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3 The Pinnacle of Trophic Pyramid of Biological Systems—Symbiosis of Biological and Nonbiological Accelerating Loops: Tec...

3 The Pinnacle of Trophic Pyramid of Biological Systems—Symbiosis of Biological and Nonbiological Accelerating Loops: Tec...

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Extreme Character of Evolution and the Maximum Energy Dissipation



241



gained, and the whole center of extreme transformation of the environmental free

energy moves from an interorganismic (strictly biological) into an intraspecies but

extraorganismic one (sociobiological and later technological for some species). It is

only achieved by means of symbiotic-like interaction of some biological systems

with nonbiological, very specific surroundings, and by creation of one biological

species of nonbiological, autocatalytic-like tools, which have indirect self-reproductive quality. These tools in future gained adaptation and helped to increase the

interspecies competitiveness—endorsing an essentially new form of organization

from the biological perspective—technology.

The materialization (emergence) in autocatalytic pure bio-loops of a new, rather

autocatalytic techno-loop, which is in a symbiotic relationship with the biological

social species, is schematically shown in Figure 4.19. It seems that only a sociobiological species can create and develop such nonbiological tools that have indirect

autocatalytic-like, self-reproductive-like properties.

Many of the local populations of mammals or birds, being in a sort of cooperation with above-mentioned multicellular organisms (individuals), live in local societies. Sometimes they permanently cooperate with organisms of different natures.

That is characteristic for species with clearly observed levels of social organization.

There is quite a large number of known social species in the biological world (ants,

bees, termites, wasps, social spiders, etc.) and a large number of other species that

do not tend to reveal such obvious social behavior, such as chimpanzees [107,114].

The collective behavior of chimps, for example, is not social in the sense that the

interest of the group significantly or even absolutely dominates the individual interest to the extent that is characteristic of some insects, such as ants. As mentioned

in Section 4.2, there are significant indications of regular, ordered social-like

behavior even for bacteria [51,52].

However, from the maximum energy dissipation perspective, only Homo sapiens

can be distinguished from these social species because it has reached fundamentally

a new level in free energy consumption, i.e., a new organization level of free

energy processing pathways. Due to this, Homo sapiens society, which was initially

local, gained global character. It should be noted that this has taken place because

of the fundamentally new level of free energy processing (which later achieved a

technological, socioeconomic form) as well as the new form of information support/mapping (which has most recently become scientific). One can see that from a

self-organizational perspective, a miniature scheme of this evolutionary mechanism

could be seen for cells, which cooperate in cell colonies or multicellular organisms,

as seen in Figure 4.19.

Social forms of cooperation (or social symbiosis) widen the adoptivity of local

populations, increase the territorial competitiveness for food, and give such communities improved chances to survive. This trophic aspect can be interpreted in

the thermodynamic sense because biomass is a type of free energy, and its

consumption is a dissipative process. Thus, from a thermodynamic perspective, biological species are just specific dissipative processes (generalized biological flows)

that overtake and compete with each other for free energy resources. In that sense, the

considerations from the maximum energy dissipation can be applied, Figure 1.2 [5].



242



The Common Extremalities in Biology and Physics



Free energy resource

of biological nature

ΔG

Biological



Biological loop

of dissipation

acceleration



Free energy resource

of biological nature ΔG

Biological



Free energy resource

of nonbiological nature

ΔG

Nonbiological



Biological loop

of dissipation

acceleration

Socio-economical loop

of dissipation

acceleration



Technological

symbiotical

acceleration loop

of dissipation



Figure 4.19 A formal scheme illustrating the transition in the global evolution of dissipative

processes from only the biological dissipative cycle (left cycle/graph) to the pretechno-cycle

(right cycle)—by establishing the symbiotic-like relations (central cycle) between

the biological cycles and nonbiological cycles. The last started as prehistorical usage

of nonbiological origin tools and were able to develop more and more complex and

useful tools.



As the dissipation of free energy accelerated in the evolution of biological

systems, the symbiotic technotronic accelerating feedback-loop emerged in nonbiological structures. Qualitative phase transition is the transition from a pure biological dissipative cycle (when just biological species are in mutual symbiological

relations and consume only biological forms of free energy) to a supercycle—when

the symbiosis of the structures of biological and nonbiological nature takes place.

In other words, at some level of biosystem evolution (as an accelerating free energy

dissipation of the environment), biosystems are able to develop a symbiotic technotronic accelerating feedback-loop linking some nonbiological structures into their

dissipative cycle. In some sense, this accelerating loop and these structures can



Extreme Character of Evolution and the Maximum Energy Dissipation



243



serve as the means of production of goods suitable for consumption in the biological part of this supercycle.



4.3.2



Biological Component: Data on the Population Growth



Self-reproductivity is the basic property of any biological system, including social

superorganisms like ant or bee colonies. It is well known that when a biological

species grows in an unlimited energetical resource, its population tends to rise

exponentially. However, when there are steady states and relations in the trophic

pyramid, the increase in the population of producers is compensated for by an

increase in the number of consumers (with a certain lag-period). The population

changes vary periodically and throughout a time much longer than at a steady

changing period. Self-reproductivity is also a property of the social Homo sapiens

species. Moreover, the population growth of HS is still an exponential growth,

though it has different coefficients in the exponent. This data is illustrated in

Figure 4.20.

One can see from Figure 4.20C that some phases, like agricultural and industrial

phases, which can be seen in double-logarithmic scaled graphs, indicate sigmoid

types of kinetics as well as overall HS population growth. See also Figure 4.20B.

Such growth can be linked to the cooperativity, characteristic of many types of biological growth, including the population growth of biological species and their

local populations, which have limited energy-substrate resources. One can note that

the transition of HS society from the agricultural phase into the industrial leads to

another sigmoid-like growth, which indicates the cooperative behavior with new

things of nonbiotic origin. Equivalently, these can be considered to be the involvement of new energetic resources and new free energy resources of nonbiological

origin. This supports our suggestion about the symbiosis-like relationship amongst

the means of production, as illustrated in Figure 4.19. The faster growth of population in the agricultural phase can be easily explained by the fact that the population

in the industrial phase is about a hundred times higher than in the agricultural

phase.



4.3.3



Self-Reproductive-Like Growth of the Industrial (Nonbiological)

Component



Exponential growth is also characteristic of the nonbiological component. It can be

seen in Figures 4.21 and 4.22. Figure 4.21A indicates significant colinearity in the

world population growth and world gross domestic product (GDP) throughout a

large period of time. In Figure 4.21B, the first six largest world GDP producers are

shown. One can see the sigmoid character of GDP growth from Figure 4.21C; these

top-12 world GDP producers are shown in transformed double-logarithmic scale in

Figure 4.21D. From all these graphs, one can see the typical curves for biological

kinetics, which can certainly be characterized as the growth in an environment



244



The Common Extremalities in Biology and Physics



(A)



(B)

8000



6000

Population (million)

5000

4000



6

Population (billions)



7000



7



USBC

PRB

UNDESA

HYDE

Maddison

Tanton

Biraben

McEvery&Jones



3000



5

4

3

2



2000

1



1000

Years before 2010

0



(C)



1000



10,000



0



100,000,000



Agricultural



10,000,000

USCB[4]

PRB[5]



100



0

1



10



1

10,000



1000



100



UNDESA[6]

HYDE[7]

[8]

100,000

[9]

[10]

[11]

10,000

[12]

[13]

[14]



1000



–6.0 –5.0 –4.0 –3.0 –2.0 –1.0 0.0



10



1



Years before 2010

0.1



1,000,000



Tool making



10



(D)



10,000,000,000



Industrial

1,000,000,000



1000



USBC

PRB

UNDESA

HYDE

Maddison

Tanton

Biraben

McEvery&Jones



Population (billions)



2000



World population



3000



0.01



0.001



Decimal logarithm of

years from 2050



Figure 4.20 Human population growth [115]. (A) Normal coordinates, horizontal axis in

years from 2010. (B) Time axis in the logarithmic coordiantes. (C) Population growth in

double-logarithmic scales. (D) Agricultural and industrial phases in double-logarithmic scale,

on the basis of data adapted from Ref. [116].



Extreme Character of Evolution and the Maximum Energy Dissipation



(A)



245



(B)

10,000



100,000



Population (million)



100,000



10,000



10,000



1000



1000



1000



Population

GDP

100

10,000 1000



10,000



1000



100



100

World total

China

India

10

Japan

12 W. Europe

USA

F. USSR

1

10

1



100

100



10



1



0



(C)



(D)



60,000



50,000



40,000



30,000



Total Africa

China

India

Japan

France

Germany

Italy

The Netherlands

UK

12 W. Europe

Australia

Canada

USA

F. USSR

World total



9000

1000



8000

7000

6000



100



5000

4000



20,000



3000

2000



10,000



1000

0

10,000



10,000



10,000



0

1000



100



10



1



10,000



1000



100



Total Africa

China

India

Japan

France

10

Germany

Italy

The Netherlands

UK

12 W. Europe1

Australia



10



Canada

USA

F. USSR



1



0



Figure 4.21 World and countries GDP in comparison to the population in normal and

double-logarithmic scales: (A) World total; (B) the first 6 largest GDP producers; (C) main

GDP producers in normal scale; (D) world top-12 GDP producers in double-logarithmic

scale. Horizontal axis—the time (years) from the year 2010 in the logarithmic scale.

Based on the data from Angus Maddison [116À118].



246



The Common Extremalities in Biology and Physics



typical of a limited resource, linking biological and economic kinetics by similar

phenomenological properties.

Figure 4.22 compares some agricultural and industrial production indicators

with the population growth of countries that have well-documented industrial history. The indicators clearly illustrate that the industrial component has growth that

overtakes the population growth over quite a long time period (about 150 years).



(A)



(B)



10,000



10,000



1000



100,000

Total industry

Electricity, gas, water

Total GDP

Manufacturing

Population



1000



100



100



10

1800

(C)

1000



1850



10

Total GDP

Total industry

Manufacturing

Population (thousands)

Agriculture

1

1850

1900

1950



Manufacturing

Electricity, gas, water

Total GDP

Population



100



1913=100



1890



1930



(D)

1000



10,000

1970



1000

Manufacturing

Electricity, gas, water

Total GDP

Population



100

100



100

Population



10

10

1

1840



0.1



1880



1920



1960



10



1

1860



1885



1910



1935



10

1960



Figure 4.22 Growth of economic indicators for some countries (A—indicators for the

Netherlands; B—Great Britain; C—Germany; D—United States). Vertical axis is in

logarithmic scale. The acceleration of this growth under transition to later periods of time is

shown. One can see that the acceleration of goods production (nonbiological loop) indicates

much faster growth than the population growth [118].



Extreme Character of Evolution and the Maximum Energy Dissipation



247



The sigmoid, exponential early stage of growth, which can be associated with

the biocharacteristics of autocatalytic and self-reproductivity, is seen in various

data on economic development. It certainly is more represented in the period of

human history when various statistical data was collected. Even a short look at

the kinetics of production of the so-called “capitalistic” epoch, in various

branches of its economy, reveals nonlinear growth of the economic indicators.

This is expressed in nearly an exponential growth in both the indicators of

production and the capital assets. This autocatalytic appearance of the process

of production, mirrored in the exponential growth of the manufacturing of the

majority of goods, is characteristic of the industrial phase of production and “capitalistic” production in particular, as shown in Figures 4.21 and 4.22 (according

to the statistical data from the US Census [115] and data from Angus Maddison’s

site [116]).

Thus, due to the good availability of data on the development of the early industrialization epoch, shown in Figures 4.21 and 4.22, and the sigmoid, biological-like

kinetics for indicators, one can try to describe it quantitatively within the framework of the theory of dynamic systems. One can pursue two purposes: first, to

phenomenologically relate the economic kinetics and evolution with biological

kinetics; and second, to search for the features manifesting the extremity (or stability)

of economic processes from the perspective of extreme energetic and regulatory

aspects, which are closely related to optimal control.

Indicators of economic growth [119] (as well as parameters and values of biological kinetics in its various applications) have an informative character. In

many cases, the parameters of this kinetics make it possible to judge about the

efficiency of a macroeconomic process, Figure 4.22 (data adapted from Refs.

[115À117]).

One can conclude that the kinetic data on HS population growth and economic

indicators show exponential character of growth at early stages and logistic/sigmoid

growth across a longer term interval, which make these kinetics similar to biological growth kinetics. Early exponential growth indicates that the growth occurs in

unlimited resource conditions. The later sigmoid stage indicates the limitation of

the free energy and other material resources. Global success of HS and the exponential growth of the nonbiological industrial component of HS society indicate a

symbiotic type of relationship between a biological part and the means of production as a nonbiological autocatalytic-like component. Together, these two parts

create the supercycle symbiosis of biological and nonbiological accelerating

loops. These loops form a super-dissipative social global cycle. It is characterized

by further acceleration of the global dissipation rate, which is the involvement

of all possible nonbiological free energy resources, essentially new metabolism

(industrial-economic system), and qualitatively new complex informational processes that provide cognitive support in exploration of the environment and further

development of industry/technology/economy. The HS cooperation with nonbiological means of production enormously extended the HS abilities for the utilization of

qualitatively new free energy resources. Moreover, at end of the day, this allowed

HS to subordinate all biogeocenosis.



248



The Common Extremalities in Biology and Physics



4.3.4



Symbiotic Accelerative Cycle of Biological and Nonbiological

Things



It is also known that the formalism of dynamic systems can be applied to the

description of economic growth, as seen, for example, in Refs. [120À124].

Therefore, a question arises as to the relationship between the dynamic kinetic

models of biological and economical systems. Can a continuous ideological/

methodological adaptation from models of biological dynamic systems to models

of economic kinetics be possible? Can this transition be formulated in the terms of

the optimal control approach? It seems necessary to consider the transition from

the trophic relations of biological species to the use of nonbiological structural

forms of free energy in the global bioenergetic path of consumption. This direction

can also support a consideration of kinetic processes in both these areas from the

ideological perspective of the maximum energy dissipation/least action principle.

Our initial hypothesis is that the autocatalytic quality of nonbiological components

(including the means of production) is stimulated indirectly by the involvement of a

biological component: the labor force. Together the autocatalytic and self-reproductive

components form a super-reproductive cycle, which accelerates both the biological

component—the labor force—and the nonbiological component—the means of production. These ideas can be employed to develop a dynamic model of socioeconomic

growth. The problem of the implementation of the similar formal phenomenological

models of economics with respect to the models of biological kinetics is interesting.

It has the purpose of subsequent interpretation of parameters of biological models

of optimal control on the basis of the well-studied optimal control applications to

economics.

Microeconomics in the classical description of industry production considers the

industrial function that mirrors the dependence of the industrial output Q on the

production factors (inputs). See, for example, Refs. [124,125À128]:

Q 5 QðL; K; MÞ;



ð4:27Þ



where L represents the labor force, K, the value of capital assets or means of production, M, materials for the labor force (workforce).

The industrial CobbÀDouglas function is frequently used for the formal characterization of such a process:

Q 5 BLa1 K a2 M a3 ;



ð4:28Þ



where B, a1, a2, and a3 are referred to as the parameters of production

[124,125À128]. Each of these parameters is usually smaller than 1.0. Moreover,

the statistics of the real data in many economic branches (industries) show that the

sum of the last three parameters is approximately equal to unity [124,125À128].

The form of the three-factor industrial CobbÀDouglas function (4.28) shows

explicitly the involvement of all the three K, L, and M components of production in

the industrial act, and it also shows that these components are in a multiplicative



Extreme Character of Evolution and the Maximum Energy Dissipation



249



form. We shall bear in mind that for the above biological models of symbiosis, the

reproduction rate of every symbiotic species was also proportional to the multiplication of population densities of the species. We apply this ideology to the case of

dynamic models of economic production kinetics.

It is quite reasonable to assume that the process of production, such as the act in

which the product with a consumable (utilization) value for a customer is created,

is the action which brings together the following: an individual (representing labor

force L), the tools (means of production, materialized labor, or capital assets K),

and some material subject (subject of labor action representing biological or nonbiological resources, material M). Such a collision of elements yields a new product,

and its value increase is naturally proportional to the values of each of the participating components. One can say that the volume of the increase in manufactured

output is proportional to the multiplication of the volumes of all three components.

The material production has a self-reproductive-like growth as was discussed

above in a global sense. Therefore, it is believed that the quantity and biological

kinetics of the material being produced is proportional to that which was already

produced. Formally, it could be expressed by the following formula:

dQ

5 αLKM:

dt



ð4:29Þ



In well-investigated historical processes of industrial production by Homo sapiens, one can find a large number of production levels, branches, or industries in

which the products made at one of the levels are used as semiproducts for further

processing. This obviously means that the biosocial economic process has multiple levels, and each of the levels formally has the property of accumulation of

capital assets or, possibly, of materialized work. One should note that it is due

to the social relationships of the ownership that these capital assets acquire an

autocatalytic, self-reproductive property; i.e., they are directed to further production. From a social perspective, it is probably private ownership that makes the

accumulation of goods production in the form of the capital assets the most steady

and extreme process.

As a result, the part of the manufactured material values Q will be distributed

somehow both into the division (branch) of the labor force L and into the form of

the capital assets K, which corresponds to some branch. Perhaps the level of raw

material and semifinished parts M does not have explicitly pronounced selfreproductive properties. If Q is considered to be multileveled, the corresponding

semifinished goods can formally be considered to have self-reproductive properties.

Thus, if one takes the capital assets and circulation funds to be formative parameters that actually build up the capital assets, that determine the production in the

given level or branch, the appropriate equations can be written as:

dqi

5 fi ðq1 ; q2 ; q3 ; . . . qN Þ;

dt



i 5 1; 2; . . . ; N;



250



The Common Extremalities in Biology and Physics



where N is the number of levels or branches considered, and qi is the volume of

production at the corresponding levels (industrial outputs).

If we were to ignore many intermediate stages in the first approximation, it

would be possible to reduce this model, concentrating just on the symbiotic relationship between the biological and nonbiological components, to a two-level

model according to the scheme of Figure 4.19.

So, in this reduced case, the free energy utilization pathway (Figure 4.19) and

the corresponding formal system will contain two levels. The first level will

describe the consumption and transformation in the nonbiological sector. The second level will describe pure biological consumption of the products made in the

nonbiological sector. The relationships between these two levels are in clear symbiosis, since the development of one stimulates the development of the other, which

is indirect evidence for such symbiotic relations that one can see, for example, in

Figure 4.20C, agricultural and industrial phases. It is possible, therefore, to expect

a direct analogy with the symbiosis pathways in biological kinetics.

It is reasonable to revise the main assumptions while constructing a simple twolevel model of relationships between the nonbiological self-reproductive-like levels

and the biological entirely self-reproductive levels. In its simplest form, we can

write a two-dimensional system of differential equations, similar to biological, that

would reflect the phenomenology of the kinetics of development of the sociobiological level or means of production q, and the purely biological level—labor L,

which is linearly related to the population. We can also assume that the resource of

environment is unlimited, similar to the case of the elementary two-level models

for biological kinetics. It will result in self-reproductive parts of the second order.

Let us consider the equation for biological components. We can formulate the

equation as:

dl

5 fl 1 ðl; qÞ 2 fl 2 ðlÞ;

dt



ð4:30Þ



where f 1(l,q) describes the self-reproduction property of biological components

strengthened by symbiosis, and f 2(l) describes degradation of biological component l.

It is clear that the first term, describing the self-reproduction, also explains the

symbiosis-like relationship with the nonbiological component q. The second term

describing the degradation may be chosen in a quadratic form, as in purely biological kinetics. Then the equation simplified in such a way could be written as

dl

5 αl lq 2 β l l2 ;

dt



ð4:31Þ



where αl and β l are positive factors.

For the nonbiological level, one can proceed from a suggestion that the equation

describing the nonbiological component, in this bio and nonbio symbiosis, contains

the terms causing both the growth of this component and its degradation, as in the

biological case. It can also be expressed by the following differential equation:



Extreme Character of Evolution and the Maximum Energy Dissipation



dq

5 fq1ðl; qÞ 2 fq2ðqÞ;

dt



251



ð4:32Þ



where fq1 ðl; qÞ describes the self-reproductive-like properties, and fq2 ðqÞ describes

the degradation.

It should be noted that the term with the 1 sign in Eq. (4.32) comprises selfreproducibility of the nonbiological component q and the biological component l.

The degradation, explained by the second term in Eq. (4.32), is also natural since

this term can be proportional to the quantity of the nonbiological product. It can also

be explained by the “moral” and “physical” aging of the means of production, just

as it can be a result of biological and nonbiological competition for the sales market.

Thus, the simplest equation for the nonbiological component can be written as:

dq

5 αq lq 2 β q qγ ;

dt



ð4:33Þ



where αq, β q, and γ are positive coefficients.

The complete system will be written as:

dl

5 αl lq 2 β l l2 ;

dt

dq

5 αq lq 2 β q qγ :

dt



ð4:34Þ



The phase trajectories of system (4.34) and its trajectories in time for

a15b15b251, a252 at different initial conditions are shown in Figure 4.23. It is

necessary to note that similar systems and their qualitative behavior have been well

investigated, and in the case of biological kinetics, they have been well interpreted.

Let us bear in mind that in this simple example, both components indicate a steady

growth under certain conditions, as it also follows from the known economic data,

Figure 4.22. Figure 4.22 indicates the exponential growth (linear in a semilogarithmic scale) that is characteristic for the self-reproductive-like kinetics for the nonbiological level, which is also incorporated in the symbiotic relations to Homo

sapiens. However, with time due to the limitations in resources, the curves acquire

a sigmoid outline, and they show more complex perturbations related to the cyclic

behavior.

We also need to note that the degree γ of the term, responsible for degradation,

may be considered a parameter of “sociality” of the product (nonbiological component) manufactured and its particular distribution. It should be emphasized that the

nonbiological product does not have the direct property of self-reproduction. It

acquires this property as a result of appropriation in the ownership process, and

only the appropriated equivalents of this product—the capital assets, which materialize the labor force—have got such properties.

It is widely known that many economic indicators of production have a periodicity. This periodicity was also explained in Eq. (4.34) two-level model, as in the case



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