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# Peculiarities of global distribution of geological and social structures
6. PECULIARITIES OF THE GLOBAL DISTRIBUTION OF GEOLOGICAL AND SOCIAL STRUCTURES BY THEIR SIZE
# Peculiarities of global distribution of geological and social structures by their size
The ideal object for such a study is blocks of the Earth's crust and all the structures associated with them. The blocks were most likely formed at the time of the Earth's crust's origin, about 5 billion years ago.
During this period, the size of the Metagalaxy could have been about 1028 cm (15 \- 5 \= 10 billion years). Calculation by the Double Wave Stability model using formulas 1.16 and 1.17 gives the following predictions regarding the statistics of the size distribution of these blocks (CLASS \#8):
LB \= *l*
*\- 105K* \= 1, 6 $ 10-33 cm $ 105 $ 8 \= 1, 6 $ 107 cm \= 107.2 cm,
During this period, the size of the Metagalaxy could have been about \\(10^{28}\\) cm (15 - 5 = 10 billion years). Calculation by the Double Wave Stability model using formulas 1.16 and 1.17 gives the following predictions regarding the statistics of the size distribution of these blocks (CLASS \#8):
\\[ L_B = l \cdot 10^{5K} = 1.6 \times 10^{-33}\text{ cm} \times 10^{5 \times 8} = 1.6 \times 10^7\text{ cm} = 10^{7.2}\text{ cm}\\]
or 160 kilometers.
LE \= *l* $ (*R/L* ) *K* 12 \= 1, 6 $ 10 33 cm
(1028 /10 32 8 8
*K f f*
\\[ L_E = l \cdot \left(\frac{R}{L}\right)^{\frac{K}{12}} = 1.6 \times 10^{-33}\text{ cm} \times \left(\frac{10^{28}}{10^{32.8}}\right)^{\frac{8}{12}} = 5.4 \times 10^7\text{ cm}\\]
or 540 kilometers.
The issue of identifying statistically significant selected sizes of crustal blocks was addressed in the 1980s by a team led by the director of the Institute of Earth Physics, M.A. Sadovsky. In this size range, the scientists found156 that blocks with sizes of 120 and 500 km are the most common. Taking into account all probable errors, the coincidence of our model values with statistical data is very high. Let us further consider the following chain of logical reasoning. If the crustal blocks gravitate to ***bimodal distribution***, and since they determine the *boundaries of geographic regions*, they, in turn, should reveal the predicted bimodality when processing the statistical array. Geographical boundaries, in turn, are determined by climatic, soil, and vegetation differentiation of the Earth's surface. As established157 , *socio-economic territories are* also tied to landscape-geographic arrays. Consequently, the distribution of countries and their internal structures (states, provinces, etc.) by size should show the same bimodality.
The issue of identifying statistically significant selected sizes of crustal blocks was addressed in the 1980s by a team led by the director of the Institute of Earth Physics, M.A. Sadovsky. In this size range, the scientists found[^ref-156] that blocks with sizes of 120 and 500 km are the most common. Taking into account all probable errors, the coincidence of our model values with statistical data is very high. Let us further consider the following chain of logical reasoning. If the crustal blocks gravitate to ***bimodal distribution***, and since they determine the *boundaries of geographic regions*, they, in turn, should reveal the predicted bimodality when processing the statistical array. Geographical boundaries, in turn, are determined by climatic, soil, and vegetation differentiation of the Earth's surface. As established[^ref-157], *socio-economic territories are* also tied to landscape-geographic arrays. Consequently, the distribution of countries and their internal structures (states, provinces, etc.) by size should show the same bimodality.
Let us make a logical PROPOSITION that in the process of formation of social territories, the ***block structure of the Earth's crust*** plays a significant role ***at all scales,*** both in the static formation of ethnic groups through landscape specifics (soils, vegetation, etc.) and in the *dynamics of* settlement of peoples to natural barriers (mountain ranges, rivers, deserts, etc.). In other words, lithospheric fragments, as a matrix, give rise to the geographical structure, and the latter, in turn, gives rise to the socio-economic one.
Let us make a logical PROPOSITION that in the process of formation of social territories, the ***block structure of the Earth's crust*** plays a significant role ***at all scales***, both in the static formation of ethnic groups through landscape specifics (soils, vegetation, etc.) and in the *dynamics of* settlement of peoples to natural barriers (mountain ranges, rivers, deserts, etc.). In other words, lithospheric fragments, as a matrix, give rise to the geographical structure, and the latter, in turn, gives rise to the socio-economic one.
The data on the distribution of countries and their regions by size\* were statistically processed by the author in his time and obtained quite remarkable results158. They *confirmed the predictive power of the law of bimodality in the distribution of all scaled systems*.
The data on the distribution of countries and their regions by size were statistically processed by the author in his time and obtained quite remarkable results[^ref-158].
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
> To simplify the calculations, the notional size of any region was defined as the square root of its area.
\* To simplify the calculations, the notional size of any region was defined as the square root of its area.
They *confirmed the predictive power of the law of bimodality in the distribution of all scaled systems*.
Let us consider how social structures are distributed on the S-axis (see Fig. 1.60 and Table 1.3).
***Curve No. 1*** shows the statistical distribution of all countries of the world by size\*. Calculations of conditional sizes from areas showed the following. The ***most representative modes are*** **130 km** (30 countries) and **450 km** (58 countries) (see Table 1.3). Another significant mode, **15 km** (24 countries) is represented by dwarf and island states. We see that most of the countries of the world gravitate in one way or another to the sizes of the crustal blocks, or the two most stable sizes on the S-axis in the CLASS \#8 we have chosen for consideration. Incidentally, the closest to the exact cosmological size (162 km) is the notional size of the UK. ***Curve \#2*** shows the statistical distribution of the regions of the former USSR. In fact, all internal regional distribution in the USSR has a *bimodal character*.
***Curve No. 1*** shows the statistical distribution of all countries of the world by size.
The first mod is **180 km** (65 areas) and the second mod is **420 km**
> The distribution is clearly multimodal, *with a step of 0.5 orders of magnitude* on the S-axis. By the way, in M.A. Sadovsky's data, one can also detect an average step of 0.5 order for the crustal blocks.
(37 areas).
Calculations of conditional sizes from areas showed the following. The ***most representative modes are*** **130 km** (30 countries) and **450 km** (58 countries) (see Table 1.3). Another significant mode, **15 km** (24 countries) is represented by dwarf and island states. We see that most of the countries of the world gravitate in one way or another to the sizes of the crustal blocks, or the two most stable sizes on the S-axis in the CLASS \#8 we have chosen for consideration. Incidentally, the closest to the exact cosmological size (162 km) is the notional size of the UK. ***Curve \#2*** shows the statistical distribution of the regions of the former USSR. In fact, all internal regional distribution in the USSR has a *bimodal character*.
***Curve No. 3*** shows the generalized distribution by size of internal regions of large countries of the world: USA, Brazil, India \- states, China \- provinces.
The first mode is **180 km** (65 areas) and the second mode is **420 km** (37 areas).
Table 1.3 shows that the same two modes are distinguished in each country, with the second mode \- about 450 km \- being the most significant. The total number of regions in the first mode \- 150 km is equal to 17, and the second mode \- 450 km is represented by 73 regions.
***Curve No. 3*** shows the generalized distribution by size of internal regions of large countries of the world: USA, Brazil, India - states, China - provinces.
**Table 1.3** shows that the same two modes are distinguished in each country, with the second mode - about 450 km - being the most significant. The total number of regions in the first mode - 150 km is equal to 17, and the second mode - 450 km is represented by 73 regions.
So, all countries of the world and their hinterland regions are characterized by a ***bimodal*** size ***distribution.***
***The first mode***: 120-180 km coincides with the calculated value of the SWS stability size FOR CLASS \#8-160 km.
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\* The distribution is clearly multimodal, *with a step of 0.5 orders of magnitude* on the S-axis. By the way, in M.A. Sadovsky's data, one can also detect an average step of 0.5 order for the crustal blocks.
***The second mode***: 420-450 km is close to the calculated value of EVOLUTIONAL WAVE of stability \-EWS \- 540 km.
Both modes are related to the sizes of the Earth crust blocks and their natural boundaries. But it is not so much important for us as the fact that the model calculation of stable sizes, which was based on the factors of the integral scale symmetry of the Universe, seemingly far from geological and social processes, leads to surprisingly accurate (for such an interval of scales) predictions.
One more conclusion cannot be passed by. For all countries of the world and for their internal regional areas, the ***second evolutionary mode \- 450 km \-*** clearly dominates in the statistical distribution by size.
Figure 1.60. Distribution of social territories by size (S \- area). 1\. \- countries of the world; 2\. \- regions of the Russia; 3\. \- states of the USA, regions of China, India, Brazil
![](./media/pic1.60.jpg)
*Figure 1.60. Distribution of social territories by size (S \- area). 1\. \- countries of the world; 2\. \- regions of the Russia; 3\. \- states of the USA, regions of China, India, Brazil*
***For all... except Russia***. The only country in which the regional distribution has as dominant the ***first basic mode \- 180 km***, was the USSR (now \- Russia). What does this undoubted statistical fact of our socio-cultural reality testify to?
*First*, Russia (USSR) is ***fundamentally different from the rest of the world in*** its internal geographical and socio-territorial structure.
| TABLE 1.3. | | Intervals, Ni | | | | | | | | | | | | | Lg S, km2 | | | V,% | γ1 | γ2 |
**TABLE 1.3.**
| № | Region | \\(1_l\\) | \\(1_d\\) | \\(2_l\\) | \\(2_d\\) | \\(3_l\\) | \\(3_d\\) | \\(4_l\\) | \\(4_d\\) | \\(5_l\\) | \\(5_d\\) | \\(6_l\\) | \\(6_d\\) | \\(7_l\\) | \\(\\bar{X}\\) | \\(M_0\\) | \\(\\sigma\\) | \\(V,\\%\\) | \\(\\gamma_1\\) | \\(\\gamma_2\\) |
| :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- |
| № | Region | *1l* | *1d* | *2l* | *2d* | *3l* | *3d* | *4l* | *4d* | *5l* | *5d* | *6l* | *6d* | *7l* | X̄ | M0 | σ | | | |
| 1 | Europe | \- | 1 | 4 | \- | 2 | \- | 5 | 5 | 16 | 1 | \- | \- | \- | | | | | | |
| 2 | Asia | 1 | \- | 1 | 1 | \- | 3 | 6 | 4 | 15 | 7 | 5 | 1 | 1\* | | | | | | |
| 3 | America | \- | 1 | 11 | 3 | 3 | 1 | 7 | 3 | 9 | 1 | 6 | 3 | \- | | | | | | |
| 4 | Africa | \- | \- | 2 | \- | 3 | \- | 8 | 3 | 16 | 11 | 12 | \- | \- | | | | | | |
| 5 | Australia and Oceania | 4 | \- | 6 | 3 | 3 | \- | 4 | \- | 2 | \- | \- | 1 | \- | | | | | | |
| 6 | General Nos. 1-5 | 5 | 2 | 24 | 7 | 11 | 4 | 30 | 15 | 58 | 20 | 23 | 5 | 1 | 4,52 | 5,30 | 1,50 | 33 | 0,80 | \-0,16 |
| 7 | Regions of the Russia | \- | \- | \- | \- | 5 | 6 | 41 | 2 | 2 | \- | \- | \- | \- | | | | | | |
| 8 | "Oblast" units. | \- | \- | \- | \- | 5 | 7 | 65 | 28 | 37 | 3 | 5 | \- | \- | 4,76 | 4,64 | 0,57 | 12 | \-0,45 | 0,49 |
| 9 | United States (states) | \- | \- | 1 | \- | 2 | \- | 6 | 5 | 33 | 1 | 1 | \- | \- | 4,88 | 5,24 | 0,63 | 13 | 1,88 | 5,10 |
| 10 | China | \- | \- | \- | \- | \- | 1 | 1 | 2 | 19 | 4 | 2 | \- | \- | 5,34 | 5,28 | 0,47 | 9 | 0,99 | 2,60 |
| 11 | India | \- | \- | \- | \- | \- | \- | 6 | 2 | 11 | \- | \- | \- | \- | 4,42 | 5,23 | 1,13 | 26 | 1,10 | 0,14 |
| 12 | Brazil | \- | \- | \- | \- | 1 | 1 | 4 | 4 | 10 | 3 | 3 | \- | \- | 4,99 | 5,23 | 1,00 | 20 | 1,80 | 3,90 |
| 13 | General No. 9-12 | \- | \- | 1 | \- | 3 | 2 | 17 | 13 | 73 | 8 | 6 | \- | \- | 4,95 | 5,24 | 0,86 | 17 | 1,92 | 4,47 |
| 14 | General \#8-12 | \- | \- | 1 | \- | 8 | 9 | 82 | 41 | 110 | 11 | 11 | \- | \- | 4,90 | \- | 0,75 | 15 | 0,98 | 3,49 |
| 15 | General No. 6, 14 | 5 | 2 | 25 | 7 | 19 | 13 | 112 | 56 | 168 | 31 | 34 | 5 | 1 | 4,76 | \- | 0,75 | 24 | 1,23 | 2,02 |
| Notes: | | ) (1 \- 5\) $ *10n*, *i* \= *l SNi* \= (5 \- 10\) $ 10nl, *i* \= *d* The asterisk marks the value for the territory of the USSR | | | | | | | | | | | | | | | | | | |
| 6 | General Nos. 1-5 | 5 | 2 | 24 | 7 | 11 | 4 | 30 | 15 | 58 | 20 | 23 | 5 | 1 | 4.52 | 5.30 | 1.50 | 33 | 0.80 | \-0.16 |
| 7 | Regions of the Russia | \- | \- | \- | \- | 5 | 6 | 41 | 2 | 2 | \- | \- | \- | \- | | | | | | |
| 8 | "Oblast" units. | \- | \- | \- | \- | 5 | 7 | 65 | 28 | 37 | 3 | 5 | \- | \- | 4.76 | 4.64 | 0.57 | 12 | \-0.45 | 0.49 |
| 9 | United States (states) | \- | \- | 1 | \- | 2 | \- | 6 | 5 | 33 | 1 | 1 | \- | \- | 4.88 | 5.24 | 0.63 | 13 | 1.88 | 5.10 |
| 10 | China | \- | \- | \- | \- | \- | 1 | 1 | 2 | 19 | 4 | 2 | \- | \- | 5.34 | 5.28 | 0.47 | 9 | 0.99 | 2.60 |
| 11 | India | \- | \- | \- | \- | \- | \- | 6 | 2 | 11 | \- | \- | \- | \- | 4.42 | 5.23 | 1.13 | 26 | 1.10 | 0.14 |
| 12 | Brazil | \- | \- | \- | \- | 1 | 1 | 4 | 4 | 10 | 3 | 3 | \- | \- | 4.99 | 5.23 | 1.00 | 20 | 1.80 | 3.90 |
| 13 | General No. 9-12 | \- | \- | 1 | \- | 3 | 2 | 17 | 13 | 73 | 8 | 6 | \- | \- | 4.95 | 5.24 | 0.86 | 17 | 1.92 | 4.47 |
| 14 | General \#8-12 | \- | \- | 1 | \- | 8 | 9 | 82 | 41 | 110 | 11 | 11 | \- | \- | 4.90 | \- | 0.75 | 15 | 0.98 | 3.49 |
| 15 | General No. 6, 14 | 5 | 2 | 25 | 7 | 19 | 13 | 112 | 56 | 168 | 31 | 34 | 5 | 1 | 4.76 | \- | 0.75 | 24 | 1.23 | 2.02 |
Notes:
\\[S_{N_i} = \begin{cases}(1 - 5) \cdot 10^n, & i = l; \\ (5 - 10) \cdot 10^n, & i = d\end{cases}\\]
The asterisk marks the value for the territory of the USSR
*Secondly*, since the first fashion is connected with all ancient and most simple, but fundamental structures of the Universe, we can PROPOSE that the scale-resonance space of Russia is tuned to a different frequency than the space of the rest of the world. It is tuned to the frequency of preservation of the basic properties of the social space, or to the frequency of Yin.
We see that the comparison of a simple analysis of the statistical distribution of world regions by their size gives very deep grounds for thinking about the connection between geopolitics and the processes of structure formation in the Universe. Here only the edge of this large and fruitful topic is touched upon.
[^ref-156]: *Sadovsky M. A., Bolkhovitinov L. G., Pisarenko V. F.* Deformation of geophysical medium and seismic process. Moscow: Nauka, 1986. С. 100.
[^ref-157]: *Razumovsky V. M.* In Vn.: Socio-economic and ecological aspects of geography. L.: LSU, 1983. С. 17-28.
[^ref-158]: *Sukhonos S. I.* On the possibility of the influence of the Earth's crust blockiness on the peculiarities of the size distribution of social territories // DAN. -1988. 303. № 5. С. 1093-1096.

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# Results
7. RESULTS
The above analysis shows that the ***phenomenon of bimodal*** (in more precise consideration \- multimodal) ***distribution of systems by their sizes has a universal character***. This opens up incredible opportunities for rethinking the multitude of statistical distribution curves in all fields of science. After all, since the main modes of the overwhelming majority of systems (atoms, stars, etc.) have a clear connection to two waves of stability, all possible varieties of systems of the Universe must be somehow connected in their diversity with these waves.
We PROPOSE *that the regularities of distribution of any systems by their sizes should reflect the presence of two or three epochs of structure formation*. This is a kind of a CONNECTED MASSWIDE RESONANCE MAP.
@ -12,6 +10,6 @@ The discovery of this pattern leads to the need to consider *three corollaries o
To understand what it is, is to understand the reason for the appearance of the detected scale symmetry.
***Second,*** even if we do not go into the physical meaning of this phenomenon, remaining within the symmetry categories, it becomes clear that the presence of two neighboring stability waves cannot but lead to their very complex interaction (in particular, to the interference of two "large-scale radiations"), which should generate a whole cascade of consequences.
***Second***, even if we do not go into the physical meaning of this phenomenon, remaining within the symmetry categories, it becomes clear that the presence of two neighboring stability waves cannot but lead to their very complex interaction (in particular, to the interference of two "large-scale radiations"), which should generate a whole cascade of consequences.
***Third***, the gradual "sliding" of the evolutionary EWS to the right of the basic SWS sets a certain SUSTAINABLE ACTING VECTOR OF EVOLUTION IN THE direction of SYSTEMS WITH LARGER SIZE. We can say that the Universal evolution has on the S-axis a chosen direction, a kind of MASSIVE VECTOR. In this the local in time *scale asymmetry* manifests itself. Further, we will consider all these consequences.