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Peace Science Primer (PSP) Covers: https://peacefromharmony.org/?cat=en_c&key=1264 Dedications and Memory Gallery: https://peacefromharmony.org/?cat=en_c&key=1265 Chapter 1: https://peacefromharmony.org/?cat=en_c&key=1266 Chapter 2: https://peacefromharmony.org/?cat=en_c&key=1268 Chapter 3: https://peacefromharmony.org/?cat=en_c&key=1272 Chapter 4: https://peacefromharmony.org/?cat=en_c&key=1273 Chapter 5: https://peacefromharmony.org/?cat=en_c&key=1274 Chapter 6: https://peacefromharmony.org/?cat=en_c&key=1275 Chapter 7: https://peacefromharmony.org/?cat=en_c&key=1278 Chapter 8: https://peacefromharmony.org/?cat=en_c&key=1279 Chapter 9: Spheral Global Statistics for Planetary Holistic Thinking and Spheral AI Publication: In English: https://peacefromharmony.org/?cat=en_c&key=1280 In Russian: https://peacefromharmony.org/?cat=ru_c&key=1130
In the previous chapter, we revealed the spheral fractal structures of planetary scale and end-to-end order as natural, the most optimal and synergistic, i.e. extremely effective couplings/links of the social nature different spheres objects. This chapter moves to their reflexive level. Such objective structures require similar, fractal methods and tools for their cognition, measurement, qualimetry and calculation in the Perpetual Peace Science (PPS) spheral thinking. First of all, it needs adequate holistic statistics, for which it creates a source and innovative platform database of a cross-cutting nature, i.e. a database of relevant, spheral indices and all innovative tools for working with it and calculations in it. In systemic unity, they create a unique, higher, "algebraic" order "Spheral Global Statistics" (Globstat) as the PPS intrinsic statistical tool for holistic spheral thinking (HST) and its spheral AI (SAI). Although traditional statistics has a number of undeniable advantages, it is initially doomed to narrowness and fragmentation by the birth trauma of the "blindness of the whole" of disciplinary thinking (DT). The fragmentations of other orders are superimposed on it: national, corporate, monetary limitations, financial closure, state secrecy, political expediency and the like, which make traditional statistics a veiled form of delusion and manipulation. In this regard, it is not without reason that they say: "There are three types of lies: lies, damned lies and statistics." Therefore, its effectiveness and capabilities are minimized. The holistic and end-to-end Globstat of the planetary scale is formed not in disciplinary, but in spheral thinking and according to the laws of holistic, and not sectoral, disciplinary logic, raising traditional statistics to the highest level of perfection, capabilities and practical efficiency available to it in the SAI new digital technology. This chapter is devoted to the overcoming of the traditional statistics vices and its elevation in synergistic complementarity with the spheral Globstat in its holistic, spheral way of thinking. The "Augean stables" of vices and limitations of traditional statistics indices, accumulated over centuries, are successfully overcome by the logic, thinking and standards of the spheral Globstat that is illustrated by the spheral indices below and in the publications. 1. Two ways of thinking: two logics and two statistics The traditional statistics (TS) is as sectoral and fragmentary as the DT, within which it emerged almost 4 centuries ago and is developing in it, absorbing all its limitations and vices, including the main one - the "blindness of the whole" of social objects, starting with an individual, a household and ending with a country and humanity. Of course, it is not useless, it has great practical significance, but it is ineffective and far from adequate. The holistic, spheral statistics (SS) does not originate from partial, sectoral indices "from below", mechanically, otherwise it would have arisen long ago, almost 4 centuries ago. It has the opposite source of generation: not from below, but from above, from a society holistic, theoretical understanding, from its spheral nature, which is planetary and end-to-end, penetrating each and every social object, without exception, as established above. But both statistics (TS and SS), as well as both ways of thinking (DT and HST), in which they arise and live are inseparably, complement each other and in integration provide a qualitatively new synergetic effect, especially important for the SAI digital technology, ensuring its superiority. Let us consider the mutual complementarity of the two statistics from the side of each of them, of which the SS turns out to be the methodologically determining and generating one. It is based on the PIOT resource spheres fractal structure, which is disclosed above and has received expression in the key, basic matrix of spheral fractals, which corresponds to the basic matrix of fractal spheral indices of size 4х41 of the following type:
P1 + P2 + P3 + P4 I1 + I2 + I3 + I4 O1 + O2 + O3 + O4 T1 + T2 + T3 + T4
on this basic matrix of spheral indices (BMSI), finite or infinite series of recursive matrices of these indices are constructed for any social object of the required dimension according to the algorithm: 4x4n, where ‘n’ is a series of natural numbers. It may be different depending on the peculiarity of the object or the practical goal, the details of which are not possible or necessary to go into now. The first machine printout of such spheral indices matrix in hundreds of matrix levels was made at the statistical design institute back in 1980, the fragment of which was published here: [https://peacefromharmony.org/?cat=en_c&key=923].
The SS began to be developed and researched more than 40 years ago, in 1980, at the statistical state institute of urban governance and planning of St. Petersburg (at that time Leningrad), a city with 5 million inhabitants. SS is reflected in hundreds of statistical spheral tables from schools and universities to dozens of countries in numerous individual and collective publications, the main ones of which are listed in the bibliography. The most important and fundamental of them is the GGHA book "Gandhica" by 82 coauthors from 25 countries, 2019, in Russian, English (https://peacefromharmony.org/?cat=en_c&key=848) and French, dedicated to the research and verification of universal spherons based on world statistics. They also include Olga Kashina's unique study of the dynamics of Russia's spherons over 50 years [https://peacefromharmony.org/?cat=ru_c&key=899]; a framework of spherical indicators of the four spheres of the SP (https://peacefromharmony.org/?cat=en_c&key=1019) and many others. Such statistical studies are unique and unprecedented in world statistics that is obviously, why they are ignored by the TS, which finds dozens of unfounded shortcomings in them to ignore them, like a fox ignores grapes it cannot reach. We will not go into the list and illustration of the SS tables, because they go beyond our Primer, are superfluous being at the level of "algebra". For a general understanding of spheral statistics, this is enough. Now we need to understand the main thing - the interaction of the two statistics and the role of each. Each of them is defined by its own necessary logic of cognition and its own necessary paradigm of thinking. TS embodies the simplest and most accessible vector of DT and empirical cognition from parts, details to the general and the whole in inductive logic, the generalization in which does not rise above large, but sectoral fragments of social reality. SS implements the most complex and least accessible vector of theoretical knowledge from the whole to its fundamental parts – spheres/holons that constitute it and to their components in the deductive logic of the spheral “substantially new way of thinking” according to Einstein, the substantiality of which is precisely its spheral, transdisciplinary integrity. Its complexity and difficulty lies in the scientific knowledge of the social whole as a system of 16 constant spheres in the system of four eternal spheral coordinates of social space and time. The two named opposite logics of cognition determine two fundamental, but complementary vectors of their interaction. TS fills logical/theoretical spheral indices-constants with empirical, variable and real content. SS in turn, classifies, compresses, orders and focuses the chaotic space of empirical indices in the matrices of spheral, constants indices. The merit of each of them is formed in the context and content of its own logic and paradigm of thinking, but always in complementarity with the other. The TS main advantage is its connection with reality. TS is formed and lives in the empirical logic of cognition in the DT partial paradigm. The SS main advantage is its penetration into the eternal, fundamental and deepest, invisible laws and structures of the humanity social nature, all its changes, ensuring its eternal life, survival and stability throughout its history from beginning to end. The SS advantage is formed and lives in the theoretical, spheral logic of cognition and in the paradigm of holistic spherical thinking (HST), including at the level of intuition and guesses of brilliant thinkers throughout history, until it becomes a well-known and accessible innovative heritage of humanity in all schools. Many of these thinkers are considered in our Primer, and their achievements are integrated into its PPS. The SS emergence more than 40 years ago and the first steps of the main mechanism of its interaction with the TS in the algorithms of composition and decomposition (aggregation and disaggregation) of the indicators of two statistics are considered in more detail in the aforementioned 1992 book “The Spheral Approach”. So we do not touch on their here, and the examples illustrating them are shown below. 2. Matrices of spheral statistics indices The SS is statistics of the PIOT spheral resources indices, through which the statistics of the PDEC spheral processes, the SP SIOT spheres and the SIOT spherons employed in them are expressed. The spherons (P) statistics is the SS center, determining the peripheral, infrastructural spheral statistics. The SS is built on the PIOT spheral indices system, which generalize, organize and complement the TS indices system, which still remains torn and fragmented in many respects discussed above. The SS matrices system built on alphanumeric indicators of the PIOT resources, called spheral indices. All indices matrices, derived from the basic 4x4n matrix, are called spheral matrices, which form the SS, fundamentally different from the TS statistics, but connected with it. All TS indices are integrated into spheral indices, classified by it in spheral logic and ordered in the sociocybernetic system of the structural social genome. The spheral matrix rows express the product outputs of the corresponding spheres of PIOT production, and the columns express the resource inputs of the corresponding spheres of PIOT production using them as resources. The dual, constant-variable, integral-fractal nature of the social spheral object is expressed in the binary, alphanumeric designation of these resources and the corresponding spheral indices. In their structure, the letter part expresses their constancy, integrity, and the digital part expresses their fractal variability and changeability. The entire infinite series of spheral matrices based on the base matrix is constructed according to one algorithm: each row of any matrix is transformed into a column of the underlying matrix, and each row indices appears in the underlying matrix as the sum of four indices expressing a set of resources necessary and sufficient for its reproduction. This generating algorithm expresses the principle of "all spheres of PIOT in all spheres of PIOT" (Fig.12, Ch.7). It makes spheral matrices, their rows and columns similar and nested fractals, which are adequate and reflect real spheral fractals, which were considered in the previous chapter. The mathematical concept of Mandelbrot's fractals expresses not only the fractals of social reality, but also the fractals of their spheral matrices of statistical indices in his following definition: "A fractal is a structure consisting of parts that are in some sense similar to the whole" (Mandelbrot, 1982). The new mathematics of spheral fractals and the knowledge of the "fractal nature of society", to paraphrase Mandelbrot, begin with the spheral indices matrices. This mathematics constitutes a necessary attribute of the HST as a "substantially new [holistic, spheral] manner of thinking" (Einstein) and determines the key, qualimetric attribute of the SAI superiority. The system of spheral/fractal matrices creates a single logical and network statistical space of humanity, a global digital language of spheral indices in spheral matrices that is its fundamental advantage, which is embodied in the SAI superiority. This digital language becomes a common denominator of traditional indicators, overcoming their innate, national fragmentation, confrontation and disharmony. It systematizes, integrates and opens the way to a digital planetary economy, a digital global perpetual peace through a conscious and mathematically balanced prevention of all wars and a nonviolent resolution of all conflicts by means of the SAI. The spheral indices aggregate indices of traditional statistics and are disaggregated in them in reverse using a special digital “Spheral Information Statistical Technology” (SIST). We will not touch on it here because of its “algebraic” complexity, which goes beyond our Primer. [See: Semashko, 2018; 5; 6; 6a-d; https://peacefromharmony.org/?cat=en_c&key=1138 and others]. Network and end-to-end spheral statistics create the best qualimetric and digital information language for calculating planetary social reality through SAI, preventing any possibility of violence/conflict "at the root" within each spheron. 3. The spheral indices measurement units and monetary unit problems The spheral indices measurement units can be generalized natural units or their value/monetary, time and energy units. This is an extremely complex issue, which the GGHA touched upon theoretically several times (https://peacefromharmony.org/?cat=en_c&key=1109), but refused to study them because it is not available at its volunteer level and requires top-class professionals. SS is limited to natural units for spherons (people) and value, monetary units for other spheres of products/resources. But the value unit in the DT also turns out to be torn by national currencies, and the so-called "reserve" currency discredits itself in many respects and is also inadequate as the measurement single monetary unit, but is used due to the lack of a better, adequate and fair one. The GGHA tried back in 2009, in the book “Harmonious Civilization” (pp. 122-129: https://peacefromharmony.org/?cat=en_c&key=390) to create a project of an alternative reserve currency “HARMON” on spheral grounds, but it was postponed for the future. See also here (https://peacefromharmony.org/?cat=en_c&key=1109). Recently, we have discovered a monetary theory of the famous Spanish financier, Professor Pedro Gomez: The Interest Pattern. In search of the lost monetary anchor. April 2025 (https://peacefromharmony.org/?cat=en_c&key=1276). This theory shows how to maintain an “exact amount of money to print so that money maintains a stable value, does not generate inflation and does not desynchronize the four fundamental variables (4FV)”, but in a slightly different terminology: capital goods (Things), public goods (Information), monetary mass (Organization), human resources (People). This theory offers a solution to the problem of the "optimal amount of money in circulation", which remained unsolvable for five hundred years. This theory serves to ensure "the four fundamental variables of the economy (4FV pág.7) evolve proportionally because the healthiest economies are not those that grow the most but those that best harmonize the growth." Here, in essence, a global spheral monetary law is formulated, ensuring the SP spheres harmonization, and therefore defining the harmonizing function of the monetary unit, an alternative to its disharmonious role in the SP modern economy as a whole. This is a great – world spheral discovery in the planetary monetary theory within the HST! Along with this theory, there is hope for a similar global value unit in the SS and in the SAI. But it is the future question. 4. Tables of spheral statistics: examples We cannot and will not load this paragraph, in accordance with our synopsis format, with hundreds of statistical tables of spheral indices of various scales, created over more than four decades, many of which are published in thousands of our sources. We will limit ourselves to only a few of the most important examples of spheral indices. The first is the spherons spheral indices classifier in Fig. 16, the constant end-to-end structure of which is illustrated in Fig. 10 of chapter 6. 
Fig. 16. Spheron indices classifier A total of 8 spheral indices are presented in the table, of which 5 are basic (in red), and 3 are intermediate, calculated (in green), they are auxiliary for the transition from traditional indices of national statistics to spheral indices. It is necessary to emphasize the special, fundamental importance of spheron statistics, which lies in the fact that it expresses their quantitative measure and dynamics as genetic, fundamental sources and bases of nonviolence by their nature, as eternal actors of perpetual peace: spherons are objectively (spontaneously and stochastically) aimed at perpetual peace and mutual survival, excluding their mutual destruction. Wars/violence of their transient parts (partons) occur only due to the conscious hostility of these partons, according to private attributes of power, property, greed, superiority and similar subjective passions and in no other way without any fundamental grounds. The spherons measure by any attributes can change in a wide range of their statistical equilibrium and structural harmony, which makes their perpetual peace dynamic, passing through a number of stages calculated by spheral statistics. Their partons are capable of generating various social disharmonies, failures, crises, pathologies, local conflicts and wars. But they are never able to overcome the immanent harmony and nonviolence of spherons as a whole that is the only way of being of spherons, guaranteeing perpetual peace to humanity. The spherons are communicating structural demographic vessels of a swarm nature: a decrease in the number of one leads to an increase in the number of others and vice versa. For example, the technosphere robotization, reducing the number of its spheron, ensures an increase in the immaterial spherons number. The infospheron growth engaged in digitalization reduces the number of other spherons in their least qualified parts. This is the general trend of employment of the present and future, reflected by SS. Therefore, the spherons number statistics within the dynamics of their structural harmony is statistics of genetic survival, perpetual peace and sustainable development of humanity as a whole, and every nation. No other, sectoral or national statistics have such fundamental, holistic and planetary significance. The spherons classifier is expanded and detailed in the following table of their branch decomposition in traditional indices of their employment in Fig. 17. 
Fig. 17. Decomposition of spheron indices in traditional indices of their branch employment,
in natural units of number for a certain year The presented tables of spheron indices are analyzed in detail and varied in the GGHA above-mentioned works, especially in "Gandhica", 2019. The spheron statistics is only the fourth, but the most important and complex part of spheral statistics, with which it begins. Its other parts, concerning other resources, are formed in the corresponding statistical studies. Spheron statistics is the defining and goal-setting part of Globstat in accordance with the generative role/function of spherons as the only social actors. This is only the fourth part of Globstat, which is supplemented by statistics of other necessary and sufficient resource clusters: information (I), organization (O) and things (T) (all material goods and services). 5. The spheral thinking and statistics advantages, predetermining the planetary SAI superiority The deep, developed over millions of years, spheral integral structures, laws and constants of social nature are the most perfect, effective and productive of all possible and known on Earth. The evolution of the human mind goes to them very slowly, approaches with difficulty, with long stops and mistakes, learning from them and gradually improving its thinking in increasing the level of its generalization and integrity. Not knowing another, higher level, a human easily falls into, even constantly finds himself in a historically error of recognizing the achieved level of knowledge and thinking as a ceiling, above which he does not want and is not able to recognize anything else. Most likely, it is precisely this kind of absolutization of one's limited, disciplinary thinking, which originated at the mythological level approximately 10 thousand years ago, that explains the humanity existence and prosperity of bloody wars. The further, the more and more dangerous, having reached today, in the West nuclear civilization, in 80 years, the full maximum of 100% possibility and close to it probability of nuclear genocide in "Mutual Assured Destruction" (MАD) according to the conclusion of the "Doomsday" nuclear scientists (https://peacefromharmony.org/?cat=en_c&key=924). (See Chapter 2 in more details). All the above-disclosed superiorities of spheral thinking, its PPS and its Globstat predetermine of their spheral AI (SAI) superiority, which are summarized in the next, final chapter. We will not talk about the natural, expected resistance to these "crazy" conclusions and "insane" ideas that violate the "genocidal-suicidal comfort" of nuclear civilization for all 80 years. New, true ideas of spheral thinking, based on insurmountable historical facts (we named only 12 of them), verified by world statistics and the practice of each individual and humanity are also insurmountable. It is only a matter of time, only of national susceptibility to innovations of a fundamental order and level of entrepreneurship of business and government. The smartest and bravest will secure world leadership. Today, the planetary scale of the humanity civilizationally prepared nuclear catastrophe for 80 years requires an equally planetary, scientifically conscious, acceptable and accessible to all peoples holistic spheral thinking (HST). only it is able to overcome the dominant DT "blindness of the whole", (which created 100% reality of this catastrophe, through and by the HST highest cognitive instrument of SAI. The SAI, through the highest intensity of global competition in the AI field, with its attributes of cognitive and technological superiority, may well become in the near future that planetary Archimedes' lever, which will be able to "shift the arms race into a peace race" according to the wise prediction of M.L. King. From the spark of spheral thinking and the SAI, its flame will inevitably flare up, most likely in the synergetic symbiosis of the President Donald Trump’s "Common Sense Revolution" and the President Vladimir Putin’s "Multipolar World Order" organically complementing each other within the framework of the PPS planetary and end-to-end spheral thinking with its SAI. We move on to considering the key attributes of the SAI superiority as a fundamental and integral cognitive tool of humanity and each planetary citizen in the next, final chapter. The chapter text for discussion and editing was prepared by: Leo Semashko https://peacefromharmony.org/?cat=en_c&key=253 05-07-25 ---------------------------
Chapter 9. Spheral Global Statistics forSAI Dear peacemakers-coauthors, We are happy to send for your consideration Chapter 9, "Spheral Global Statistics for Planetary Holistic Thinking and Spheral AI", 7 pages. It is published in 2 languages on our website here: In Russian: https://peacefromharmony.org/?cat=ru_c&key=1130 In English: https://peacefromharmony.org/?cat=en_c&key=1280 And in the attachment. With peace and love, LeoSemashko 05-07-25 ----------------------------
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