph 7 looks very good! Your Rudi From the House of Mir, USA, Prof. Rudolf Siebert https://peacefromharmony.org/?cat=en_c&key=51 25-03-25 ------------------------
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