CC BY
8
16. ThucydidesTrap. ■■ URL: https://fofeignpolicy.com/ 201 ?/06/09/the-thucyd ides-trap/
17. ISO 3166-1 alpha-3 [e-re source] / ISO Online Browsing Platform. - URL https://www.iso.org/objVui/
18. The New York Times. The Morning, October 09. 2022. Ian Prasad Phiibrick. North Korea's Threat. -U RL: h tips://www.nytimes.com/2022/10/09/briefi ng/ nort h-korea- n uc lea r-tests.h Em!
19. World Bank. 2022. Lebanon Public Finance Review: Pon/i Finance? - Washington, DC. - https:/
/openknowledge.worldbank.org/handle/10986/ 37824
20. World Bank. Press release, August 2, 2022. Lebanon's PonvA Finance Scheme Has Caused Unprecedented Social and Economic Pain to the Lebanese People. - https://www.worldbank.org/ en/news/press-re!ease/2022/08/02/!ebanon-s-ponzi- finance-scheme-has-c a used-unprecedented-social-and-economic-pain-to'the-lebanese-people
МИР В ЭКОНОМИЧЕСКИХ ИНДЕКСАХ, ЗАВИСЯЩИХ ОТ РАЗМЕРА СТРАНЫ. VI. ГЛОБАЛЬНЫЙ МИЛИТАРНЫЙ РОЙ НАД ПЛОСКОСТЬЮ {ВВП, НАСЕЛЕНИЕ}
Сейдаметова Зарема Сейдалиевна, доктор педагогических тук, профессор Темненко Валерий Анатольевич, кандидат физико-математических наук, доцент
Крымский инженерно-педагогический университет имени Февзи Якубова, Симферополь, Республика Крым
Цель исследования - учитывая Милитарный Индекс Mi как экономическую переменную, изучить и описать 1D-, 2D- и 3D-распределения стран мира в пространствах экономических индексов. Для достижения этой цели построено одномерное распределение стран по Мил тарному Индексу Ml в виде Парето-диаграммы и гистограммы; построено 3D распределение стран в трехмерном пространстве экономических индексов {Р.% DI, Ml} (глобальный милитарный рой); построены и детально описаны 20-проекции глобального милитарного роя на плоскости экономических индексов {PI, М1}и{Р1, Mi}, где Продуктовый индекс Р! определяется размером ВВП страны, а Демографический индекс DI определяется численностью населения. Научная новизна заключается в указанных 1D-, 2D- и 3D распределениях стран, впервые построенных в данной статье. Изучение этих распределений выявляет в результате характеристики статистической связи Милитарного индекса с другими экономическими индексами.
Ключевые слова; мировая экономика; экономические индексы; милитарный индекс; продуктовый индекс; демографический индекс.
D0I 1Q.24923/2222-243X.2022-45.18
УДК 339.97:330.43 THE WORLD IN ECONOMIC INDICES DEPENDING
ON A COUNTRY'S SIZE VI THE GLOBAL MILITARY SWARM О VER {GDP, POPULA ТЮЩ-PLANE
The purpose of the study is to study and describe the ID, 2D and 3D distributions of the countries of the world in the spaces of economic indices taking into account the Military Index Mi as an economic variable. To achieve this purpose, a one-dimensional distribution of countries according to the Military Index Ml was constructed in the form of a Pareto diagram and a histogram; a 3D~distribution of countries was built in the three-dimensional space of economic indices {PI, Di, Ml} (the global military swarm); 2D-projections of the global military swarm on the planes of economic indices (Pi, Ml} and {DI, Mi} are constructed and described in detail, where the Product index PI is determined by the size of the country's 0DP, and the Demographic index DI is determined by the population size. The scientific novelty of the research is in these ID-, 2D- and-3D distributions of countries, that construc ted in this paper fot the first time. The study of these distributions reveals, as a result, the characteristics of the statistical relationship of the Military Index with other economic indices.
Keywords: world economy; economic indices; the military index; the product index; the demographic index.
Introduction
In the previous paper the normalized Military Index Mi was introduced. This index describes the military capabilities of the countries. The normalized index Ml was introduced using some monotone nonlinear mathematical transformation of the weü-known scale of assessing the military capabilities of countries "The Global Firepower ranking" [1]. The electronic appendix to the previous paper (https://bit.ly/3SviXZL) provides
ВАК РФ 5.2.5
0 Seidameto va Z.S., 2022 Ф Temnenko V.A., 2022
SEIDAMETOVA Zarema SeidaNevna, DSc of Pedagogical sciences, Professor
TEMNENKO Va/erii Anatolievich, PhD of Physics and Mathematical sciences, Associate Professor
Fevzi Yakubov Crimean Engineering-Pedagogical University, Simferopol, Republic of Crimea
a complete list of countries for which the Military Index Ml is known in 2021, as well as other economic indices. There are 137 countries on this list.
The purpose of this study is to interpret the Military Index Mt as one of the economic characteristics of each country, to build 1D-, 2D-and 3D-distributions of the countries of the world in such spaces of economic indices in which one of the coordinate axes is the axis of the Ml index. This purpose structures the following tasks: 1) build and describe one-dimensional distributions of countries according to the Mi Military index in the form of a Pareto diagram and a histogram; 2) construct and describe the general features of the 3D distribution of countries in the three-dimensional space of economic indices {PI, Di, Mi} ("the global military swarm"); 3) build and describe 2D-projections of the giobai military swarm on the planes of economic indices {Pi, Mi} and {Di, Ml}, where the Product index PI is determined by the size of the country's GDP in 2021, and the Demographic Index DI is determined by the population size of the country in 2021. The theoretical basis of this study is the previous paper, as well as papers [2], [3], 14], [5]. The practical significance of this study is to identify statistical relationships between the economic indices Pi, DI and the Military Index Ml.
Main part
Distribution of countries according to the Military index Ml. The fig. 1 shows the Pareto chart of the distribution of countries according to the Mifitary Index Mi in 2021. This chart is based on the electronic supplement (https://bit.ly/3SviXZL) of the previous paper. On the Pareto chart, countries are arranged in descending order of the index Ml. We calculated the index Ml using formulas (1) and (2} of the previous paper, using Powerlndex f for each country from the database [1]. The list 11] contains 142 countries. For the remaining countries in ¡"1 ], the Powerlndex value is not given.
These countries not included in the list [1 ] are small countries with small GDP and small population. Among countries with an unknown Military index Mi, only one country has a Product Index Pi greater than one percent: Hong Kong
SAR (PM.60). But Hong Kong, in the political sense, has already been absorbed and almost "digested" by China, and its military potential has no independent significance. Among countries with an unknown value of the Military index Ml, there are six countries with a Product Index PI from 0.1 to 0.5. All other countries with an unknown Mf Military index have a Product Index PI of ¡ess than one tenth of a percent. Countries that do not have a Military Index M! also have a low Demographic index DI. Only three countries without a known Military Index Ml have a Demographic Index Di above one percent in 2021: Malawi (DM.52), Senegal (DM.22) and Guinea (DM,01). All other countries with unknown Ml have Dicl.O.
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Fig. 1. Pareto chart of the distribution of countries according to the Military Index Ml in 2021
Pareto chart on the fig. 1 ailows to see the following obvious facts: 1) there are three countries with very large values of the Military Index Ml; they are United States (MM 00), Russia (Mi=89.64) and China (MI-87.75); 2) there is a group of about twenty countries following on the Pareto chart behind this trio of military supergiants; in this group, Mi is greater than 10 but less than 45; 3) there is a group of about twenty countries, "closing" the Pareto chart; in this group MISI.
There are histograms of the distribution of countries according to the Military index Ml on the fig. 2a and 2b. The first histogram (fig. 2a) displays all 142 countries from the list ¡"1 ]. On this histogram, as well as on the Pareto diagram in fig. 1, one can see an isolated trinity of the already mentioned military supergiants and two dozen military giants following the supergiants in the interval from Ml 10 to Mi 45. In the region of small Mi (Mf <10) fig. 2a creates an idea of a monotonous
increase in the density of countries on the histogram as the index Ml decreases. However, this is a faise impression. Fig. 2b shows a more detailed picture of the distribution of countries by Mi at small Ml. This figure shows that the distribution of countries by Mi is non monotonous: the maximum concentration of countries on the histogram is concentrated in the interval from Ml«1.0 to Ml«2.0. On the histogram in fig. 2b, with a certain degree of conditionality, a group of countries with an index Mi from Mt»2.0 to M!«5.0 and a group of countries with an index Ml from M!«5.0 to MM 0.0 can be distinguished with a certain degree of conventionality as some substructural elements.
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Fig. 2. Histogram of the distribution of countries according to the Military Index MI in 2021
We can say that the Pareto diagram and the histogram of the distribution of countries according to the Military index Ml allow us to select such intervals of the axis Ml for a more detailed study: 1} Military supergiants (Ml>45); 2) Military giants (10<MI<45); 3) Countries on the
interval along the Mi axis from Mi=5 to Ml=10; 4) Countries on the interval along the Ml axis from Mi=2 to Mf=5; 5) Countries on the interval along the Mi axis from Ml=1 and Ml=2; 6) Countries with lowMI (Ml<1).
The Global Military Swarm in 2021. The fig. 3, built according to the data of the electronic appendix (https://bit.ly/3SviXZL) to the previous paper, presents a 3D image of the state of the world in 2021 in a three-dimensional space of indices {Dl, PI, Mi). Fig. 3a shows the whole 3D cube in this space with dimensions 100x100x100. There are 137 dots-countries in this figure. Five countries with a known Ml index are not listed at https://bit.ly/3SviXZL because other 2021 economic indices are not known for them. The position of each country in the figure is determined by the trio of its indices Dl, Pi, Ml. in this figure, the supergiants are clearly visible isolated from all other points: USA and China (supergiants according to the criteria of all three indices, i.e. economic, demographic and military supergiants); India (supergiant only by the demographic index, according to the other two indices, this country belongs to the class of "giants"; the definition of the terms supergiant, giant accordi ng to the Pi and Dl indices is given in [2] and [3]); Russia (supergiant only by military index). In addition to these four supergiants in Fig. 3a, one can consider another one and a half dozen countries-points belonging to the class of giants. All other dot-countries form a quasi-continuous array in this figure, in which it is * r s ? * s; difficult to isolate individual
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dots.
On fig. 3b on a scale slightly enlarged compared to fig. 3a shows only a part of the global cube of economic indices 35x35x35. This part of the global cube contains all the countries of the world, except for the above-mentioned supergiants.
In the fig. 3b you can see how isolated points are about three dozen countries, the rest again appear as an almost continuous array in which it is difficult to see individual countries.
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Fig. 3.The Global MilitarySwarm 2021 in the 3-dimensional {DI, PI, Ml}-$pace
To study the structure of this global military swarm, special tools are needed. The one-dimensional distributions of countries according to the military index (fig. 1 and fig. 2) carry too little information. The three-dimensional distribution in {DI, Pi, M!}-space is not very convenient for analysis.
Distribution of countries on the plane {Pi, Ml}. Fig. 4 (a, b, c, d, e) shows the distribution of countries on the plane of economic indices {PI, Mi} in 2021 .The Product index P! introduced by us in [2] is related to GDP by a simple relationship:
PI =
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max{GDP}
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(i)
where the numerator is the country's GDP in 2021, expressed in current US dollars, and the denominator is the maximum GOP value achieved in 2021 in some country in the world (such a country is the United States).ThePI product index is expressed as a percentage, but we will generally
omit the percent symbol {%) in the PI entry.
In all figures 4, countries are designated by standard three-letter abbreviated names according to the international standard [6]. These abbreviated names are given in the electronic appendix to the previous paper. Fig. 4 is based on data provided in this appendix.
Fig. 4a shows the names of three countries of military supergiants (USA, Russia, China) and fifteen countries from among the military giants. We define a country as a military giant if its Military Ml belongs to the interval (10, Mi№], where Mi№=44.l 3 is the Indian Military Index. The country with the lowest Ml, whose name is inscribed in Fig. 4a, is Israel (MI-16.08). in the group of Military Giants there are six more countries whose names we have not shown in Fig. 4a, in order not to clutter the figure. These countries have a Military Index less than Israel. These are Spain (Mt=l4.5l), Saudi Arabia (Ml=14.19),Taiwan Province of China (Ml—1 3.07), Ukraine (Ml=12.87), Canada (Mi=11.66) and Poland (Ml=10.03) The country name "Taiwan" is given in the form as it is used in the IMF databases.
Fig. 4a shows the main diagonal of the figure. On this line Mi-Pi. We called this diagonal the "security boundary by economic criterion". The same "security boundary" is shown in the remaining figures 4 b, c, d, e. There are (as of 2021) only two countries in the worid with an MI/PI ratio less than one. These are Ireland (Ml=1.80, Mi/ Pi=0.83) and Iceland (Ml=0.053, Ml/Pi=0.48). The USA are directly on this "security boundary" (Ml = 100, Pl = 100). Almost on this "security boundary" is Germany (Ml=18.18, M)/PI=0.99). All other countries in 2021 had an Ml/Pi ratio greater than one.
Fig. 4b, 4c, 4d, 4e are obtained sequentially from fig. 4a using the "magnifying glass method" - by zooming in along the axes of the indices Pi and Mi in order to see the details of the distribution of countries on the {PI, Ml}-plane at small vaiues of PI and Ml.
Fig. 4b Is inscribed with the ISO abbreviated names of 28 countries whose military index Mi belongs to the interval (5, 10J. These countries, approximately equivalent in terms of military
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capabilities, represent a mixture of countries with very different levels of economic productivity. Six of them are among the most productive, called 'hot' economies (Sweden, Switzerland, Norway, United Arab Emirates, Netherlands, Singapore) Three countries belong to the so-called "warm" economies (Greece, Czech Republic, PortugaljThe rest belong to low-productive "cold" economies.
For definitions of the terms "hot", "warm", and "cold" economies, see [21 and [3]. Some countries with a "cold" economy must stress their economic capabilities hard enough to provide those high enough values of the Military Index shown in fig. 4b.The record holders are Venezuela (MI/PI=31.0) and Myanmar (MI/PI=24.71). The high level of military concern inherent in these countries.
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On fig. 4c the abbreviated names of thirty-three countries are inscribed, the Military Index of which belongs to the interval (2; 5]. This group of countries, approximately equivalent in military capabilities, is a mixture of countries that differ very much in economic productivity. Six countries from this group are among the most productive "hot" economies (Denmark, Austria, Finland, Belgium, Qatar, New Zealand). Seven countries of this group belong to fairly productive "warm" economies (Hungary, Slovak Republic, Croatia, Kuwait, Oman, Lithuania, Slovenia). Twenty countries of this group groups belong to "cold", low-productive economies. Some of them, in order to maintain the desired level of the Military Index Ml, must strain their economic capabilities quite strongly. Record holders in this sense are Chad fM l/PI =41.33), Yemen (MI/PI= 29.49), Georgia (Mi/PI=25.58).
On fig. 4d, we focus on the group of countries that have a Military Index Ml belonging to the interval (1; 2]. This group includes 33 countries. The figure shows the abbreviated names of eighteen countries in this group. The names of the remaining countries in this group are not shown in the figure so as not to clutter up the figure. The entire list of countries in this group can be found by the reader using the electronic appendix to the previous paper https://bit.ly/3SviXZL, in which the countries are listed in descending order of the index Ml,
In this group of thirty-three countries, only one country belongs to highly productive "hot" economies. This is Ireland (Ml=1.80, MI/PI-0.83). Four countries belong to the "warm" economies:
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Latvia (№11=1'.83, Ml/PI=10.73), Bahrain (Ml=1.79, MI/PI=10.58), Uruguay (Ml=1.70, Ml/Pi=6.57), Estonia (Ml=1.57, Mi/Pi=9.94). The rest of the countries in this group belong to low-productive "cold" economies. Some of them have a very high MI/PI ratio, which is necessary in order to provide the desired level of the Military index with a low GDP, The record holders here are South Sudan (MI/PI=73.86), Kyrgyz Republic (MI/PI-50.93), Tajikistan (MI/PI=41.56).
Fig. 4e shows the abbreviated names of the nineteen least militarized countries with a Military Index Mi of less than one percent In this group, two countries belong to the "hot" economies. These are Luxembourg (Ml=0.93, MI/PI=2.48) and Iceland (Mi=0.053, MI/PI=0.48). All other countries in this group belong to the "cold" economies. Someofthern have an abnormally high MI/PI ratio, which is necessary to maintain an acceptable level of the Military Index for the country, despite the low GDP value.The record holders here are Eritrea (M!=l .00, Ml/PM 01.37), Central African Republic (Ml=0.80, MI/PI=70.93) and Suriname (MN0.56, Ml/ Pl=45.12).
Distribution of countries on the {Dl, Mi}~ plane. Fig. 5 (a, b, c, d, e) shows the distribution of countries on the plane "Military Index Mi / Demographic index Dl".
Demographic Index Dl was introduced by us in papers [2], [3]. It is defined by the following formula:
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The numerator of this formula Is the population of the country in 2021, and the denominator is the population of the most populous country in 2021 (China). The index Dl is defined as a percentage, but we usuafiy omit the percent symbol (%) when writing this index.
Figure 5 does not need a detailed description. The transition from fig. 5a to fig. 5e follows the same "magnifying glass method" that was used in constructing fig. 4. in fig. 5 is inscribed with abbreviated names of the same countries as in fig.4.
What is the difference between figures 4 and 5?The difference between these drawings is in the position of the "security boundary". This "security boundary" according to the demographic criterion is drawn as a line with a slope MI/DI=(MI/ Dl) =0.4478. India has this MI/DI ratio. Another
IND
country has almost the same MI/DI ratio: Dem. Rep. of Congo (MI/DI=0.4429). Only two countries in the world have a MI/DI ratio below this "Indian security boundary". These are Tanzania (Mi=1.46; Ml/ Dl=0.346) and Somalia (Mi=0.35; MI/DI =0.325). All other countries in the world have Mi/Dl> (MI/DI )№
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Conclusions
The paper presents and analyzes the one-dimensional distribution of countries according to the Military index Ml. The two-dimensional distributions of countries on the planes "Military Index / Product index" and "Military index / Demographic Index" are also presented and described. These two-dimensional distributions characterize the impact of each country's economic and demographic capabilities on that country's military capabilities. It is noted that some low production countries with a "cold" economy must significantly strain their economic opportunities to build an acceptable value of the Military index for them.
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1. The Global Firepower ranking. - URL: https:// www.gjobalfirepower.com/counTries-listing.php
2. Seidametova Z.S. The World in economic indices depending on a country's size. I. The World on the {Population, GDP}-piane / Z.S. Seidametova, V.A. Temnenko // KANT, № $ (44), 2022. - С. 68-74.
3. Seidametova Z.S, The World in economic indices depending on a country's size. li. Global Scale Matrix / Z. S. Seidametova, V. A. Temnenko // KANT, № 3 (44), 2022. - C. 74-79.
4. Seidametova Z.S. The Worid in economic indices depending on a country's size. HIThe Absolute Power Index / 7... S. Seidametova, V. A.Temnenko // Ученые записки Крымскою инженерно-педагогического университета, №4(78), 2022. - С. 131-138.
5. Seidametova Z.S, The World in economic indices depending on a country's size. IV. The Absolute Power / Productivity Matrix 11. S. Seidametova // Ученые записки Крымскою инженерно-педагогического университета, № 4 (78), 2022. - С. 138-144.
6. ISO 3166-1 alpha-3 [e-resource] / ISO Online Browsing Platform. - URL: https://www.iso.org/ obp/ui/
