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In human societies, we observe a wide range of types of stratification, i.e., in terms of financial class, political power, level of education, sanctity, and military force. In financial, political, and social sciences, stratification is one of the most important issues and tools as the Lorenz Curve and the Gini Coefficient have been developed to describe some of its aspects. Stratification is greatly dependent on the access of people to wealth. By “wealth”, we mean the quantified prosperity which increases the life expectancy of people. Prosperity is also connected to the water‐food‐energy nexus which is necessary for human survival. Analyzing proxies of the water‐food‐energy nexus, we suggest that the best proxy for prosperity is energy, which is closely related to Gross Domestic Product (GDP) per capita and life expectancy. In order to describe the dynamics of social stratification, we formulate an entropic view of wealth in human societies. An entropic approach to income distribution, approximated as available energy in prehistoric societies, till present‐day economies, shows that stratification can be viewed as a stochastic process subject to the principle of maximum entropy and occurring when limits to the wealth of society are set, either by the political and economic system and/or by the limits of available technology.
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Article
Stratification: An Entropic View of Society’s Structure
G.-Fivos Sargentis * , Theano Iliopoulou , Panayiotis Dimitriadis , Nikolaos Mamassis
and Demetris Koutsoyiannis


Citation: Sargentis, G.-F.; Iliopoulou,
T.; Dimitriadis, P.; Mamassis, N.;
Koutsoyiannis, D. Stratification: An
Entropic View of Society’s Structure.
World 2021,2, 153–174. https://
doi.org/10.3390/world2020011
Academic Editor: Manfred
Max Bergman
Received: 25 February 2021
Accepted: 26 March 2021
Published: 30 March 2021
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Licensee MDPI, Basel, Switzerland.
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distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Laboratory of Hydrology and Water Resources Development, School of Civil Engineering,
National Technical University of Athens, Heroon Polytechneiou 9, 157 80 Zographou, Greece;
tiliopoulou@hydro.ntua.gr (T.I.); pandim@itia.ntua.gr (P.D.); nikos@itia.ntua.gr (N.M.); dk@itia.ntua.gr (D.K.)
*Correspondence: fivos@itia.ntua.gr
Abstract:
In human societies, we observe a wide range of types of stratification, i.e., in terms of
financial class, political power, level of education, sanctity, and military force. In financial, political,
and social sciences, stratification is one of the most important issues and tools as the Lorenz Curve
and the Gini Coefficient have been developed to describe some of its aspects. Stratification is greatly
dependent on the access of people to wealth. By “wealth”, we mean the quantified prosperity
which increases the life expectancy of people. Prosperity is also connected to the water-food-energy
nexus which is necessary for human survival. Analyzing proxies of the water-food-energy nexus, we
suggest that the best proxy for prosperity is energy, which is closely related to Gross Domestic Product
(GDP) per capita and life expectancy. In order to describe the dynamics of social stratification, we
formulate an entropic view of wealth in human societies. An entropic approach to income distribution,
approximated as available energy in prehistoric societies, till present-day economies, shows that
stratification can be viewed as a stochastic process subject to the principle of maximum entropy and
occurring when limits to the wealth of society are set, either by the political and economic system
and/or by the limits of available technology.
Keywords: inequality; stratification; socioeconomic; entropy; stochastic analysis
«
τγρχ
o
ντι π αντδ
o
θήσεται καπερισσευθήσεται
,
πδτ
o
µὴ ἔχ
o
ντ
o
ς κα
ὃ ἔχει ρθήσεται π ατo» (Kαινή∆ιαθήκη, KατάMατθαίoν25:29) [1]
“For everyone who has, will be given more, and he will have an abundance. Whoever does
not have, even what he has will be taken from him.” (New Testament, Matthew 25:29)
1. Introduction
Social stratification in the history of human societies occurs persistently and organi-
cally, as if it obeys a natural law. There is a wide range of types of stratification in societies,
i.e., in terms of financial class, political power, level of education, sanctity, and military
force. In economic, political, and social sciences, stratification is one of the most important
issues [2,3].
After the Middle Ages, emblematic approaches examining social stratification were
formulated, the most widely known are those of Adam Smith (1723–1890), David Ricardo
(1772–1823), Thomas Robert Malthus (1766–1834), Social Darwinists (late 1800s), and Karl
Marx (1818–1883).
Smith noted that “wherever there is great property, there is great inequality, for
one very rich man, there must be at least five hundred poor”. He also pointed out the
important role of morality in social functioning and noted that without the welfare of the
laboring classes the prosperity of the nation is both morally unacceptable and practically
impossible [4,5].
Unlike Smith, Ricardo supported the iron law of wages [
6
], according to which
working-class wages must be fixed at a “natural price” that would only cover the costs
of marginal survival, arguing that, from prehistoric times, most grangers also lived in
World 2021,2, 153–174. https://doi.org/10.3390/world2020011 https://www.mdpi.com/journal/world
World 2021,2154
misery [
7
]. Exceeding Ricardo’s cynicism, Malthus suggested that the most effective so-
lution would be the abandonment and natural extermination of malnourished people
claiming that population growth acted as a deterrent to the progress of a society because
the population was supposedly much larger than what the earth could sustain [8].
Herbert Spencer (1820–1903) and Francis Galton (1822–1911), inspired by Charles
Darwin’s propositions that are described in “Origin of Species” (1859) [
9
], advocated the
concept of survival of the fittest in the social world, an approach called Social Darwinism
(n.b., Galton was also the father of eugenics). According to this, the state should not
interfere in the spontaneous processes of society, leaving the ‘strongest’ people to survive
and the ‘weak’ to perish, which would presumably lead to ever higher levels of society’s
development [10,11].
Subverting the prevailing theories, Marx argued that social classes were formed
unnaturally during the historical period of humankind as a result of extreme material
inequalities created by the over-exploitation of the working-class labor by the owners of the
means of production [
12
]. Thus, he formulated the rule “From each according to his ability,
to each according to his needs” [13,14]. Another influential economic approach of the last
century was presented by John Keynes (1883–1946) in “The General Theory of Employment,
Interest and Money” [
15
]. Arguably, the prevailing theory of modern times is neoliberalism,
a policy model that emphasizes the value of free market competition. The theory was
supported by the Chicago School and notably expressed by the works of Milton Friedman
(1912–2006) [
16
] and Friedrich Hayek (1899–1992) [
17
]. Critiques on neoliberalism have
been expressed pertaining to its relation with inequality, e.g., as described by Zoya Hasan
in “Democracy and the crisis of inequality” [
18
] and Walter Rodney (1942–1980) in “How
Europe Underdeveloped Africa” [19].
In economic analysis, common tools to show stratification are the Lorenz Curve
[2022]
and the Gini Coefficient [
23
25
], which have been developed to describe the income distri-
bution [
26
29
]. There are several famous financial approaches and analyses of the world’s
income distribution [
30
,
31
] which led to new economical-mathematical and philosophical
formulations [
32
]. Perhaps the most famous of the related mathematical inventions is the
Pareto distribution, originally formulated by Vilfredo Pareto to describe the power-law
type distribution of land-ownership in society [
33
]. Today, the Pareto distribution has
become a standard tool in financial analysis, e.g., [34].
Entropy has also been used in many related books and papers, within various ap-
proaches describing society. Ryu [
35
] presents an information efficient technique to deter-
mine the functional forms of income distributions using maximum entropy estimation of
income distributions. In another paper by Ryu [
36
], a bottom poor sensitive Gini coefficient
(pgini) is defined by replacing income observations with their reciprocal values in the
Gini coefficient using maximum entropy estimation of income shares. Fu et al. [
37
], using
entropy divergence methods, seek a probability density function solution that is as close to
a uniform probability distribution of income. Dinga et al. [38] introduce a new concept of
social entropy and a new concept of social order, both based on the normative framework
of society. From these two concepts, typologies (logical and historical) of societies are
inferred and examined in terms of their basic features. Davis [
39
] brings out how the
physical/mathematical notions of entropy can be usefully imported into the social sphere.
Mayer et al. [
40
], based on entropic unit free measures, such as Shannon entropy, provide a
theoretical framework for studying the dynamics of coupled human and natural systems.
Johansson [
41
] relates entropy with the complexity of a number of products, as represented
by the number of their functional parts, to their actual economic value. Neto et al. [
42
]
describe an elementary process of social interaction exploring a particular concept, “so-
cial entropy”, i.e., how social systems deal with uncertainty and unpredictability in the
transition from individual actions to systems of interaction. Mavrofides et al. [
43
] shed
light on the notions of entropy and energy as conceived in the theoretical framework of
social sciences.
World 2021,2155
In this paper we make the working hypothesis that the social stratification is related
to the principle of maximum entropy. We try to investigate the entropic characteristics
of societies and examine whether stratification is a process consistent to the principle of
maximum entropy. In order to see this, we investigate the income distribution in prehistory
and antiquity, and we validate it from an entropic viewpoint. We choose the entropic view
because according to Koutsoyiannis:
Entropy and its ability to increase (as contrasted to energy and other quantities that
are conserved) is the driving force of change. This property of entropy has seldom
been acknowledged; instead in common perception entropy is typically identified with
disorganization and deterioration as if change can only have negative consequences [
44
].
Social structures are constantly changing, and this property of entropy is essential in
order to understand and predict these changes.
For this evaluation we formulate and use the tools of total entropy of income distribu-
tion
Φ[x]
which, as we show, is related to Gross Domestic Product (GDP) per capita (the
best-known growth index) and an entropic index of inequality,
Φ
, which is correlated
with the Gini index, but shows more robust performance. Both of them are validated by
real-world income data. Note that underlined symbols denote random variables.
In order to study stratification in prehistory and antiquity, we have to define the wealth
in these periods in non-monetary values. To this end, we study the water-food-energy
nexus, which is necessary for human survival. From these three variables, data show that
the best proxy for prosperity is energy, as energy is best correlated with life expectancy
and GDP per capita and, on top, can be reliably estimated in the prehistory and antiquity,
which, e.g., cannot be done in the case of food.
Anthropologists believe that, in prehistory, humans lived as nomads without stratifi-
cation [
45
48
], or with a faint one [
49
]. Hunter-Gathers needed a small amount of energy to
collect food, but, when they clustered in agricultural societies, energy needs were increased.
Therefore, they used animals to cover new needs and produce surplus energy. This signifies
a new technology which, however, is limited by a rather low technological limit. Assuming
egalitarian society and equal distribution of energy per capita in Hunter-Gatherers, we see
that, if we assume more energy and maximize entropy, society’s structure follows an expo-
nential stratification. This fact is consonant to Surplus Theory of Social Stratification [
50
,
51
]
as “the equal distribution of wealth in societies with surpluses is so rare as to be almost
non-existent” [
52
]. Interestingly, extreme stratification occurs in much later periods of
fast-growing technological limit and installation of new energy sources, such as the period
of mercantilism and the industrial revolution.
In order to investigate the dynamics of income distribution in entropic terms, we
evaluate current economic data. First, we compare data from United Kingdom and Sweden
in the period 1970–2010, i.e., from two totally different countries in terms of political
orientation (neoliberal-social democratic). Results show characteristic differences and
insights which are not derived by the usual financial tools as GDP per capita, Lorenz Curve
and Gini coefficient. By another evaluation, we revisit the Greek financial crisis, seeing that,
after First Memorandum [
53
] in 2010, the total entropy reduced abruptly and followed
by a new immigration type, known as brain-drain [
54
], targeting the United Kingdom, a
country with much higher entropy.
The remaining of the paper is structured in the following sections. In Section 2, we
evaluate the aspects of the water-food-energy nexus as proxies for wealth concluding that
the best proxy for wealth in prehistory is energy per capita. In Section 3, we analyze the
characteristics of income inequality from prehistory till the present day and formulate two
new entropic measures, an index of growth and an index of inequality. In Section 4, we
discuss the results of the evaluation in view of the principle of maximum entropy, whereas
we draw conclusions and discuss wider scientific reflections in Section 5.
World 2021,2156
2. Prosperity: The True Wealth
Stratification is dependent on the access of people to wealth. By “wealth”, we mean
the quantified prosperity which increases the life expectancy of people, e.g., as seen for GDP
(Figure 1a,b). In this regard, Confucius famously said that “the first wealth is health” [
55
,
56
].
Prosperity is also connected to the water-food-energy nexus which is necessary for
human survival. According to the United Nations report [
57
], “Agriculture is the largest
consumer of the world’s freshwater resources, and more than one-quarter of the energy
used globally is expended on food production and supply.” Therefore, we investigate
separately each aspect of the nexus to assess its relevance as an index of prosperity, here
studied through the GDP per capita.
World 2021, 2, FOR PEER REVIEW 4
2. Prosperity: The True Wealth
Stratification is dependent on the access of people to wealth. By “wealth”, we mean
the quantified prosperity which increases the life expectancy of people, e.g., as seen for
GDP (Figure 1a,b). In this regard, Confucius famously said that “the first wealth is health”
[55,56].
Prosperity is also connected to the water-food-energy nexus which is necessary for
human survival. According to the United Nations report [57], “Agriculture is the largest
consumer of the world’s freshwater resources, and more than one-quarter of the energy
used globally is expended on food production and supply.” Therefore, we investigate sep-
arately each aspect of the nexus to assess its relevance as an index of prosperity, here stud-
ied through the GDP per capita.
(a) (b)
Figure 1. GDP per capita per year related to life expectancy; (a) global average through 1870–2011;
(b) average per country in 2018 [58].
2.1. Water
Although the withdrawal of water has been globally increased over the last 100 years,
since the population is growing just as fast, it appears that the water withdrawal per capita
has remained almost stable (Figure 2a). It is also seen that water withdrawal per capita is
not a good proxy of the GDP per capita, as the data show a big scatter (Figure 2b). This
may be explained considering natural factors, such as the climate and the economical pro-
file, of each country [59].
(a) (b)
Figure 2. GDP per capita per year related to freshwater withdrawal; (a) global average through
1870–2011; (b) average per country in 2018 [60–63].
Figure 1.
GDP per capita per year related to life expectancy; (
a
) global average through 1870–2011;
(b) average per country in 2018 [58].
2.1. Water
Although the withdrawal of water has been globally increased over the last 100 years,
since the population is growing just as fast, it appears that the water withdrawal per capita
has remained almost stable (Figure 2a). It is also seen that water withdrawal per capita is
not a good proxy of the GDP per capita, as the data show a big scatter (Figure 2b). This may
be explained considering natural factors, such as the climate and the economical profile, of
each country [59].
World 2021, 2, FOR PEER REVIEW 4
2. Prosperity: The True Wealth
Stratification is dependent on the access of people to wealth. By “wealth”, we mean
the quantified prosperity which increases the life expectancy of people, e.g., as seen for
GDP (Figure 1a,b). In this regard, Confucius famously said that “the first wealth is health”
[55,56].
Prosperity is also connected to the water-food-energy nexus which is necessary for
human survival. According to the United Nations report [57], “Agriculture is the largest
consumer of the world’s freshwater resources, and more than one-quarter of the energy
used globally is expended on food production and supply.” Therefore, we investigate sep-
arately each aspect of the nexus to assess its relevance as an index of prosperity, here stud-
ied through the GDP per capita.
(a) (b)
Figure 1. GDP per capita per year related to life expectancy; (a) global average through 1870–2011;
(b) average per country in 2018 [58].
2.1. Water
Although the withdrawal of water has been globally increased over the last 100 years,
since the population is growing just as fast, it appears that the water withdrawal per capita
has remained almost stable (Figure 2a). It is also seen that water withdrawal per capita is
not a good proxy of the GDP per capita, as the data show a big scatter (Figure 2b). This
may be explained considering natural factors, such as the climate and the economical pro-
file, of each country [59].
(a) (b)
Figure 2. GDP per capita per year related to freshwater withdrawal; (a) global average through
1870–2011; (b) average per country in 2018 [60–63].
Figure 2.
GDP per capita per year related to freshwater withdrawal; (
a
) global average through
1870–2011; (b) average per country in 2018 [6063].
World 2021,2157
On the other hand, municipal water withdrawal shows a weak correlation to GDP,
as access to water is not evenly distributed and people who live in richer countries with
higher technological potential have better access (Figure 3). Still, in this case, as well, the
statistical relationship is not very robust, as access to water is also greatly dependent on
geographic location and climate. For these reasons, water is not evaluated here as the
main indicator of prosperity. Yet, we note that water infrastructure is closely related to life
expectancy because proper water supply and sanitation enhance public health.
World 2021, 2, FOR PEER REVIEW 5
On the other hand, municipal water withdrawal shows a weak correlation to GDP,
as access to water is not evenly distributed and people who live in richer countries with
higher technological potential have better access (Figure 3). Still, in this case, as well, the
statistical relationship is not very robust, as access to water is also greatly dependent on
geographic location and climate. For these reasons, water is not evaluated here as the main
indicator of prosperity. Yet, we note that water infrastructures is closely related to life
expectancy because proper water supply and sanitation enhance public health.
(a) (b)
Figure 3. GDP per capita per year related to: (a) municipal water withdrawal per capita per year,
average per country in 2018; (b) access to safe drinking water, average per country in 2018 [64,65].
2.2. Food
Contrary to water, food seems to be a more robust proxy for prosperity (Figure 4). It
is obvious that, living prosperously (in terms of higher GDP) is associated with higher
caloric supply, following the same pattern of GPD and life expectancy, as seen in the case
of the United Kingdom (Figure 5). Even in this case, in which we have a long series of
data, it is difficult to adjust this proxy to prehistory and antiquity as the food was related
to the culture of living at the time, and relevant data are not readily available.
(a) (b)
Figure 4. GDP per capita per year related to daily caloric supply; (a) global average through 1960–
2011; (b) average per country in 2018 [66].
Figure 3.
GDP per capita per year related to: (
a
) municipal water withdrawal per capita per year,
average per country in 2018; (b) access to safe drinking water, average per country in 2018 [64,65].
2.2. Food
Contrary to water, food seems to be a more robust proxy for prosperity (Figure 4). It is
obvious that, living prosperously (in terms of higher GDP) is associated with higher caloric
supply, following the same pattern of GDP and life expectancy, as seen in the case of the
United Kingdom (Figure 5). Even in this case, in which we have a long series of data, it
is difficult to adjust this proxy to prehistory and antiquity as the food was related to the
culture of living at the time, and relevant data are not readily available.
World 2021, 2, FOR PEER REVIEW 5
On the other hand, municipal water withdrawal shows a weak correlation to GDP,
as access to water is not evenly distributed and people who live in richer countries with
higher technological potential have better access (Figure 3). Still, in this case, as well, the
statistical relationship is not very robust, as access to water is also greatly dependent on
geographic location and climate. For these reasons, water is not evaluated here as the main
indicator of prosperity. Yet, we note that water infrastructures is closely related to life
expectancy because proper water supply and sanitation enhance public health.
(a) (b)
Figure 3. GDP per capita per year related to: (a) municipal water withdrawal per capita per year,
average per country in 2018; (b) access to safe drinking water, average per country in 2018 [64,65].
2.2. Food
Contrary to water, food seems to be a more robust proxy for prosperity (Figure 4). It
is obvious that, living prosperously (in terms of higher GDP) is associated with higher
caloric supply, following the same pattern of GPD and life expectancy, as seen in the case
of the United Kingdom (Figure 5). Even in this case, in which we have a long series of
data, it is difficult to adjust this proxy to prehistory and antiquity as the food was related
to the culture of living at the time, and relevant data are not readily available.
(a) (b)
Figure 4. GDP per capita per year related to daily caloric supply; (a) global average through 1960–
2011; (b) average per country in 2018 [66].
Figure 4.
GDP per capita per year related to daily caloric supply; (
a
) global average through 1960–2011; (
b
) average per
country in 2018 [66].
World 2021,2158
World 2021, 2, FOR PEER REVIEW 6
Figure 5. GDP per capita per year related to daily caloric supply and life expectancy; (a) United
Kingdom’s, GDP, caloric supply data from: 1270–2016 life expectancy data from: 1800–2016
[66,67].
2.3. Energy
A clear correlation is observed in GDP per capita and energy consumption, as shown
in Figure 6. Wilhelm Ostwald was the first who correlated energy consumption with life
expectancy in 1909 [68]. As we know energy production and energy consumption in pre-
history and antiquity, and we have strong indicators of the way of living [69–72], we em-
ploy the energy per capita as a substitute of income in these periods (Figure 6).
(a) (b)
Figure 6. GDP per capita per year related to consumption of energy per capita per year; (a) global
average data from: 1870–2011; (b) country’s average data from: 2018. [73].
2.4. Validation of Energy as Proxy of Wealth
In the previous paragraphs we saw that, from the water-food-energy nexus, the
proxy which is most robustly related to GDP per capital is energy. Thus, for the analysis
of social stratification in prehistory and antiquity, instead of GDP per capita, we use en-
ergy consumption per capita.
In order to obtain an overview of the role of energy in society’s evolution, we also
plot the maximum temperatures achieved by humans (Figure 7a) and the power of the
largest prime movers (Figure 7b) in history and before.
Figure 5.
GDP per capita per year related to daily caloric supply and life expectancy; United
Kingdom’s, GDP, caloric supply data from: 1270–2016 life expectancy data from: 1800–2016 [66,67].
2.3. Energy
A clear correlation is observed in GDP per capita and energy consumption, as shown
in Figure 6. Wilhelm Ostwald was the first who correlated energy consumption with
life expectancy in 1909 [
68
]. As we know energy production and energy consumption in
prehistory and antiquity, and we have strong indicators of the way of living [
69
72
], we
employ the energy per capita as a substitute of income in these periods (Figure 6).
World 2021, 2, FOR PEER REVIEW 6
Figure 5. GDP per capita per year related to daily caloric supply and life expectancy; (a) United
Kingdom’s, GDP, caloric supply data from: 1270–2016 life expectancy data from: 1800–2016
[66,67].
2.3. Energy
A clear correlation is observed in GDP per capita and energy consumption, as shown
in Figure 6. Wilhelm Ostwald was the first who correlated energy consumption with life
expectancy in 1909 [68]. As we know energy production and energy consumption in pre-
history and antiquity, and we have strong indicators of the way of living [69–72], we em-
ploy the energy per capita as a substitute of income in these periods (Figure 6).
(a) (b)
Figure 6. GDP per capita per year related to consumption of energy per capita per year; (a) global
average data from: 1870–2011; (b) country’s average data from: 2018. [73].
2.4. Validation of Energy as Proxy of Wealth
In the previous paragraphs we saw that, from the water-food-energy nexus, the
proxy which is most robustly related to GDP per capital is energy. Thus, for the analysis
of social stratification in prehistory and antiquity, instead of GDP per capita, we use en-
ergy consumption per capita.
In order to obtain an overview of the role of energy in society’s evolution, we also
plot the maximum temperatures achieved by humans (Figure 7a) and the power of the
largest prime movers (Figure 7b) in history and before.
Figure 6.
GDP per capita per year related to consumption of energy per capita per year; (
a
) global average data from:
1870–2011; (b) country’s average data from: 2018. [73].
2.4. Validation of Energy as Proxy of Wealth
In the previous paragraphs we saw that, from the water-food-energy nexus, the proxy
which is most robustly related to GDP per capital is energy. Thus, for the analysis of
social stratification in prehistory and antiquity, instead of GDP per capita, we use energy
consumption per capita.
In order to obtain an overview of the role of energy in society’s evolution, we also plot
the maximum temperatures achieved by humans (Figure 7a) and the power of the largest
prime movers (Figure 7b) in history and before.
World 2021,2159
World 2021, 2, FOR PEER REVIEW 7
(a) (b)
Figure 7. (a) Temperatures created by human actions in different eras. (b) Power of the largest prime movers in different
eras [74–76] (diagrams present data in logarithmic scale as order of magnitude).
3. Stratification and Entropy
3.1. Prehistorc Societies
In prehistory, humans lived in tribes (Hunter-Gatherers), having almost the same
technological limit consisting of their own power (~120 W) and metabolized their food,
~2500 kcal, producing and using ~3 kWh per day muscular energy. So, energy in Hunter-
Gatherers societies was equally distributed. Population was sparse and the natural re-
sources were ample with ~100 ha sufficing to produce food for one human.
Generally, anthropologists assume that Hunter-Gatherers lived without stratification
[48–50], but some approaches show that there was a stratification in prehistory [51]. A
related paper estimates average Gini coefficient, an overall measure of wealth inequality,
assuming multiple parameters in Hunter-Gatherers, equal to 0.25 [49], which shows a
faint stratification.
In order to cluster in tribes [77,78], humans had to use smaller areas to collect food.
(Figure 8). In the period of pastoralism, humans were clustered 50 times more than
Hunter-Gatherers, and, when traditional farming was developed, clustering increased re-
spectively (Table 1). At the same time, energy required per ha was ~100 and ~200 times
more (Figure 9) [75,76,79–87]. Sackett found that adults in foraging and horticultural so-
cieties work, on average, about 6.5 h a day, whereas people in agricultural societies work
on average 8.8 h a day [88].
(a) (b)
Figure 8. Typical types of food production in different eras related to: (a) population density; (b) energy needs (diagrams
present data as order of magnitude) [75,76,79–87].
Figure 7.
(
a
) Temperatures created by human actions in different eras. (
b
) Power of the largest prime movers in different
eras [7476] (diagrams present data in logarithmic scale as order of magnitude).
3. Stratification and Entropy
3.1. Prehistorc Societies
In prehistory, humans lived in tribes (Hunter-Gatherers), having almost the same
technological limit consisting of their own power (~120 W) and metabolized their food,
~2500 kcal, producing and using ~3 kWh per day to energy. So, energy in Hunter-Gatherers
societies was equally distributed. Population was sparse and the natural resources were
ample with ~100 ha sufficing to produce food for one human.
Generally, anthropologists assume that Hunter-Gatherers lived without stratifica-
tion [
48
50
], but some approaches show that there was stratification in prehistory [
51
]. A
related paper estimates average Gini coefficient, an overall measure of wealth inequality,
assuming multiple parameters in Hunter-Gatherers, equal to 0.25 [
49
], which shows a faint
stratification.
In order to cluster in tribes [
77
,
78
], humans had to use smaller areas to collect food.
(Figure 8). In the period of pastoralism, humans were clustered 50 times more than Hunter-
Gatherers, and, when traditional farming was developed, clustering increased respectively
(Table 1). At the same time, energy required per ha was ~100 and ~200 times more
(
Figure 9
) [
75
,
76
,
79
87
]. Sackett found that adults in foraging and horticultural societies
work, on average, about 6.5 h a day, whereas people in agricultural societies work on
average 8.8 h a day [88].
Figure 8.
Typical types of food production in different eras related to: (
a
) population density; (
b
) energy needs (diagrams
present data as order of magnitude) [75,76,7987].
World 2021,2160
Table 1.
Prehistoric human, different types of living, minimum area, and energy needs for food
production (present data as order of magnitude) [75,76,7987].
Type of Living Area (ha) Energy Per Capita per Day for Food (kWh)
Hunter-Gatherers 100 1
Pastorals (pastoralism) 2 2.50
Granger (agriculture) 1 3.50
World 2021, 2, FOR PEER REVIEW 8
Table 1. Prehistoric human, different types of living, minimum area, and energy needs for food
production (present data as order of magnitude) [75,76,79–87].
Type of Living Area (ha) Energy Per Capita per Day for Food (kWh)
Hunter-Gatherers 100 1
Pastorals (pastoralism) 2 2.50
Granger (agriculture) 1 3.50
(a) (b)
Figure 9. (a) Population density related to energy needs. (b) Energy needs per capita per day in different types of societies
(diagrams present data as order of magnitude) [75,76,79–87].
Table 1 shows that Hunter-Gathers needed a relatively small amount of their energy
to collect food. Survival needs arising from human clustering are energy intensive, and
more powerful means than humans, as horses and ox (~500 W, ~10 times more) [75,76,89]
were employed. The importance of energy becomes clear if we consider that since Ho-
meric times the size of ox’s or cattle’s herd signified the wealth of a person. The unit of
wealth measurement in Roman Empire was the head of an animal (Latin: capis), which
bequeathed to us the term capital.
However, clustering effect is also related to the environment (earth, weather), and its
natural resources as different areas need different effort and energy to be cultivated.
3.2. Entropic Analysis
If we regard the energy use of humans as a proxy of income in antiquity, and repre-
sent it by a continuous stochastic variable 𝑥 defined in [0, J], we can estimate the income
entropy Φ of society (Equation (1)) as:
𝛷𝑥≔
𝑓
𝑥ln
𝑓
𝑥 d𝑥
, (1)
where 𝑓𝑥 is the probability density function of the random variable 𝑥. Note that the
probability density 𝑓𝑥 should be scaled by a so-called background measure, h(x), e.g.,
a uniform probability density, so that the argument of the logarithm function be dimen-
sionless. Here, we assume ℎ𝑥  1 with dimensions 𝑥 𝑓𝑥 𝑥
 [90]. In the
case that the energy 𝑥 is constant, equal to ~3 kWh per day (muscular energy) for every
Hunter-Gatherer, the entropy becomes theoretically equal to −∞.
To frame our results within the context of standard economics’ analysis of the income
distribution, we employ two well-known measures of socio-economic inequality, the Lo-
renz curve and the Gini coefficient [21–25]. As is usual with economic data we follow the
convention of expressing income distribution in tenths of the share (%) of people from the
lowest to highest income versus share y (%) of income earned. As a first illustration, Figure
10a shows the two cases of the Hunter-Gatherers and granger’s societies constructed with
Figure 9.
(
a
) Population density related to energy needs. (
b
) Energy needs per capita per day in different types of societies
(diagrams present data as order of magnitude) [75,76,7987].
Table 1shows that Hunter-Gathers needed a relatively small amount of their energy to
collect food. Survival needs arising from human clustering are energy intensive, and more
powerful means than humans, as horses and oxen (~500 W, ~10 times more) [
75
,
76
,
89
]
were employed. The importance of energy becomes clear if we consider that since Homeric
times the herd size (oxen or cattle) signified the wealth of a person. The unit of wealth
measurement in Roman Empire was the head of an animal (Latin: capis), which bequeathed
to us the term capital.
However, the clustering effect is also related to the environment (earth, weather), and
its natural resources as different areas need different effort and energy to be cultivated.
3.2. Entropic Analysis
If we regard the energy use of humans as a proxy of income in antiquity, and represent
it by a continuous stochastic variable
x
defined in [0, J], we can estimate the income entropy
Φof society (Equation (1)) as:
Φ[x]:=ZJ
0f(x)ln f(x)dx, (1)
where
f(x)
is the probability density function of the random variable
x
. Note that the
probability density
f(x)
should be scaled by a so-called background measure, h(x), e.g.,
a uniform probability density, so that the argument of the logarithm function be dimen-
sionless. Here, we assume
h(x)=
1 with dimensions
[h(x)] =[f(x)] =x1
[
90
]. In the
case that the energy
x
is constant, equal to ~3 kWh per day (muscular energy) for every
Hunter-Gatherer, the entropy becomes theoretically equal to .
To frame our results within the context of standard economic analysis of the income
distribution, we employ two well-known measures of socio-economic inequality, the
Lorenz curve and the Gini coefficient [
21
25
]. As is usual with economic data we follow
the convention of expressing income distribution in tenths of the share (%) of people from
the lowest to highest income versus share y(%) of income earned. As a first illustration,
World 2021,2161
Figure 10
a shows the two cases of the Hunter-Gatherers and granger’s societies constructed
with some assumptions. We start with the Hunter-Gatherers case, using the simplest
possible assumption, i.e., that all people have the same income, as shown in Figure 10a.
World 2021, 2, FOR PEER REVIEW 9
some assumptions. We start with the Hunter-Gatherers case, using the simplest possible
assumption, i.e., that all people have the same income, as shown in Figure 10a.
(a) (b)
(c) (d)
Figure 10. (a) Share of wealth, using energy as a proxy, in the Hunter-Gatherers and granger’s society; (b) Lorenz curve.
(c) Probability distribution function of energy. (d) Probability density function of the standardized energy.
Figure 10b shows the Lorenz curve, which is the plot of the cumulative share of in-
come versus the corresponding cumulative share of the population. In the case of a perfect
socio-economic equality, it is a straight line. From the Lorenz curve, we can calculate the
Gini coefficient [24,25], which is a measure of socio-economic inequality estimated as: 𝐺
𝐴/𝐴  𝐵, where A is the area that lies between the line of equality and the Lorenz curve,
and B is the area between the Lorenz curve and the horizontal axes. Values of 𝐺 tending
to 0 indicate equality, whereas values closer to 1 indicate total inequality. Hence, for the
Hunter-Gatherer case, the Gini coefficient is 0.
In addition, Figure 10c shows the probability distribution function of the income
𝐹𝑥, and Figure 10d the standardized income probability density 𝑓𝑧, where 𝑧𝑥/𝜇,
i.e., the income standardized by its mean μ. For the Hunter-Gatherer case, the distribution
function is one with a single discontinuity at the value 𝑥3 (kWh), and the density is an
impulse at the same value of x or at 𝑧1.
The grangers’ society is somewhat more complex. The technological limit has been
increased, thanks to the use of tools and animals to cover energy needs. As a result, the
average energy per capita is increased, as well. Here, we will assume that the distribution
of available energy (income per capita) is obtained by the principle of maximum entropy
introduced by Jaynes [91]. While the concept of entropy was much earlier proposed by
Figure 10.
(
a
) Share of wealth, using energy as a proxy, in the Hunter-Gatherers and granger’s society; (
b
) Lorenz curve. (
c
)
Probability distribution function of energy. (d) Probability density function of the standardized energy.
Figure 10b shows the Lorenz curve, which is the plot of the cumulative share of income
versus the corresponding cumulative share of the population. In the case of a perfect
socio-economic equality, it is a straight line. From the Lorenz curve, we can calculate
the Gini coefficient [
24
,
25
], which is a measure of socio-economic inequality estimated as:
G=A/(A+B)
, where Ais the area that lies between the line of equality and the Lorenz
curve, and Bis the area between the Lorenz curve and the horizontal axes. Values of
G
tending to 0 indicate equality, whereas values closer to 1 indicate total inequality. Hence,
for the Hunter-Gatherer case, the Gini coefficient is 0.
In addition, Figure 10c shows the probability distribution function of the income
F(x)
,
and Figure 10d the standardized income probability density
f(z)
, where
z=x/µ
, i.e., the
income standardized by its mean
µ
. For the Hunter-Gatherer case, the distribution function
is one with a single discontinuity at the value
x=
3 (kWh), and the density is an impulse
at the same value of xor at z=1.
The grangers’ society is somewhat more complex. The technological limit has been
increased, thanks to the use of tools and animals to cover energy needs. As a result, the
World 2021,2162
average energy per capita is increased, as well. Here, we will assume that the distribution
of available energy (income per capita) is obtained by the principle of maximum entropy
introduced by Jaynes [
91
]. While the concept of entropy was much earlier proposed by
Clausius [
92
], it is the latter principle which made the concept very powerful for logical
inference. In a related paper [93], Koutsoyiannis notes that:
The entropy retains its probabilistic interpretation as a measure of uncertainty
. . .
[T]he
tendency of entropy to reach a maximum is the driving force of natural change. This
tendency is formalized as the principle of maximum entropy, which can be regarded
both as a physical (ontological) principle obeyed by natural systems, as well as a logical
(epistemological) principle applicable in making inference about natural systems.
Maximizing entropy
Φ[x]
from Equation (1) for the granger’s society, given a specified
average energy (increased in comparison to the Hunter-Gatherers’ society), we obtain an
exponential distribution of the energy per capita, bounded from below to the minimum
required energy for survival and from above to the technological limit. This is illustrated
in Figure 10c for the energy distribution and Figure 10d for the standardized energy.
Accordingly, the latter case corresponds to a Gini coefficient equal to ~0.6 and entropy
Φ[x]
equal to ~2. This theoretical exercise illustrates how, in the framework of maximum
entropy, social stratification emerges as a result of an increase in average wealth [94].
3.3. Antiquity and Medieval Societies
Lenski’s study for inequality in the prehistory and antiquity shows that the level of
inequality varied [
95
,
96
]. Generally, ancient societies were divided in two social classes,
elite (5–10%) and commoners, with small variations inside them [
97
]. While there have been
various spatial and temporal changes in social stratification, the contribution of integrated
technology on social stratification is somewhat unclear. For instance, little is known for
the technological progress from bronze age to iron age, the invention of new tools, the
influence of wind (windmills-navigation), or the use of water (England in 1700: waterwheel
~4 kW, one per 350 people [82]).
On the other hand, education, division of labor, and economic specialization, which
are results of societies’ technological progress, are mentioned as causes of stratification [
98
].
We note that, in periods where the technological limit was increased, and there was
available knowledge for large-scale projects (Pyramids, Ancient Egypt; Parthenon, Ancient
Greece, Roman infrastructure, etc.), the embodied energy of constructions was covered by
numerous crowds of slaves.
Most of our records show that life expectancy from prehistory until 1400 was till
the twenties [
99
]. In the beginning of industrial revolution, life expectancy in the United
Kingdom increased twofold, reaching the forties (Figure 11). This jump of life expectancy
in the United Kingdom, in the period between 1400 and 1800, can be associated to the rise
of a new socio-economic policy known as mercantilism. The latter policy was sparked by
the installation of new techniques using wind power by sailing ships (caravels), which
could travel against wind [
100
], explore new lands, and bring new resources to mainland
(
Figure 12
). However, the period of mercantilism was marked as a period of extreme in-
equalities (slave trade, colonization) and the beginning of minimum economic intervention
(known as “laissez-faire”). In this case, as well, the rise in inequality (accompanied by the
rise of the average prosperity) can be justified in entropic terms by the radical expansion of
the technological limit of the time.
World 2021,2163
World 2021, 2, FOR PEER REVIEW 11
Figure 11. United Kingdom’s life expectancy, data from: 1800–2016 [66,67].
Figure 12. Steps of sailing, connected areas with same color; red, ~10,000 BC rowing boat; yellow,
~1500 BC shipping with tailwind; green, ~1500 AD shipping with caravels.
3.4. Modern Societies
While the invention of money has been a substantial socio-technical evolution, today,
only 8 percent of the world’s currency exists as physical cash [101], and an intangible
amount of money is created as debt, which is indicative of the current monetary system’s
fragility. This fragility is already being discussed in the public discourse. Recently, the
Russian President Vladimir Putin, in his speech at Virtual World Economic Forum of 2021,
acknowledged that: “The widening gap between the real and virtual economies presents
a very real threat and is fraught with serious and unpredictable shocks” [102].
We have already shown that GDP per capita and energy are related (Figure 6). In the
previous examples, we have used energy as a proxy for GDP per capita. In order to track
the role of energy in society till the present day, we note that average worldwide energy
consumption is 21,000 kWh per capita per year, yet with significant variability, as, e.g., in
Qatar, the average is ~200,000 kWh per capita per day, and, in Afghanistan, the average is
~600 kWh per capita per year.
As we have ample economic data regarding GDP for modern societies, in order to
study the stratification in this case, we examine economic data for income (instead of en-
ergy data), and we discuss the income (net) distribution in different countries [103]. Here,
Figure 11. United Kingdom’s life expectancy, data from: 1800–2016 [66,67].
World 2021, 2, FOR PEER REVIEW 11
Figure 11. United Kingdom’s life expectancy, data from: 1800–2016 [66,67].
Figure 12. Steps of sailing, connected areas with same color; red, ~10,000 BC rowing boat; yellow,
~1500 BC shipping with tailwind; green, ~1500 AD shipping with caravels.
3.4. Modern Societies
While the invention of money has been a substantial socio-technical evolution, today,
only 8 percent of the world’s currency exists as physical cash [101], and an intangible
amount of money is created as debt, which is indicative of the current monetary system’s
fragility. This fragility is already being discussed in the public discourse. Recently, the
Russian President Vladimir Putin, in his speech at Virtual World Economic Forum of 2021,
acknowledged that: “The widening gap between the real and virtual economies presents
a very real threat and is fraught with serious and unpredictable shocks” [102].
We have already shown that GDP per capita and energy are related (Figure 6). In the
previous examples, we have used energy as a proxy for GDP per capita. In order to track
the role of energy in society till the present day, we note that average worldwide energy
consumption is 21,000 kWh per capita per year, yet with significant variability, as, e.g., in
Qatar, the average is ~200,000 kWh per capita per day, and, in Afghanistan, the average is
~600 kWh per capita per year.
As we have ample economic data regarding GDP for modern societies, in order to
study the stratification in this case, we examine economic data for income (instead of en-
ergy data), and we discuss the income (net) distribution in different countries [103]. Here,
Figure 12.
Steps of sailing, connected areas with same color; red, ~10,000 BC rowing boat; yellow,
~1500 BC shipping with tailwind; green, ~1500 AD shipping with caravels.
3.4. Modern Societies
While the invention of money has been a substantial socio-technical evolution, today,
only 8 percent of the world’s currency exists as physical cash [
101
], and an intangible
amount of money is created as debt, which is indicative of the current monetary system’s
fragility. This fragility is already being discussed in the public discourse. Recently, the
Russian President Vladimir Putin, in his speech at Virtual World Economic Forum of 2021,
acknowledged that: “The widening gap between the real and virtual economies presents a
very real threat and is fraught with serious and unpredictable shocks” [102].
We have already shown that GDP per capita and energy are related (Figure 6). In the
previous examples, we have used energy as a proxy for GDP per capita. In order to track
the role of energy in society till the present day, we note that average worldwide energy
consumption is 21,000 kWh per capita per year, yet with significant variability, as, e.g., in
Qatar, the average is ~200,000 kWh per capita per year, and, in Afghanistan, the average is
~600 kWh per capita per year.
As we have ample economic data regarding GDP for modern societies, in order to
study the stratification in this case, we examine economic data for income (instead of
energy data), and we discuss the income (net) distribution in different countries [
103
].
Here, we use GDP data from United Nations University (UNU) World Income Inequality
World 2021,2164
Database (WIID) [
104
]. As these data cover in detail a period of about 50 years, we select
as case studies specific countries that have undergone radical socioeconomic changes
during this period. In particular we study economic data from the UK, Sweden, and
Greece. These data are available as tenths of the share (%) of people from the lowest to
highest income versus share (%) of income earned (y), as shown in Figure 13a. The Lorenz
curve is readily calculated as the cumulative share of the people corresponding to the
cumulative income (as seen in Figure 13b), while the Gini coefficient is derived as described
in Section 3.2. To obtain the distribution of income from the income share data at hand, we
first use logarithmic interpolation between the known values of the income share (each
corresponding to a tenth of the population) to obtain the full distribution of income share y,
and we then transform the latter to actual money
x
using the following equation:
x=Cy
,
where Cis the ratio of the averages of the distributions of income money and income
share:
C:=E[x]/E[y]
. The average income money
E[x]
is obtained from data in UNU
World Income Inequality Database-WIID [
100
], whereas the average income share
E[y]
is
estimated from the income share data.
World 2021, 2, FOR PEER REVIEW 12
we use GDP data from United Nations University (UNU) World Income Inequality Data-
base (WIID) [104]. As these data cover in detail a period of about 50 years, we select as
case studies specific countries that have undergone radical socioeconomic changes during
this period. In particular we study economic data from the UK, Sweden, and Greece. These
data are available as tenths of the share (%) of people from the lowest to highest income
versus share (%) of income earned (y), as shown in Figure 13a. The Lorenz curve is readily
calculated as the cumulative share of the people corresponding to the cumulative income
(as seen in Figure 13b), while the Gini coefficient is derived as described in Section 3.2. To
obtain the distribution of income from the income share data at hand, we first use loga-
rithmic interpolation between the known values of the income share (each corresponding
to a tenth of the population) to obtain the full distribution of income share y, and we then
transform the latter to actual money x using the following equation: 𝑥𝐶𝑦, where C is
the ratio of the averages of the distributions of income money and income share: 𝐶≔
Ε𝑥 Ε𝑦. The average income money Ε𝑥 is obtained from data in UNU World Income
Inequality Database-WIID [100], whereas the average income share Ε𝑦 is estimated
from the income share data.
(a) (b)
Figure 13. 1991 Share of income in Sweden and the United Kingdom; (a) tenths of the share (%) of people from the lowest
to highest income versus share (%) of income earned (b) Lorenz curve.
We also define an entropic index of inequality ΔΦ as:
Δ𝛷𝑥≔𝛷𝑥lnE𝑥, (2)
where 𝛷𝑥 is the total entropy defined in Equation (1), and E𝑥 is the average income
money. We note that, if entropy is maximized, i.e., hence, the income distribution is expo-
nential, then the entropy equals 1lnE𝑥
. Therefore, the maximum possible values of
Δ𝛷 is 1 and corresponds to the case where indeed the entropy is maximized. A value of
Δ𝛷 smaller than 1 could correspond to a more equitable distribution of the income.
Thus, 𝛷 the total entropy, being related to the logarithm of the average income, is a
measure of prosperity, and Δ𝛷 is a measure of inequality. For the variable 𝑧 which, by
definition, has E𝑧1, Δ𝛷 and 𝛷𝑧 are identical.
The total entropy and entropic inequality index for the income data defined in Equa-
tion (1) and Equation (2), respectively, are easily obtained. We also compare countries by
their income probability distribution function (Figure 14a), as well as their standardized
income probability density distributions 𝑓𝑧 (Figure 14b).
Figure 13. 1991 Share of income in Sweden and the United Kingdom; (a) tenths of the share (%) of people from the lowest
to highest income versus share (%) of income earned (b) Lorenz curve.
We also define (Equation (2)) an entropic index of inequality Φas:
Φ[x]:=Φ[x]ln E[x], (2)
where
Φ[x]
is the total entropy defined in Equation (1), and
E[x]
is the average income
money. We note that, if entropy is maximized, i.e., hence, the income distribution is
exponential, then the entropy equals 1
+ln E[x]
. Therefore, the maximum possible value of
Φ
is 1 and corresponds to the case where indeed the entropy is maximized. A value of
Φsmaller than 1 could correspond to a more equitable distribution of the income.
Thus,
Φ
the total entropy, being related to the logarithm of the average income, is a
measure of prosperity, and
Φ
is a measure of inequality. For the variable
z
which, by
definition, has E[z]=1, Φand Φ[z]are identical.
The total entropy and entropic inequality index for the income data defined in
Equations (1) and (2)
, respectively, are easily obtained. We also compare countries by
their income probability distribution function (Figure 14a), as well as their standardized
income probability density distributions f(z)(Figure 14b).
World 2021,2165
World 2021, 2, FOR PEER REVIEW 13
(a) (b)
Figure 14. 1991 Share of income in Sweden and the United Kingdom. (a) Distribution function. (b) Probability density
function of the standardized income.
When the wealth is increased, the natural tendency of the stratification is reflected by
an exponential distribution, as shown in Figure 10d, for the case of Grangers. Modern
societies seem to be following that tendency in part, but with added regulations (using
taxing instruments) to support the creation of the middle class, yielding a more bell-
shaped distribution. This fact is evident by the comparison of England and Sweden. The
‘bell’ indicates the strength of the middle class and is clearly more pronounced in Sweden
(Figure 14b).
Our analysis also shows that the total entropy 𝛷𝑥 is tightly related to GDP per
capita which is the best-known growth index, while ΔΦ is correlated with the Gini index
which is a common index of inequality (Figures 15 for UK and Figure 16 for Sweden).
Various interesting insights can be also derived by inspecting the evolution of income
inequality in the UK and Sweden, inter-compared in Figure 16. First off, both entropy
metrics we have defined, i.e., total entropy 𝛷𝑥and entropic index of inequality ΔΦ, re-
flect the difference between the neoliberal politics of England’s Prime Minister (1979–
1990) Margaret Thatcher (1925–2013) and the Social Democrats in Sweden which exercised
political power almost uninterruptedly (except for a short parenthesis 1991–1994) until
2006 [105]. The Social Democrats seem to have succeeded in lowering inequality and
strengthening the middle class. Our analysis shows that the short parenthesis of 1991–
1994 in Sweden did not affect the inequality as much as it suggested by the Gini coefficient
(Figures 17 and 18), and, in this respect, the ΔΦ metric may be a better index of inequality
than the Gini coefficient. On the other hand, after the falling of Social Democrats in 2006,
ΔΦ shows that, in recent years, both countries are converging to the same inequality state
(Figures 17 and 18).
Figure 14.
1991 Share of income in Sweden and the United Kingdom. (
a
) Distribution function. (
b
) Probability density
function of the standardized income.
When the wealth is increased, the natural tendency of the stratification is reflected
by an exponential distribution, as shown in Figure 10d, for the case of Grangers. Modern
societies seem to be following that tendency in part, but with added regulations (using
taxing instruments) to support the creation of the middle class, yielding a more bell-shaped
distribution. This fact is evident by the comparison of England and Sweden. The ‘bell’
indicates the strength of the middle class and is clearly more pronounced in Sweden
(Figure 14b).
Our analysis also shows that the total entropy
Φ[x]
is tightly related to GDP per capita
which is the best-known growth index, while
Φ
is correlated with the Gini index which is
a common index of inequality (Figure 15 for UK and Figure 16 for Sweden).
World 2021, 2, FOR PEER REVIEW 14
(a) (b)
Figure 15. United Kingdom (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality ΔΦ.
(a) (b)
Figure 16. Sweden (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality ΔΦ.
(a) (b)
Figure 17. Sweden and United Kingdom, timeline of: (a) Gini coefficient; (b) GDP per capita.
Figure 15. United Kingdom (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality Φ.
World 2021,2166
World 2021, 2, FOR PEER REVIEW 14
(a) (b)
Figure 15. United Kingdom (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality ΔΦ.
(a) (b)
Figure 16. Sweden (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality ΔΦ.
(a) (b)
Figure 17. Sweden and United Kingdom, timeline of: (a) Gini coefficient; (b) GDP per capita.
Figure 16. Sweden (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality Φ.
Various interesting insights can be also derived by inspecting the evolution of income
inequality in the UK and Sweden, inter-compared in Figure 16. First off, both entropy
metrics we have defined, i.e., total entropy
Φ[x]
and entropic index of inequality
Φ
, reflect
the difference between the neoliberal politics of England’s Prime Minister (
1979–1990
)
Margaret Thatcher (1925–2013) and the Social Democrats in Sweden which exercised
political power almost uninterruptedly (except for a short parenthesis 1991–1994) until
2006 [
105
]. The Social Democrats seem to have succeeded in lowering inequality and
strengthening the middle class. Our analysis shows that the short parenthesis of 1991–1994
in Sweden did not affect the inequality as much as it suggested by the Gini coefficient
(Figures 17 and 18), and, in this respect, the
Φ
metric may be a better index of inequality
than the Gini coefficient. On the other hand, after the falling of Social Democrats in 2006,
Φ
shows that, in recent years, both countries are converging to the same inequality state
(Figures 17 and 18).
World 2021, 2, FOR PEER REVIEW 14
(a) (b)
Figure 15. United Kingdom (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality ΔΦ.
(a) (b)
Figure 16. Sweden (1970–2018): (a) GDP per capita and Φ[x]; (b) Gini and entropic index of inequality ΔΦ.
(a) (b)
Figure 17. Sweden and United Kingdom, timeline of: (a) Gini coefficient; (b) GDP per capita.
Figure 17. Sweden and United Kingdom, timeline of: (a) Gini coefficient; (b) GDP per capita.
World 2021,2167
World 2021, 2, FOR PEER REVIEW 15
(a) (b)
Figure 18. Sweden and United Kingdom, timeline of: (a) entropy Φ[x]; (b) entropic index of inequality ΔΦ.
Another interesting example is the assessment of the situation in Greece during the
period 2010–2015 [106,107] in comparison to the one in the UK. The Greek financial crisis
started in 2010 when the First Memorandum was implemented. In this year there was an
abrasive downturn to the GDP per capita. Soon after, in 2012, the GDP per capita seems
to have been stabilized (Figure 19). It is interesting that, during this period, the total en-
tropy 𝛷𝑥 shows a big gap between the two countries. This was accompanied with a
widespread pessimism of the population and a tendency to leave the country after 2010
with main target of immigration the United Kingdom, a country with higher total entropy
𝛷𝑥 [108].
Figure 19. Greece and United Kingdom, timeline of total entropy Φ[x] and immigration flows
from Greece to United Kingdom, over the same period.
4. Discussion
Wider reflections from the entropic view of social stratification may be made. For
instance, the expansion of the technological limit during the industrial revolution has
caused increased inequality, yet, at the same time, it had a favorable effect to the prosper-
ity of the population. The latter was clearly explained by Hans Rosling [109].
Another interesting fact is how the Coronavirus pandemic made the richest people
on the planet richer diminishing the middle class [110]. In other words, it seems that, once
the system is shocked by a sharp change, its structural rearrangement follows the ten-
dency to maximize entropy, approaching the entropy-maximizing exponential distribu-
tion.
Figure 18. Sweden and United Kingdom, timeline of: (a) entropy Φ[x]; (b) entropic index of inequality Φ.
Another interesting example is the assessment of the situation in Greece during the
period 2010–2015 [
106
,
107
] in comparison to the one in the UK. The Greek financial crisis
started in 2010 when the First Memorandum was implemented. In this year there was an
abrasive downturn to the GDP per capita. Soon after, in 2012, the GDP per capita seems to
have been stabilized (Figure 19). It is interesting that, during this period, the total entropy
Φ[x]
shows a big gap between the two countries. This was accompanied with a widespread
pessimism of the population and a tendency to leave the country after 2010 with main
target of immigration the United Kingdom, a country with higher total entropy
Φ[x]
[
108
].
World 2021, 2, FOR PEER REVIEW 15
(a) (b)
Figure 18. Sweden and United Kingdom, timeline of: (a) entropy Φ[x]; (b) entropic index of inequality ΔΦ.
Another interesting example is the assessment of the situation in Greece during the
period 2010–2015 [106,107] in comparison to the one in the UK. The Greek financial crisis
started in 2010 when the First Memorandum was implemented. In this year there was an
abrasive downturn to the GDP per capita. Soon after, in 2012, the GDP per capita seems
to have been stabilized (Figure 19). It is interesting that, during this period, the total en-
tropy 𝛷𝑥 shows a big gap between the two countries. This was accompanied with a
widespread pessimism of the population and a tendency to leave the country after 2010
with main target of immigration the United Kingdom, a country with higher total entropy
𝛷𝑥 [108].
Figure 19. Greece and United Kingdom, timeline of total entropy Φ[x] and immigration flows
from Greece to United Kingdom, over the same period.
4. Discussion
Wider reflections from the entropic view of social stratification may be made. For
instance, the expansion of the technological limit during the industrial revolution has
caused increased inequality, yet, at the same time, it had a favorable effect to the prosper-
ity of the population. The latter was clearly explained by Hans Rosling [109].
Another interesting fact is how the Coronavirus pandemic made the richest people
on the planet richer diminishing the middle class [110]. In other words, it seems that, once
the system is shocked by a sharp change, its structural rearrangement follows the ten-
dency to maximize entropy, approaching the entropy-maximizing exponential distribu-
tion.
Figure 19.
Greece and United Kingdom, timeline of total entropy
Φ
[
x
] and immigration flows from
Greece to United Kingdom, over the same period.
4. Discussion
Wider reflections from the entropic view of social stratification may be made. For
instance, the expansion of the technological limit during the industrial revolution has
caused increased inequality, yet, at the same time, it had a favorable effect to the prosperity
of the population. The latter was clearly explained by Hans Rosling [109].
Another interesting fact is how the Coronavirus pandemic made the richest people on
the planet richer diminishing the middle class [
110
]. In other words, it seems that, once the
World 2021,2168
system is shocked by a sharp change, its structural rearrangement follows the tendency to
maximize entropy, approaching the entropy-maximizing exponential distribution.
A relevant scientific question would be: How does a state’s policy intervene to regulate
the society’s inherent tendency to maximize entropy? Confucius said that “When wealth
is concentrated, the people are de-clustered. When wealth is distributed, the people are
clustered” [
111
,
112
]. In 1776, Adam Smith first pointed out that the economy, must have
ethical basis noting that “laissez-faire” led to a behavior of extreme inequality [
5
]. He
pointed out the role of the state is to sustain an ethical basis and redistribute wealth
creating the middle class which can be viewed as the “bell” in the distribution (Figure 13d).
In “The General Theory of Employment, Interest and Money” [
15
], John Keynes
(1883–1946) notes the same: when wealth is concentrated, a big share of the wealth is
invested in safe and unproductive values which block the function of the economy [
113
].
Keynes pointed out that the continual redistribution of wealth and the limitation of its
unproductive deposits are functional obligations of the state to society to avoid recession.
The historical documentation of the influence of inequality today is pointed out by
Robert Reich [114]:
Consider that the two peak years of inequality over the past century—when the top 1
percent garnered more than 23 percent of total income—were 1928 and 2007. Each of
these periods was preceded by substantial increases in borrowing, which ended notoriously
in the Great Crash of 1929 and the near-meltdown of 2008.
Recently, Russian President Vladimir Putin noted that [102]:
The systemic socioeconomic problems are evoking such social discontent that they require
special attention and real solutions. The dangerous illusion that they may be ignored or
pushed into the corner is fraught with serious consequences. In this case, society will still
be divided politically and socially.
Therefore, it becomes clear that, an indiscriminate restriction of available wealth (as it
happens today in finance capitalism [
115
]) leads to the exponential distribution of wealth
eliminating the middle class and creating favorable grounds for a crash of the economy, as
happened in the past.
5. Conclusions
This work puts forward an entropic evaluation of social development and economic
stratification, instead of the usual economic analysis based on indicators as the GDP per
capita, the Gini index and the Lorenz Curve. Indeed, it turns out that the entropic repre-
sentation can interpret social and economic changes from prehistory to the present day
providing a quantitative evaluation of the dynamics of economy. In particular, we have for-
mulated two new measures; total entropy
Φ
, an entropic index related to economic growth;
and an entropic index related to inequality
Φ
. The indices are validated using extensive
case studies from prehistory till modern day economies. Both are readily applicable in
economic analysis and have theoretical support by the principle of maximum entropy.
The analysis of long-term social and economic growth shows that the latter are associ-
ated with spontaneous social stratification as also suggested by the principle of maximum
entropy. However, the reason why social stratification has been disputed as a natural
human tendency by most anthropologists relates to the counter-example of the Hunter-
Gatherers. For example, Gowdy [48] writes:
Assumptions about human behavior that members of market societies believe to be univer-
sal, that humans are naturally competitive and acquisitive, and that social stratification
is natural, do not apply to many hunter-gatherer peoples.
In our view, stratification did not arise in the Hunter-Gatherers’ society because
their technological limit was constrained by their muscular power and resulting energy
barely sufficed to cover survival needs let alone to create surplus. As the technological
limit increased (agriculture) and people clustered, available wealth increased creating a
World 2021,2169
surplus. In entropic terms, this translates to the formulation of an exponential distribution,
consistent with the maximization of entropy under the constraint of a specified mean.
Overall, our analyses suggest that technological development is the force which increases
inequality, and at the same time, offers a better and longer life to all the members of
the community. This finding is also in agreement with recent approaches on modern
economy [116,117].
The analyses of modern-day economies presented herein, particularly of Greece, UK
and Sweden, result in interesting findings, consistent to the principle of maximum entropy.
Additional applications can be carried out by analyzing data from different countries
worldwide. Such analyses would be useful as many countries strive towards equality in
terms of living standards and opportunities provided to their people [
102
,
118
], yet still
great inequalities exist between the richest and the poorest both in the nation-scale and
the international scale [
119
,
120
]. The presented entropic evaluation may be helpful in
understanding and evaluating these aspects. Although the methodology is of general
applicability, a potential limitation relates to the difficulty of obtaining long-term economic
data worldwide. Nevertheless, entropy can be incorporated in socio-economic analysis
by both ways: as a predictive tool, to identify the spontaneous tendency given existing
limitations; and as a diagnostic tool, to characterize change in a probabilistically consistent
manner.
This paper suggests an understanding of social stratification from an entropic view-
point, which may help to inform people, so better decisions may be made. Although it may
be tempting to draw political conclusions from this analysis, we insist on the separation
between politics and science. As pointed out by Koutsoyiannis [
121
], history teaches that
mixing up science with politics (cf. Eugenics and Lysenkoism) or religion (cf. Giordano
Bruno and Galileo) has had tragic results both for science and society. For this reason,
we would like to stress that we have to be very careful using this concept (and any other
scientific concept) to justify political theories and social policies.
Author Contributions:
Conceptualization, D.K. and G.-F.S.; methodology, D.K. and G.-F.S.; valida-
tion, G.-F.S. and D.K.; formal analysis, G.-F.S. and D.K.; investigation, G.-F.S. and D.K.; data curation,
G.-F.S..; writing—original draft preparation, G.-F.S., T.I., and D.K.; writing—review and editing, P.D.,
N.M.; visualization, G.-F.S.; supervision, D.K.; project administration, G.-F.S. All authors have read
and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
Life expectancy. Available online: https://ourworldindata.org/life-
expectancy (accessed on 5 October 2020). United Nations, 2019 Revision of World Population
Prospects. Available online: https://population.un.org/wpp/ (accessed on 30 November 2020). Total
Population. Available online: https://clio-infra.eu/Indicators/TotalPopulation.html, (accessed on 30
November 2020). AQUASTAT: Food and agriculture organization of the United Nations. Available
online: http://www.fao.org/nr/water/aquastat/data/query/index.html (accessed on 5 November
2020). Gleick P.H. Basic water requirements for human activities: Meeting basic needs, Water
International, 21, pp. 83–92, 1996. FAOSTAT, United Nations Food and Agricultural Organization
(FAO). Available online: http://www.fao.org/faostat/en/#data/FBS (accessed on 12 October 2020).
Bank of England, Home Statistics Research datasets. Available online: https://www.bankofengland.
co.uk/statistics/research-datasets (accessed on 25 November 2020). Smil, V., Conversion of Energy:
People and Animals, Editor(s): Cutler J. Cleveland, Encyclopedia of Energy, Elsevier, 2004, pp.
697–705, ISBN 9780121764807. Available online: https://doi.org/10.1016/B0-12- 176480-X/00094-2
(accessed on 1 March 2021). Smil, V., World History and Energy, Editor(s): Cutler J. Cleveland,
Encyclopedia of Energy, Elsevier, 2004, pp. 549–561, ISBN 9780121764807, Available online: https://
doi.org/10.1016/B0-12-176480-X/00025-5 (accessed on 1 March 2021). UNU World Income Inequality
Database-WIID Available online: https://www.wider.unu.edu/database/wiidhttps://www.wider.
unu.edu/database/wiid (accessed on 23 January 2021). Lazaretou, S. The Greek brain drain: the
World 2021,2170
new pattern of Greek emigration during the recent crisis, Economic Bulletin, Bank of Greece, issue
43, pp. 31–53, July 2016. Eurostat: Emigration by age group, sex, and citizenship, Available online:
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=migr_emi1ctz&lang=en (accessed on 26
January 2021).
Acknowledgments:
We thank the editors of World-MDPI for the invitation to contribute with a
paper and the processing of the paper, as well as two anonymous reviewers, for comments that
helped improve and enrich the manuscript, and a third anonymous reviewer for the enthusiastic
review. D.K. and G.F.S. would like to thank T. Xanthopoulos, writer of the book trilogy “Requiem
with Crescendo”, for inspiring thoughts on relevant issues presented in the inauguration of the
book. G.F.S. also thanks him for his help in delving into political and economic theories, and the
endless discussions on relevant philosophical issues. As “Requiem with Crescendo” deals with social
inequality, it has been the inspiration of this work.
Conflicts of Interest: The authors declare no conflict of interest.
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... When studying the material wealth (or income) in a certain society, current or past, we assume two characteristic quantities: the mean μ, which is related to the total energy available to the society [119], and the upper limit of wealth (or income) , which is mainly determined by the available technology (knowhow), and can thus be called the technological upper limit. We define the ratio: ...
... We can thus say in conclusion that for > 2 , the entropy increases both with the mean μ and the technological limit . In this respect, entropy constitutes a measure of society's wealth (see also [119]). One could say that the mean μ is more representative, as a measure of wealth, than the entropy . ...
... This has recently been introduced as an index of inequality by Sargentis et al. [119] (albeit denoted as Δ ). The quantity cannot exceed a maximum value of 1, corresponding to an exponential distribution. ...
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While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches to it, we show that entropy has a universal stochastic definition, which is not disorder. Hence, we contend that entropy should be used as a mathematical (stochastic) concept as rigorously as possible, free of metaphoric meanings. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept, and promotes entropy as the mother of creativity and evolution. As the social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether maximum entropy, applied to the distribution of a wealth-related variable, namely annual income, can give an objective description. Using publicly available income data, we show that income distribution is consistent with the principle of maximum entropy. The increase in entropy is associated to increases in society’s wealth, yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in the development of and increase in the entropy of income. Such findings are contrary to the theory of ecological economics and other theories that use the term entropy in a Malthusian perspective.
... At the beginning, humans survived, perpetuated and spread as hunter gatherers, dominating the environment, reaching a relative equilibrium [56] and displaying remarkable resilience [57]. The possibility of human clustering [58,59] was very small, since man needed large areas to meet nutritional needs [60]. The great step toward civilization was primarily due to the capability of human clustering through language and technology. ...
... Same conclusions are delivered by Atkinson for modern economies [87]. Recent studies [60,83] draw similar conclusions, presenting the dynamics of stratification in societies with an entropic approach [88]. Roser and Ortiz-Ospina [89], based on the publication of Milanovic et al. [90], visualize how inequality increases with higher average income. ...
... The importance of energy becomes clear if we consider that since the Homeric times, the cattle's size signified the wealth of a person. The unit of wealth measurement in the Roman Empire was an animal's head (Latin: capis; Greek κεφαλή), which bequeathed to us the term capital [60] (Greek κεφάλαιον). In 1909, Wilhelm Ostwald first noted that energy consumption is correlated with life expectancy [109]. ...
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Environmental determinism is often used to explain past social collapses and to predict the future of modern human societies. We assess the availability of natural resources and the resulting carrying capacity (a basic concept of environmental determinism) through a toy model based on Hurst–Kolmogorov dynamics. We also highlight the role of social cohesion, and we evaluate it from an entropic viewpoint. Furthermore, we make the case that, when it comes to the demise of civilizations, while environmental influences may be in the mix, social dynamics is the main driver behind their decline and eventual collapse. We examine several prehistorical and historical cases of civilization collapse, the most characteristic being that of the Minoan civilization, whose disappearance c. 1100 BC has fostered several causative hypotheses. In general, we note that these hypotheses are based on catastrophic environmental causes, which nevertheless occurred a few hundred years before the collapse of Minoans. Specifically, around 1500 BC, Minoans managed to overpass many environmental adversities. As we have not found justified reasons based on the environmental determinism for when the collapse occurred (around 1100 BC), we hypothesize a possible transformation of the Minoans’ social structure as the cause of the collapse.
... For example, 560 we can study the economy of a country without considering all processes on Earth or on 561 the universe. 563 3.1 Lebesgue background measure and the exponential distribution 564 In studying the material wealth in a certain society, current or past, we assume two 565 characteristic quantities: the mean of wealth μ, which is related to the total energy availa-566 ble to the society [106], and an upper limit of wealth , which is mainly determined by 567 the available technology (knowhow) and thus we call it technological upper limit. We 568 define the ratio: ...
... We can 616 thus say in conclusion that for > 2 the entropy increases both with the mean μ and 617 the technological limit . In this respect the entropy constitutes a measure of society's 618 wealth (see also [106]). 619 One could say that the mean μ is more representative, as a measure of wealth, than 620 the entropy . ...
... This has been recently introduced as an index of inequality by Sargentis et al. [106] (albeit 637 denoted as Δ [ ]). The quantity [ ] cannot exceed a maximum value of 1, correspond-638 ing to an exponential distribution. ...
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While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches on it, we show that entropy has a universal stochastic definition which is not disorder. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept and promotes entropy as the mother of creativity and evolution. As social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether the maximum entropy, applied to the distribution of wealth quantified by annual income, can give an objective description. Using publicly available income data, we show that the income distribution is consistent with the principle of the maximum entropy. The increase of entropy is associated to increase of society’s wealth yet a standardized form of en-tropy can be used to quantify inequality. Historically, technology has played a major role in de-velopment and increase of the entropy of income. Such findings are contrary to the theories of ecological economics and other theories which use the term entropy in a Malthusian perspective.
... Humans need a constant supply of water, food, and energy to live. These resources are connected to life expectancy, prosperity, and wealth [1], and are necessary in sufficient quantity and quality. The survival limits of humans are seven days at most without water, and about 45 days without food [2], which also represents the energy source for the human body. ...
... Thus, food and water require constant replenishment. As energy is essential for prosperity [1], the whole structure of society has been diachronically shaped and has evolved through systematic expansion of its energy consumption. ...
... In prehistory, humans relied on energy and water to transition from hunter-gatherers to farmers, and this gave them the ability to cluster in smaller spaces like cities [1] and the increase of clustering gives rise to civilization [66]. Today, humanity is facing a major challenge: the rapidly growing demand for WEF. ...
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Water, energy, land, and food are vital elements with multiple interactions. In this context, the concept of a water-energy-food (WEF) nexus was manifested as a natural resource management approach, aiming at promoting sustainable development at the international, national, or local level and eliminating the negative effects that result from the use of each of the four resources against the other three. At the same time, the transition to green energy through the application of renewable energy technologies is changing and perplexing the relationships between the constituent elements of the nexus, introducing new conflicts, particularly related to land use for energy production vs. food. Specifically, one of the most widespread "green" technologies is photovoltaic (PV) solar energy, now being the third foremost renewable energy source in terms of global installed capacity. However, the growing development of PV systems results in ever expanding occupation of agricultural lands, which are most advantageous for siting PV parks. Using as study area the Thessaly Plain, the largest agricultural area in Greece, we investigate the relationship between photovoltaic power plant development and food production in an attempt to reveal both their conflicts and their synergies.
... This gave them the ability to cluster in smaller spaces such as villages and, later, cities. The increase in clustering was a stride of civilization [2,3], but cities always depended on external resources (e.g., in antiquity, Athens imported wheat from the area of the Black Sea [4,5]). ...
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... A related paper by Kohler et al. showed that the increasing of technology and available energy (use of animals) in ancient times was related to the stratification of society [13]. Recent studies [14,15] delivered also the same conclusions, presenting the dynamics of stratification in society with an entropic approach [16]. The same conclusions were delivered by Atkinson for modern economies [17]. ...
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The pursuit of wealth has been a basic occupation of humans; as it turns out, wealth increases life expectancy. Analyzing global data, we show that money, probably connected with medical care, increase life expectancy. However, the base of real wealth is access to the Water–Energy–Food nexus, and the access to this also increases life expectancy. The first objective of this study was to compare the present values of wealth with antiquity, and we showed that about 1.4 billion people live in the present under the average lower wages of antiquity. As a case study, we analyze the construction of the Hadrianic aqueduct. We present a detailed description of the construction and the used methods, and we identify the total requirement of labor–time. Then, we investigate the wages of various occupations in the first century AD. The second objective of this study was the estimation of the total cost of daily wages for the construction of the project and the effect of the aqueduct on Athenians’ quality of life. Finally, we show that, today, about two billion people live with less available water than Athenians had with the Hadrianic aqueduct in the second century A.D.
... Sixteen such parameters denoted by P 11 , P 12 , P 13 , P 14 , P 21 , P 22 , P 23 , P 24 , P 31 , P 32 , P 33 , P 34 , P 41 , P 42 , P 43 & P 44 will represent a particular distribution of people belonging to different categories occupying different positions of power. The Social Entropy [6,12] of this distribution will then be given by ...
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Analysis based on the Entropy estimates of the society is carried out on a mathematical model in this paper, to make an assessment of Reservation policy presently in operation in India. The Reservation Policy was provisioned in the constitution of India under the policy of affirmative action. The policy makers had identified some communities of India that were being discriminated socially. They identified them by noticing their dismal representation in positions of power and respect, within the society. It was argued that these communities are required to be treated differently to give them equal opportunity in the society. The policy makers had provisioned in the same policy that the effectiveness of this policy will be analyzed at regular intervals to decide its continuation or improvisation. An attempt is made here to scientifically analyze the effectiveness of this policy and suggest possible improvements in the same. As per the understanding of Entropy, a policy such as the Reservation Policy, that is intended to encourage equality must be associated with increase in the Entropy of the society. After a careful mathematical analysis, it is shown here that the policy, in its present form, is designed to increase the entropy of the society in the short-term scenario but is an iso-entropic policy in the long term. A way has been suggested to complement the policy to make the entropy increased effectively and permanently.
... Strides of civilization are connected to technological issues, which have improved the quality of life [1,2], such as the installation of hydraulic works (hydraulic civilization [3]); architectural creations [4]; great technological inventions, which have changed history (e.g., the evolution of wheels [5]); a combination of technological issues, which has created a remarkable duration of social stability (e.g., Minoan civilization 3000-1100 BC [6][7][8]); and admirable technological creations, such as the Mechanism of Antikythera [9]. However, civilizations are generally characterized by their artistic creations. ...
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The creation of innovative tools, objects and artifacts that introduce abstract ideas in the real world is a necessary step for the evolution process and characterize the creative capacity of civilization. Sculpture is based on the available technology for its creation process and is strongly related to the level of technological sophistication of each era. This paper analyzes the evolution of basic sculpture techniques (carving, lost-wax casting and 3D scanning/printing), and their importance as a culture footprint. It also presents and evaluates the added creative capacities of each technological step and the different methods of 3D scanning/printing concerning sculpture. It is also an attempt to define the term "material poetics", which is connected to sculpture artifacts. We conclude that 3D scanning/printing is an important sign of civilization, although artifacts lose a part of material poetics with additive manufacturing. Subsequently, there are various causes of the destruction of sculptures, leaving a hole in the history of art. Finally, this paper showcases the importance of 3D scanning/printing in salvaging cultural heritage, as it has radically altered the way we "backup" objects.
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Living organisms pass through life seeking prosperity in a materialistic world. There are different meanings of prosperity. Some people think that it is measured in money, others relate it to pleasure and life satisfaction, while others link it to spirituality. However, it could be argued that the basic human needs related to the Water, Energy and Food (WEF) compose a nexus not only necessary for the survival of humans, but able to explain their prosperity as well. Unfortunately, decision-making in modern world is largely driven by economic aspects and monetarist policies. Koutsoyiannis (personal communication) notes that water, energy and food are not derived by money; rather money and economic growth derives from the availability and the access to water, energy and food. In this thesis, we study critical issues of prosperity rationally, using publicly available data, historical evidences and stochastic tools. The studied issues are based on the WEF nexus but extend to various other societal, environmental and cultural aspects of human life in societies, ranging from social stratification and urban clustering, to the aesthetic quality of surrounding environment.
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