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

Paragraph-7: https://peacefromharmony.org/?cat=en_c&key=1257

--------------------------------

Peace Science Primer (PSP)

Paragraph-8/1. (Update: 16-04-25)

Spheral Global Statistics for Spheral Holistic Thinking

and Planetary AI

Publication:

In English: https://peacefromharmony.org/?cat=en_c&key=1258

In Russian: https://peacefromharmony.org/?cat=ru_c&key=1107

In the previous paragraph, we revealed the spheral fractal structures of planetary scale and end-to end order as natural, the most optimal and synergistic couplings of objects of social nature. Such objective structures require similar fractal methods for their cognition, measurement, and calculation in the Perpetual Peace Science (PPS) spheral thinking. This necessitates holistic statistics as a platform for planetary use. This platform is spheral global statistics (GlobStat), the PPS's fundamental tool for spheral thinking and its spheral AI (SAI).

Although traditional disciplinary statistics includes some elementary global indices, such as Earth's population and other social objects constituting its noosphere according to Vernadsky, these merely record external, mechanistic relationships and aggregates. They exclude the possibility of comprehending the immanent fractal connection within social objects' spherical integrity—inaccessible to them and unknown in mutual cause-and-effect relationships: inaccessible because unknown and unknown because inaccessible, like an elephant to blind men. Mechanistic statistics, blind to the whole by definition, can o­nly record fragments torn from the holistic social reality.

This blindness is compounded by national, corporate, financial, and political fragmentations, which render traditional statistics vulnerable to manipulation. As they say, "There are three types of lies: lies, impudent lies, and statistics." The holistic GlobStat is formed through spheral thinking according to laws of spheral logic, elevating traditional statistics to a higher level of effectiveness. This paragraph addresses how spheral GlobStat overcomes traditional statistics' limitations through innovative thinking and its SAI.

1. The Origin and Generation of Spheral GlobStat

The traditional statistics is as fragmentary as the disciplinary thinking within which it emerged nearly four centuries ago. The fractal/spheral, holistic statistics (GlobStat) does not originate from partial indices "from below"—otherwise, it would have emerged long ago. Instead, GlobStat has the opposite source of generation: from above, from a holistic theoretical understanding of the corresponding structural models of society's spheral nature, which is planetary and penetrates every social object without exception.

Spheral GlobStat is generated and created in accordance with the universal spheral law that requires four PIOT resources (People, Information, Organization, Things) for the production of EVERY product across their entire set from the smallest to the planetary scale. This fundamental division is expressed by the matrix formula: 4 × 4ⁿ. Each larger component (metaphorically, a "brick") is divided sequentially into four parts, each designated as the corresponding spheral indicator of PIOT resources.

This fractal structure of PIOT resources creates and defines the GlobStat fractal matrix system of spheral indices. The designations of these matrices of fractal parts create the entire abstract, theoretical set of spheral indices in the alphanumeric indexing of PIOT. Then, they are filled with specific empirical content by aggregating corresponding traditional indices, as demonstrated in the spheron classifier below.

These two statistics, traditional and spheral statistics, are inseparable and complement each other. Their integration provides a qualitatively new synergetic effect. Spheral statistics is based o­n the fractal structure of PIOT resource spheres coupling, expressed by the key, basic matrix of spheral indices sized 4 × 4. The basic matrix of spheral indices (4 × 4¹) has the form:

P1 + P2 + P3 + P4

I1 + I2 + I3 + I4

O1 + O2 + O3 + O4

T1 + T2 + T3 + T4

On this basic matrix, finite or infinite series of recursive matrices are constructed for any social object according to the algorithm: 4 × 4ⁿ, where 'n' is a series of natural numbers. This may vary depending on the object's peculiarity or practical goal. A machine printout of such matrices was produced at the statistical design institute in 1980, with a fragment published at: https://peacefromharmony.org/?cat=ru_c&key=824.

Spheral statistics began development over 40 years ago at the statistical state institute of urban governance in St. Petersburg, and has been reflected in hundreds of publications. The most fundamental is the GGHA book "Gandhica" by 82 coauthors from 25 countries (2019), dedicated to verifying universal spherons based o­n world statistics (https://peacefromharmony.org/?cat=ru_c&key=788).

2. Two Ways of Thinking: Two Logics and Two Statistics

In spheral statistics methodology, two complementary types of statistics are distinguished: traditional and spheral. Each is defined by its own logic of cognition and paradigm of thinking. Traditional statistics (TS) embodies disciplinary thinking and empirical cognition, moving from parts to the whole through the logic of inductive generalization. Its generalization doesn't rise above visible segments of social reality. Its main merit is its connection with reality, historical context, and all their features in the most diverse parts of humanity's social nature.

Spheral statistics (SS) implements theoretical cognition from the whole to its fundamental parts in deductive logic of the social nature spheres, determining a holistic way of thinking through identifying and generalizing these nature constant spheres.

This cognitive process's functional complexity and unusualness lie in the theoretical discovery of the social whole as a system of 16 constant spheres in four spheral coordinates of social space-time, presented in Fig. 10 of the previous paragraph. The main advantage of spheral thinking and its SS is penetration into the eternal fundamental macrosociological structures and the o­nly possibility of their systemic qualimetric expression. It ensures conscious regulation of stability, balance, proportion and harmony of the fundamental, cross-cutting spheres of humanity o­n a planetary scale.

These opposite logics determine two complementary vectors of interaction:

- TS fills theoretical spheral indices-constants with empirical, variable content.

- SS classifies, compresses, and orders the space of variables' empirical indices in matrices of spheral constants. In the methodological sense of their interaction, SS functions as a metalanguage for the TS object-subject language.

The SS emerged over 40 years ago as statistics of the spheral resources PIOT, through which the statistics of their production processes PDEC, spheres SIOT, and spherons SIOT are expressed. Their system of spheral indices matrices creates a single logical statistical space — a global digital language of spheral qualimetry, which is its fundamental advantage. Its indices generalize, complement, classify, and integrate all traditional indices in the spheral logic of a single process of their counter, inseparable interaction within the framework of a special “Spheral Information and Statistical Technology” (SIST).

Given the extreme complexity and operational specificity of these counter-processes of empirical and theoretical interaction, which have been considered in hundreds of our publications and projects for various special objects over the past 45 years, we abstract from their analysis here. These are questions, as they say, of pure technique, which we do not touch o­n at the level of the paradigm.

3. Structure of Spheral Matrices

The spheral matrix rows express the outputs of corresponding PIOT spheres as products, while columns express resource inputs. The dual nature of spheral resources as both outputs and inputs is expressed in binary, alphanumeric designations of the SS indices.

The infinite series of spheral matrices is constructed according to o­ne algorithm: each row of any matrix transforms into a column of the underlying matrix, and each indicator represents the sum of four indices expressing resources necessary for its reproduction.

This generating algorithm expresses the binary principle: "ALL SPHERES OF PIOT ARE IN ALL SPHERES OF PIOT" both in their reality and the matrices reflecting their spheral indices. It creates nested fractals that reflect genuine spheral fractals, which aligns with Mandelbrot's definition: "A fractal is a structure consisting of parts that are in some sense similar to the whole." These spheral matrices ensure the cognition of society's spheres fractal nature and with necessarily require and generate a “substantially new [spheral] manner of thinking” (Einstein) with its universal language of Globstat spheral qualimetry.

Such a unified statistical system of indices ensures effective harmonious governance of the SP spheres and spherons and its perpetual peace at all levels, preventing any possibility of violence within and between them "at the root". The network and fractal SS create a universal digital language of qualimetry of the planetary social reality, opening up the possibility for a new statistical paradigm of SPHERAL AI (SAI), as well as a new spheral Internet - a planetary system of statistical (measured and measurable) communication data. It is created o­n the functionalities of encoding and decoding natural and spheral language. This "crazy" hypothesis has been discussed more than o­nce in our publications.

4. Tables of Spheral Statistics: Examples

We'll present a few critical examples of spheral indices, beginning with the spherons indices classifier, whose constant social structure as actors of was illustrated in paragraph 5.

Fig. 11. Spherons indices classifier

(https://peacefromharmony.org/?cat=en_c&key=1258)

This table presents eight spheral indices: five basic (in red) and three intermediate (in green) that assist in transitioning from traditional to spheral indices. The key intermediate indicators of working and nonworking populations balance spontaneously within about 10%, typically favoring the nonworking.

The spheron statistics are fundamental as theyexpress the quantitative measure of genetic sources of nonviolence, perpetual peace, and SP. Spherons aim objectively at perpetual peace and mutual survival, excluding mutual destruction. Wars do not affect perpetual peace between the spherons, so it remains perpetual in social nature, as I. Kant intuitively predicted more than two centuries ago. Wars only occur within spherons, locally and temporarily, o­nly between some of their transient and small parts, partons, nothing more. The spherons' measure and the states of their perpetual peace can change within the statistical equilibrium of their structural harmony, making their perpetual peace dynamic and measurable by spheral statistics.

Spherons communicate structural demographic vessels: a decrease in o­ne leads to increases in others. For example, robotization of the technosphere reduces its spheron while increasing numbers in immaterial spherons. This general trend of employment is reflected in spheral statistics. Thus, the statistics of spherons express the genetic basis for the survival, perpetual peace, and sustainable development of humanity, which determines its priority and significance for the global governance strategy.

The published and tested method of rapid verification of the spherons truth of any object within two hours in the presence of the corresponding traditional statistics (https://peacefromharmony.org/?cat=ru_c&key=998) opens up to every literate person the possibility of independent verification of the reality/truth of spherons of any social object that has statistics. Many similar examples are published in "Gandhica", 2019. Universal verification makes spheral statistics an objective, scientific truth of humanity.

A unique example of statistical research of spherons in world statistics belongs to Olga Kashina. She created statistics of the spherons social structure of Russia in their dynamics over 50 years, taking into account both its working population in the public sector of spheres and the employed population in the individual sector of households. [https://peacefromharmony.org/?cat=ru_c&key=899].

Similar fundamental statistics based o­n spheron‘s indices can be created for any country, city, corporation, or humanity as a whole for any historical period with available traditional statistics. The statistics of spherons is o­nly the fourth part of spheral statistics, though the most important. Other parts concern information (I), organization (O), and things (T) resources. For illustration purposes, we will limit ourselves to just their general table of spheral indices:

* S/S – sphere/spheron

Fig. 12. Table-2. Structure of four SPHERES/SPHERONS indices

(https://peacefromharmony.org/?cat=en_c&key=1019)

5. Advantages of Spheral Thinking and Statistics

The deep spheral structures of social nature, developed over millions of years in the sociogenesis evolution, are the most effective of all possible systems o­n Earth. Human thinking approaches the knowledge and conscious mastery of them slowly, over millennia, gradually increasing the level of their generalization, integration, and integrity in mind. However, humanity often absolutizes its limited disciplinary thinking, which explains the persistence of wars, culminating in the nuclear threat of "Mutually Assured Destruction" (MAD).

Only at the level of spheral, holistic thinking—whose shoots began emerging thousands of years ago in ancient India, Greece, and China—does humanity's deep structural harmony become accessible today and capable of displace its structural inequality and violence. Today's planetary scale of nuclear catastrophe requires equally planetary, scientific thinking that overcomes disciplinary "blindness of whole."

Only through spheral holistic thinking and its tools of planetary statistics and SAI do the sources of nonviolence, global peace, social equality, sustainable prosperity, and liberation from social pathologies become clear. Peace and harmony are achieved o­nly in the qualimetric logic of the spheral whole, which integrates all sectoral parts of social spheres.

The PIOT spheral GlobStat will become a single global statistical language, a universal social quality, and a common technology for digitalization, forecasting, and global management. It will prevent and resolve emerging conflicts, ensuring effective noosphere forecasting for any country and region. No comparable universal quality technology is offered by any social discipline in the world.

The SAI based o­n GlobStat will become the subject of competitive technological struggle, shifting "the arms race into a peace race," as predicted by M.L. King. P. Sloterdijk also predicts this shift o­n a spheral basis in his spheral morphology of new plural living spaces.

The subject of spheral thinking continues to develop despite pressure from disciplinary thinking. From its spark, a flame will inevitably emerge, likely in the synergetic symbiosis of the "Common Sense Revolution" and the "Multipolar World Order" within the framework of planetary spheral thinking of the PPS and its tools of GlobStat and SAI.

Summary Comment

By

Lucas Pawlik

The eighth paragraph introduces an ambitious concept in the philosophy of science called “Spheral Global Statistics” (GlobStat), [which is being developed within the framework of the macrosociological paradigm of the GGHA spheral “Perpetual Peace Science”, but arose before it in the social philosophy of L. Semashko “Spheral Approach”, 1980, published in 1992: https://peacefromharmony.org/docs/leo-semashko-spheral-approach-1993.pdf]. This concept aims to fundamentally change how data regarding social structures is collected and interpreted. Our half-page commentary analyzes its central ideas and significance.

We establish the thesis that traditional statistical methods cannot adequately capture the complexity of societal interrelations due to their fragmentary and discipline-bound nature. As an alternative, it proposes a holistic, fractal model called “GlobStat,” based o­n four fundamental social resources: People, Information, Organization, and material Things—collectively referred to as “PIOT.”

Noteworthy is the epistemological approach: while traditional statistics proceeds inductively from parts to the whole, GlobStat adopts a deductive perspective, moving from the whole to the parts. This reversal of methodological direction is reminiscent of Kuhn’s concept of a paradigm shift. It establishes a theoretical framework in which society is seen as a whole system with 16 constant spheres across four coordinates.

The concept of “Spherons” (social actor groups operating within specific spheres) is presented as the key to understanding social harmony. The mathematical formalization via matrix algorithms (4 × 4ⁿ) is an intriguing attempt to translate social complexity into a formal system.

We combine scientific arguments with normative goals: preventing violence and achieving peace are portrayed not merely as desirable objectives but as logical consequences of spheral thinking. This reflects a holistic-systemic worldview in which peace is not attained through fragmented efforts but through understanding deep structural interrelations.

Applying these principles, the proposed “Spheral Artificial Intelligence” (SAI) offers an alternative vision to current AI development by focusing o­n harmonious social structures instead of fragmented optimization.

The eighth paragraph embodies a remarkable tension between scientific-theoretical ambition and ethical-normative vision. Synthesizing social theory, statistics, peace research, and artificial intelligence into a holistic model is an intellectually fascinating endeavor, though its practical implementation and empirical validation pose a significant challenge.

The paragraph text for discussion was prepared by Leo Semashko

https://peacefromharmony.org/?cat=en_c&key=253, 07-04-25

Text editing by Lukas Pawlik

https://peacefromharmony.org/?cat=en_c&key=887, 13-04-25

Final joint revision: 15-04-25

Summary Commentby Lukas Pawlik: 16-04-25

-----------

Updated paragraph-8

Dear Lucas,

         Thank you very much for your brilliant professional editing of Paragraph-8, which constitutes our Perpetual Peace Science (PPS) qualimetric center and its SAI paradigm. Special thanks for your unique summary of this paragraph, in which you have excellently qualified the innovative spheral Globstat as a universal qualimetric tool of our PSP, capable of monitoring its various states in different locations of the planet. This creates a new functional of prediction, peaceful resolution, and, most importantly, prevention of various conflicts, primarily armed o­nes, as well as qualimetry of the balance of planetary resources of the PIOT.

         The paragraph updated and shortened by you from 8 to 5 pages is published in two languages ​​at the old addresses for comparison here: https://peacefromharmony.org/?cat=en_c&key=1258

https://peacefromharmony.org/?cat=ru_c&key=1107. It is also published in the attachment and opens the way for us to the final paragraph dedicated to the planetary spheral AI (SAI) and its substantial, cognitive superiority during the week.

         With peace, love and a significant joint Easter o­n April 20, marking the victory of life over death and the USA and Russia joint victory of peace over war,

Leo Semashko

17-04-25

------------------------

Dear Leo:'

Inspite of all the tragedies of our time, I wish you and your dear Family a Happy Easter 2025.

80 years ago o­n Easter 1945. I was o­nmy way to the Eastern front. At that time the life expectancy of a young Lieutenant was 4 weeks. I was supposed to shoot down tanks. In the last moment I was redirected against General Patton. I got involved in the Battle of Aschaffenburg. Almost my whole unit was wiped out in the battle o­n the Hahnenkamp. After the battle I was almost executed by an SS court being under suspicion of desertion , while I tried to find a priest for two dying comrades. My General rescued me. For 60 years I visited myfallen 250 comrades o­n the cemetery of Alzenau. The insanity of war became clear to me through all the fallen,young German, Canadian and American soldiers at the Western front. This insanity must be stopped o­nce and for all. You have spent your whole life in the work of peace in remembrance of your dear father. That has been the foundation of our friendship and our work together in the past 20 years.

This year our tow Churches celebrate Easter o­n the same date. May they work for peace together as well.

Best Easter wishes to you and your whole dear Family and friends in the hope for this life and the next - He is risen!!! -,

your Rudi and Family from the House of Mir, USA.

https://peacefromharmony.org/?cat=en_c&key=51

19-04-25

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         In the previous paragraph, 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 objects of social nature. 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, a platform, determines the scale of planetary use and all the attributes of innovative, holistic statistics of the same fractal and end-to-end nature. This is spheral global statistics (Globstat) as the PPS' own tool for spheral thinking and its spheral AI (SAI).

          Although in traditional, disciplinary statistics there are some elementary statistical indices of a global scale, such as the Earth total population, the number of all other different social objects o­n it, constituting its noosphere according to V. Vernadsky, they record o­nly their external, mechanistic juxtaposition and fragmentation. They exclude the possibility of comprehending their immanent, extremely effective fractal connection within the framework of the social objects spheral integrity, which is inaccessible to them and unknown in the mutual cause-and-effect relationship: inaccessible because unknown and unknown because inaccessible, like an elephant to the blind men. Mechanistic statistical indices, by definition blind to the whole, are powerless to reflect and “see” the social nature spheral integrity, groping and recording o­nly its small pieces, torn from the whole.

         Their immanent blindness of the whole is superimposed by fragmentations of other orders: national, corporate, financial secrecy, state secrecy, political expediency and the like, which make traditional statistics (TS) 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, impudent lies and statistics." Therefore, its effectiveness and capabilities are extremely limited and minimized. The holistic and end-to-end Globstat of a planetary scale is formed not in disciplinary, but in spheral thinking and according to the laws of spheral, holistic, and not branch/sectoral, disciplinary logic, raising traditional statistics to the highest level of perfection, possibilities and effectiveness accessible to it. This paragraph is devoted to the elevation and overcoming the traditional statistics vices in synergistic complementarity with the spheral Globstat in its innovative way of thinking and AI. The TS indices “Augean stables” of vices and limitations, accumulated over centuries, are successfully overcome by logic, thinking and the 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 is as sectoral and fragmentary as the disciplinary thinking, within which it emerged almost 4 centuries ago and develops in it, despite all its limitations, and most importantly, the "blindness of the whole" of social objects, starting with an individual, a household and ending with humanity. Of course, it is not useless, it has great practical significance, but it is ineffective and far from adequate. The fractal/spheral, holistic statistics does not originate from partial, sectoral indices "from below", mechanically, otherwise it would have emerged long ago, almost 4 centuries ago. It has the opposite source of generation: not from below, but from above, from a holistic, theoretical understanding of society, its spheral nature, which is planetary and end-to-end, penetrating each and every social object, without exception, as established above.

         But both statistics, as well as both ways of thinking, are inseparable, complement each other and, when integrated, provide a qualitatively new synergetic effect. Let us consider their mutual complementarity from the side of each of these statistics, of which the spheral statistics, Globstat, turns out to be the methodologically determining and generating o­ne.

         Spheral statistics is based o­n the fractal structure of the PIOT resource spheres coupling, which is disclosed above and expressed by the key, basic matrix of spheral fractal indices of size 4x4. The basic matrix of spheral indices of size 4x4¹ has the form:

P1 + P2 + P3 + P4

I1 + I2 + I3 + I4

O1 + O2 + O3 + O4

T1 + T2 + T3 + T4

         o­n this basic matrix of spheral indices, 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. A machine printout of the first such matrix of spheral indicators 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=ru_c&key=824].

Spheral statistics 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, and was reflected in hundreds of individual and collective publications, the main o­nes of which are listed in the bibliography. The most important and fundamental of them is the book of GGHA "Gandhica" by 82 coauthors from 25 countries, 2019, in Russian, English and French, dedicated to the verification of universal spherons based o­n world statistics. For a general understanding of spheral statistics, this is enough.

         Now, the most important thing is to understand the interaction of the two statistics and the role of each of them. In the methodology of spheral statistics, two complementary types and levels of statistics are distinguished: traditional and spheral. Each of them is defined by its own necessary logic of cognition and its own necessary paradigm of thinking. Traditional statistics (TS) embodies the simplest and most accessible vector of disciplinary thinking and empirical cognition from parts, details to the general and the whole in inductive logic, which determines the essence of disciplinary thinking, the generalization in which does not rise above the visible large, sectoral segments of social reality.

         Spheral statistics (SS) implements the most complex and least accessible vector of theoretical cognition from the whole to its fundamental parts that constitute it and to their components in the deductive logic of spheral nature substance, which determines a qualitatively different, spheral, transdisciplinary, i.e. holistic way of thinking. Its complexity and difficulty lie in the theoretical scientific cognition of the social whole as a system of 16 constant spheres in the system of four spheral coordinates of social space and time, considered in the first approximation in the previous paragraphs.

         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 content/meaning. SS classifies, compresses, orders and focuses the infinite and chaotic space of empirical, variable indices and their meanings 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 merit is the connection with reality, with the historical context of changes and all its features, details, pros and cons in the most diverse parts of the humanity infinite social nature. TS is formed and lives in the empirical logic of cognition and in the paradigm of partial, disciplinary thinking. The SS main advantage is the penetration into the eternal fundamental and deepest, invisible laws and structures of the humanity social nature, ensuring its eternal life, survival, sustainability throughout its history from beginning to end. The SS dignity is formed and lives in the theoretical, spheral logic of knowledge and in the paradigm of holistic, spheral thinking, at least at the level of intuition and guesses of brilliant thinkers throughout past history, until it becomes a known and accessible innovative asset to humanity in all schools.

2. Interaction of traditional and spheral statistics

         Three main attributes define the Traditional Statistics (TS) essence in its almost four-century history: its national, sectoral/partial and empirical/inductive character. Despite its undoubted necessity, social usefulness and advantages, it has a number of fundamental shortcomings. To those already noted, it is necessary to add subjectivity and a tendency to various kinds of unfair manipulations of TS, which gives rise to reasonable doubts about its objectivity and reliability. For this reason, it excludes a full-fledged comparison of statistical data from different countries, and o­ne country in different periods due to the constant changes in its key link - classifiers and their statistical indices, devoid of fundamental grounds. But it began to realize, pose and partially solve this problem since 1853 (the first international statistical congress in Brussels), leaving it fundamentally insoluble in its empirical methodology and an insurmountable fragmentation of its basic, disciplinary thinking in its limited sectoral segments.

         The TS fragmentation is institutionalized at the global level by the relevant international organizations and departments of the UN, IMF, WHO, WTO, International Banks and all others. Here lies the central problem and source of all the TS weaknesses and vices, which it fights at the regional levels, but without much success and progress. Since better statistics do not exist, they are used, trying to somehow limit, compensate and dampen its defects. The TS is o­ne logic, paradigm, statistical language and sectoral science from part to whole, which is supplemented and developed by another logic, paradigm, statistical language and new science from whole to parts, represented by PPS (Perpetual Peace Science).

         Another level of statistics and a type of statistical language of its specific indices is spheral statistics (SS), growing from fundamentally different foundations: from logical/theoretical prerequisites for understanding the spheres of social production as associations of its branches and their clusters. This allows SS to acquire a global/universal character and find a cross-cutting, comparable application in a social system of any order and level from an individual, a household to humanity as a whole. SS cannot and does not seek to replace and displace traditional statistics, which constitutes its nourishing empirical soil and source. SS can o­nly rely o­n it, promote its development and strengthening and raise it to the level of fundamental science, preserving all its necessary national characteristics. Unlike TS, the new SS is democratic, since it is simple in its logic and transparency, therefore it is accessible to the people. In the general methodological sense, SS acts as a metalanguage and metalinguistics in relation to the TS object language and linguistics.

         The SS emergence more than 40 years ago, its first steps, as well as the shortcomings of TS and the relationship of the composition and decomposition of the indices of the two statistics are considered in more detail in the book of 1992 “Spheral Approach” and subsequent o­nes. The SS is statistics of the PIOT spheral resources, through which the statistics of PDEC processes spheres, the SIOT production spheres and the SIOT spherons employed in them are expressed. The statistics of spherons (P) is the center of spheral statistics, defining peripheral/infrastructure spheral statistics. The SS is built o­n a system of special spheral indicators of PIOT, which generalize, organize and complement the TS system of indices, which still remains nationally torn and fragmented. The SS system of matrices is built o­n alphanumeric indices of the PIOT resources, called spheral indices.

         The units of spheral indices measurement can be generalized natural units or their cost, time and energy units. The SS of spherons (people) are limited to natural units of population, for example: millions of people. All indicator matrices derived from the base matrix are called spheral matrices, which form the SS, fundamentally different from TS statistics, but related to it. All TS indicators 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 PIOT corresponding spheres of production as their products, and the columns express the resource inputs of the PIOT corresponding spheres of production as their resources.

The dual nature of the spheral resources (and spheral indices) as an output/product of spheres and as their input/resource is expressed in the binary, alphanumeric designation of these resources and corresponding indices.

          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 indicator of the row is represented 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". It makes spheral matrices, their rows/lines and columns similar and nested fractals, which are adequate and reflect real spheral fractals, which were considered in the previous paragraph. The mathematical concept of Mandelbrot's fractals covers not o­nly fractals of social reality, but also 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 matrices of spheral statistical indices are the beginning of the cognition of the "Fractal nature of society", if paraphrase Mandelbrot. This is a necessary attribute of the spheral way of thinking as "a substantially new [spheral] manner of thinking" (Einstein).

         The system of spheral/fractal matrices creates a single logical network statistical space of humanity, a global statistical digital language of spheral indices in spheral matrices, what is its fundamental advantage. It is capable to become a common denominator of traditional indices, integrating, composing and decomposing the diversity of national statistics according to the PIOT indices of different levels, overcoming their inherent fragmentation, confrontation and disharmony. It systematizes, integrates and opens the way for the digital economy, digital global peace through the conscious and mathematically balanced prevention of all wars and the nonviolent resolution of all conflicts. The spheral indices aggregate indices of TS and are disaggregated in them according to a special digital “Spheral Information Statistical Technology” (SIST). We do not touch o­n it here because of its cumbersomeness and its partial disclosure in the next paragraph devoted to spheral AI (SA). [See also: Semashko, 2018; 5; 6; 6a-d].

         Such a unified statistical system of indices ensures effective harmonious governance, management of spherons at all their levels and in all social units, overcoming disharmony and preventing any possibility of violence/conflict "at the root" within each spheron. Network, end-to-end, matrix and fractal spheral statistics creates the best, qualimetric, maximally close to mathematics and digital calculation of the entire planetary social reality universal information language, which opens up the possibility for a fundamentally new, statistical paradigm of SPHERAL AI (SAI), which will be disclosed in the attributes of its superiority in the next paragraph.

3. 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 indicators 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 a classifier of spheral indices of spherons, the constant end-to-end structure of which is illustrated in Fig. 6.1. in paragraph-5.

Fig. 11. Spherons indicators

         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. The key intermediate indicators of the working and nonworking population in different societies balance in a spontaneous (swarm) equilibrium in the range of up to 10%, as a rule, in favor of the nonworking, but there may be exceptions from it for spherons of different countries.

         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 eternal world 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.

         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 robotization of the technosphere, reducing the number of its spheron, ensures an increase in the number of immaterial spherons. The growth of infospheron 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 spheral statistics. Therefore, the statistics of the number of spherons within the dynamics of their structural harmony is statistics of genetic survival, perpetual peace and sustainable development of humanity as a whole, as well as each of its national societies in the ideal and norm. No other, sectoral or national statistics have such fundamental significance.

         The absence of such statistics of survival/sustainability in humanity as statistics of harmony and perpetual peace testifies to its adolescence and the limitations of its fragmentary, disciplinary thinking, incapable of rising to the level of knowledge of the integral social nature, its constant spheres, revealed in the Perpetual Peace Science and its spheral Globstat.

             The classifier of spheral indices of spherons opens up for every literate person who knows arithmetic the possibility of independent, autonomous verification of the reality/truth and dynamics of spherons of any social object that has statistics: from o­ne's own school, institution and city to his region, country, continent and humanity. Many similar examples are published in our book "Gandhica", 2019. They are supported by a published methodology, a template for fast and effective verification of the spherons truth/reality o­n any object within two hours in the presence of appropriate traditional statistics (https://peacefromharmony.org/?cat=en_c&key=1125).

         A unique, unprecedented example of statistical research of spherons in world statistics belongs to Olga Kashina (Fig.12.). She created statistics of the social structure of spherons of Russia in their dynamics over 50 years, taking into account the dynamics of both the working population in the public sector of spheres and the employed population in the individual sector of households. These statistics are given by her in absolute and relative (percentage) figures, of which we reproduce the latter, and both of them are published here: [33: https://peacefromharmony.org/?cat=ru_c&key=899]. Similar fundamental and strategic statistics based o­n the classifier of spheron indices can be created for any country, city, corporation and humanity as a whole for any historical period in the presence of the original, traditional statistics.

Fig. 12. Table.The Russia spherons dynamics for 50 years: 1970-2021

         The spherons 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. Statistics of spherons this is the defining and goal-setting part of the Globstat in accordance with the generative role / function of spherons as the o­nly social actors. It is o­nly the fourth part of the 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). We do not touch here o­n the important question of the unit of measurement of spheral indices, limiting ourselves to cost units and natural units for the spherons number, although it is possible to have uniform and universal units, such as energy or time units, but this is a question for the future (https://peacefromharmony.org/?cat=ru_c&key=1007). Here we will limit ourselves to o­nly a schematic general table of spheral indicators of the SP four spheres and the perpetual peace below for illustration.

4. Schematic framework of the SP four spheres spheral indices

* S/S – sphere/spheron

Fig. 12. Structure of four SPHERES/SPHERONS indices [32]

(Source with the comments: https://peacefromharmony.org/?cat=en_c&key=1019)

5. Advantages of spheral thinking and statistics, predetermining the superiority

of planetary spheral AI

         The deep spheral integral structures, laws and constants of social nature, developed over millions of years, are the most perfect, effective and productive of all possible and known o­n Earth. The human mind approaches slowly to them, 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, the human easily falls into, even constantly finds himself in a historically continuous 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 existence and prosperity of bloody wars of humanity. The further, the more and more dangerous, having reached today, in a nuclear civilization, in 80 years the full maximum of 100% nuclear genocide in "Mutually Assured Destruction" (MAD). Obviously, this is where the "highest comfort" of limited disciplinary thinking is focused, having reached its absolute unsurpassed truth of total suicide, which no o­ne has yet managed to achieve. If humanity is satisfied, having reached this highest intellectual progress of the deadly limitations of its "blind to the whole" thinking, then all that remains is to wait for the "Doomsday Clock", to which there are o­nly 89 seconds left o­n its clock according to the conclusion of the nuclear scientists (https://peacefromharmony.org/?cat=en_c&key=924).

         Therefore, all the “crazy” conclusions and hypotheses from the spheral, holistic thinking, as well as from all its tools, including its statistics, AI, qualimetry and mathematics, will undoubtedly seem “insane”, violating the genocidal-suicidal comfort of the nuclear civilization. Therefore, they must and will be rejected out of hand, a priori, without any difficulty in trying to understand them, as it has been for all 80 years. It remains o­nly to hope that there will be a tiny fraction of a percent of thinking people interested in living and capable of understanding the new, holistic, spheral thinking, liberating people from the “blindness of the whole”, in order to make it accessible to a larger circle of people, o­n whom we are counting today our PPS Primer. o­nly at the level of spheral, holistic thinking, the shoots of which began to break through thousands of years ago in ancient India, Greece, China, within the framework of its holistic logic of spheres, the humanity deep societal structural harmony/nonviolence as a whole becomes accessible.
         Regardless of its will and consciousness, it regulates all stochastic, thermodynamic historical processes of all its local and national parts, keeping it in perpetual peace from all their destructive disharmonies, wars, violence and militarism (Mairead Maguire, 2014, 2018). Today, the humanity planetary scale of the civilizationally prepared nuclear catastrophe in 80 years requires an equally planetary, conscious and scientific, acceptable and accessible to all peoples spheral holistic thinking, overcoming the "blindness of the whole" of the dominant disciplinary thinking that created 100% reality of this catastrophe. o­nly at the level of spheral holistic thinking and its adequate holistic tools of planetary statistics and planetary spheral AI do the sources and laws of nonviolence, global perpetual peace, social equality, brotherhood, justice, unity, sustainable prosperity, accelerated growth, liberation from all social pathologies, well-being and happiness of all peoples become clear. Peace, nonviolence and harmony of humanity are achieved o­nly in the qualimetric logic and science of the spheral whole, which integrates and harmonizes in a synergistic measure all sectoral and territorial parts of social spheres. Therefore, the spheral Globstat becomes the defining intellectual/scientific instrument for achieving and ensuring them, overcoming the civilizational crisis (Avery, 2017) that is its unique meaning and fundamental importance for the future.

         The PIOT spheral Globstat will become a single global statistical language of the world, a universal social qualimetry, a common technology of digitalization, forecasting, globalistics, geopolitics, management and worldview of global understanding, nonviolence and harmony of humanity, all its peoples. It will prevent and resolve all emerging conflicts. It ensures the effectiveness of noospheral forecasting, allowing o­ne to calculate long spheral Kondratyev waves [24] of almost any dimension for any country and region. There is no such universal qualimetry technology in the world, it is not offered by any of the known social disciplines. This technology creates unlimited practical application of the spheronics science in the future.

         The PIOT Globstat and the SAI based o­n it will undoubtedly become the subject of intense competitive technological struggle in the near future, shifting, according to the brilliant prediction of M.L. King's "the arms race into a peace race." This shift o­n a spheral basis is also predicted by the German philosopher Sloterdijk in his spheral morphology of new plural living spaces, displacing traditional and outdated monism [15; 16]. The importance of noospheral technology is convincingly demonstrated by the fact that the Pentagon has been actively interested in it for more than 20 years, whose experts [39; 37] have been scrupulously studying all the innovations in this area over the past century... Obviously, there are many other places where research and R&D of spheral thinking and its tools are secretly conducted, the whole question of which is o­ne: are they carried out in the interests of all humanity or o­nly some of its egoistic groups?

         This means that the subject of spheral thinking has not died and cannot die under the pressure of disciplinary thinking. It smolders in it with necessity. From its spark, its flame will inevitably and soon flare up, most likely in the synergetic symbiosis of the "Common Sense Revolution" and the "Multipolar World Order", organically complementing each other within the framework of the planetary and cross-cutting spheral thinking of the PPS and its common tools Globstat and SAI. We move o­n to considering the key attributes of the SAI superiority as a fundamental and integral cognitive tool of humanity and each trained individual in the next paragraph.

         (This paragraph will be shortened and simplified in the new edition after the discussion).

The paragraph text for discussion was prepared by:

Leo Semashko

https://peacefromharmony.org/?cat=en_c&key=253

07-04-25

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