Dynamic Origin of Evolution and Social Transformation
We analyse the unreduced, nonperturbative dynamics of an arbitrary manybody interaction process by means of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and evolution in an a priori conservative, time-independent system. It...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
2013
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irk-123456789-758942015-02-06T03:02:07Z Dynamic Origin of Evolution and Social Transformation Kirilyuk, A.P. We analyse the unreduced, nonperturbative dynamics of an arbitrary manybody interaction process by means of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and evolution in an a priori conservative, time-independent system. It appears together with the universal dynamic complexity definition, where this unified complexity conservation and transformation constitute the essence of evolution. We then consider the detailed structure of this universal evolutionary process showing its step-wise, ‘punctuated’ character, now provided with the exact mathematical description. Comparing the expected features of a revolutionary complexity transition near a step-like complexity upgrade with the currently observed behaviour of world’s social and economic systems, we prove the necessity of complexity revolution towards the superior civilisation level of well-defined nature, the only alternative being an equally dramatic and irreversible degradation, irrespective of efforts applied to stop the crisis at the current totally saturated complexity level. Ми аналізуємо нередуковану, непертурбативну динаміку довільного процесу взаємодії багатьох тіл за допомогою узагальненої методи ефективного потенціалу і розкриваємо точно визначене універсальне походження зміни (виникнення), часу та еволюції в апріорі консервативній, незалежній від часу системі. Вона з’являється разом з визначенням універсальної динамічної складності, згідно з яким збереження та перетворення цієї уніфікованої складності і створюють еволюцію. Далі ми розглядаємо детальну структуру цього універсального еволюційного процесу, яка демонструє східчастий, переривистий характер, споряджений тепер точним математичним описом. Порівнюючи очікувані особливості революційного переходу складності біля її східчастого підвищення з сучасною поведінкою світових суспільних та економічних систем, ми доводимо необхідність революції складності до вищого рівня цивілізації добре визначеної природи, з єдиною можливою альтернативою такої ж драматичної та необоротньої деґрадації, незалежно від зусиль, які докладаються для подолання кризи на сучасному, цілком насиченому рівні складності. Мы анализируем нередуцированную, непертурбативную динамику произвольного процесса взаимодействия многих тел с помощью обобщённого метода эффективного потенциала и выявляем хорошо определённую универсальную природу изменения (возникновения), времени и эволюции в априори консервативной, независящей от времени системе. Она обнаруживается вместе с определением универсальной динамической сложности, сохранение и преобразование которой и составляют сущность эволюции. Мы затем рассматриваем детальную структуру этого универсального эволюционного процесса, демонстрирующую ступенчатый, прерывистый характер, снабжённый теперь точным математическим описанием. Сравнивая ожидаемые особенности революционного перехода сложности вблизи её ступенчатого роста с наблюдаемым сейчас поведением мировых общественных и экономических систем, мы доказываем необходимость революции сложности к высшему уровню цивилизации хорошо определённой природы, с единственной возможной альтернативой столь же драматической и необратимой деградации, независимо от усилий, прилагаемых для преодоления кризиса на текущем, полностью насыщенном уровне сложности. 2013 Article Dynamic Origin of Evolution and Social Transformation / A.P. Kirilyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2013. — Т. 11, № 1. — С. 1-21. — Бібліогр.: 19 назв. — анг. 1816-5230 PACSnumbers:03.67.-a,05.45.-a,05.45.Df,05.65.+b,45.50.Jf,89.65.-s,89.75.-k http://dspace.nbuv.gov.ua/handle/123456789/75894 en Наносистеми, наноматеріали, нанотехнології Інститут металофізики ім. Г.В. Курдюмова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We analyse the unreduced, nonperturbative dynamics of an arbitrary manybody
interaction process by means of the generalised effective potential
method and reveal the well-specified universal origin of change (emergence),
time and evolution in an a priori conservative, time-independent system. It
appears together with the universal dynamic complexity definition, where
this unified complexity conservation and transformation constitute the essence
of evolution. We then consider the detailed structure of this universal
evolutionary process showing its step-wise, ‘punctuated’ character, now provided
with the exact mathematical description. Comparing the expected features
of a revolutionary complexity transition near a step-like complexity
upgrade with the currently observed behaviour of world’s social and economic
systems, we prove the necessity of complexity revolution towards the superior
civilisation level of well-defined nature, the only alternative being an
equally dramatic and irreversible degradation, irrespective of efforts applied
to stop the crisis at the current totally saturated complexity level. |
| format |
Article |
| author |
Kirilyuk, A.P. |
| spellingShingle |
Kirilyuk, A.P. Dynamic Origin of Evolution and Social Transformation Наносистеми, наноматеріали, нанотехнології |
| author_facet |
Kirilyuk, A.P. |
| author_sort |
Kirilyuk, A.P. |
| title |
Dynamic Origin of Evolution and Social Transformation |
| title_short |
Dynamic Origin of Evolution and Social Transformation |
| title_full |
Dynamic Origin of Evolution and Social Transformation |
| title_fullStr |
Dynamic Origin of Evolution and Social Transformation |
| title_full_unstemmed |
Dynamic Origin of Evolution and Social Transformation |
| title_sort |
dynamic origin of evolution and social transformation |
| publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/75894 |
| citation_txt |
Dynamic Origin of Evolution and Social Transformation / A.P. Kirilyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2013. — Т. 11, № 1. — С. 1-21. — Бібліогр.: 19 назв. — анг. |
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Наносистеми, наноматеріали, нанотехнології |
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| fulltext |
1
PACS numbers: 03.67.-a, 05.45.-a,05.45.Df,05.65.+b,45.50.Jf,89.65.-s, 89.75.-k
Dynamic Origin of Evolution and Social Transformation
A. P. Kirilyuk
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03680 Kyyiv-142, Ukraine
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-
body interaction process by means of the generalised effective potential
method and reveal the well-specified universal origin of change (emergence),
time and evolution in an a priori conservative, time-independent system. It
appears together with the universal dynamic complexity definition, where
this unified complexity conservation and transformation constitute the es-
sence of evolution. We then consider the detailed structure of this universal
evolutionary process showing its step-wise, ‘punctuated’ character, now pro-
vided with the exact mathematical description. Comparing the expected fea-
tures of a revolutionary complexity transition near a step-like complexity
upgrade with the currently observed behaviour of world’s social and econom-
ic systems, we prove the necessity of complexity revolution towards the supe-
rior civilisation level of well-defined nature, the only alternative being an
equally dramatic and irreversible degradation, irrespective of efforts applied
to stop the crisis at the current totally saturated complexity level.
Ми аналізуємо нередуковану, непертурбативну динаміку довільного про-
цесу взаємодії багатьох тіл за допомогою узагальненої методи ефективно-
го потенціалу і розкриваємо точно визначене універсальне походження
зміни (виникнення), часу та еволюції в апріорі консервативній, незалеж-
ній від часу системі. Вона з’являється разом з визначенням універсальної
динамічної складності, згідно з яким збереження та перетворення цієї
уніфікованої складності і створюють еволюцію. Далі ми розглядаємо де-
тальну структуру цього універсального еволюційного процесу, яка демон-
струє східчастий, переривистий характер, споряджений тепер точним ма-
тематичним описом. Порівнюючи очікувані особливості революційного
переходу складності біля її східчастого підвищення з сучасною поведін-
кою світових суспільних та економічних систем, ми доводимо необхід-
ність революції складності до вищого рівня цивілізації добре визначеної
природи, з єдиною можливою альтернативою такої ж драматичної та не-
оборотньої деґрадації, незалежно від зусиль, які докладаються для подо-
лання кризи на сучасному, цілком насиченому рівні складності.
Наносистеми, наноматеріали, нанотехнології
Nanosystems, Nanomaterials, Nanotechnologies
2013, т. 11, № 1, сс. 1—21
© 2013 ІМФ (Інститут металофізики
ім. Г. В. Курдюмова НАН України)
Надруковано в Україні.
Фотокопіювання дозволено
тільки відповідно до ліцензії
2 A. P. KIRILYUK
Мы анализируем нередуцированную, непертурбативную динамику про-
извольного процесса взаимодействия многих тел с помощью обобщённого
метода эффективного потенциала и выявляем хорошо определённую уни-
версальную природу изменения (возникновения), времени и эволюции в
априори консервативной, независящей от времени системе. Она обнару-
живается вместе с определением универсальной динамической сложно-
сти, сохранение и преобразование которой и составляют сущность эволю-
ции. Мы затем рассматриваем детальную структуру этого универсального
эволюционного процесса, демонстрирующую ступенчатый, прерывистый
характер, снабжённый теперь точным математическим описанием. Срав-
нивая ожидаемые особенности революционного перехода сложности
вблизи её ступенчатого роста с наблюдаемым сейчас поведением мировых
общественных и экономических систем, мы доказываем необходимость
революции сложности к высшему уровню цивилизации хорошо опреде-
лённой природы, с единственной возможной альтернативой столь же дра-
матической и необратимой деградации, независимо от усилий, прилагае-
мых для преодоления кризиса на текущем, полностью насыщенном
уровне сложности.
Key words: complexity, chaos, self-organisation, fractal, many-body prob-
lem, origin of time, revolution of complexity.
(Received July 3, 2012)
1. INTRODUCTION
In our time of great and rapid changes in natural, technical and social
systems, the origin, direction and efficiency of evolutionary processes
is of special, not only theoretical but also increasingly practical inter-
est. Despite progressively growing efforts to put the evolution theory
on a firm rigorous basis, the problem often formulated also in terms of
the origin of time remains practically unsolved within the convention-
al analysis. Two major, fundamentally separated approaches, statisti-
cal and dynamical ones, are reduced to mere postulation of empirically
observed changes, either in the form of permanently growing entropy
(usually for relatively gradual and smoothly distributed changes), or
in the form of model-based dynamical structure formation with artifi-
cially inserted time variable (for stronger and uneven changes).
Recent nonperturbative analysis of real many-body interaction
problem with arbitrary interaction potential reveals a qualitatively
new, totally dynamic origin of change, time and randomness in the
form of fundamental dynamic multivaluedness, or redundance, of un-
reduced interaction results [1—11]. In a given paper, we review this
analysis (Sec. 2) and the ensuing origin of any system evolution (Sec.
3). We then consider its application to social system evolution and
transformation, with special attention to current critical development
problems (Sec. 4). We thus show how the obtained mathematically rig-
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 3
orous and now truly complete solution to unreduced many-body inter-
action problem leads to consistent understanding of modern critical
point of human species and civilisation evolution and successful tran-
sition to its progressive branch [8]. We conclude with an overview of
major features and perspectives of the expected new kind of civilisa-
tion after this nontrivial ‘phase transition’ (Sec. 5).
2. UNREDUCED MANY-BODY INTERACTION
We analyse arbitrary (pair-wise) interaction in any many-body system
with the application of a general Hamiltonian equation for a distribu-
tion function called here existence equation and coinciding in form
with the quantum mechanical Schrödinger equation or classical Hamil-
ton—Jacobi equation [1—11]. We later show (Sec. 3) that it is indeed the
universal description of any many-body interaction. The existence
equation actually just describes the initial configuration of a system of
N interacting entities:
( ) ( ) ( ) ( )
= >
+ Ψ = Ψ
0
,
N N
k k kl k l
k l k
h q V q q Q E Q , (1)
where ( )
k k
h q is the generalised Hamiltonian describing the (known)
dynamics of the k-th system component with its degrees of freedom qk,
( , )
kl k l
V q q is the arbitrary interaction potential for the k-th and l-th
components, Ψ( )Q is the system state-function fully describing its
configuration ≡
0 1{ , ,..., }
N
Q q q q , and E is the generalised Hamiltonian
eigenvalue (generalised energy). As becomes clear in further analysis
(Sec. 3), this generalised Hamiltonian/energy represents a universal
measure of dynamic complexity defined below (thus extending respec-
tive usual notions). Explicit time dependence, if any, enters the same
description of Eq. (1) by energy replacement on the right with a time
derivative operator.
One can conveniently rewrite the general interaction problem for-
mulation of Eq. (1) in terms of known eigenmodes of the system com-
ponents that gives an equivalent system of equations [1—11]:
( ) ( ) ( ) ( ) ( ) ( ) ′ ′
′≠
ξ + ξ ψ ξ + ξ ψ ξ = η ψ ξ 0 nn n nn n n n
n n
h V V , (2)
where ξ ≡
0
q is a special, common degree of freedom (usually system
component or configuration space coordinates), ′ ξ( )
nn
V are matrix ele-
ments of interaction potential between component eigenmodes num-
bered by ,n n′ , and η = − ε
n n
E with eigenmode eigenvalues εn (see [1—
11] for the mode details).
As the problem remains nonintegrable for arbitrary interaction po-
tential and more than two system components, usual approach pro-
4 A. P. KIRILYUK
ceeds with its dimensional reduction to a severely simplified but ex-
plicitly or approximately integrable ‘model’ such as
( ) ( ) ( ) ( ) ξ + ξ ψ ξ = η ψ ξ 0 nn n n nh V (3)
for Eqs. (2), with any integrable potential ξ( )
nn
V . Thus obtained ex-
plicit solution to that another, simplified problem of Eq. (3) involves,
however, not only significant and irreducible departures from reality
but especially fundamental absence of any true novelty, the desired
evolutionary change and related intrinsic time flow. Trying to find
these features in the un-reduced interaction process while preserving
its analytical description, one may start with the straightforward sub-
stitution of variables in the original system of Eqs. (2) formally reduc-
ing system dimensionality but at the expense of equivalent, much more
complicated and essentially nonlinear effective interaction potential
[1—11]. This method known as ‘optical potential’ in the theory of scat-
tering (e.g., [12, 13]) leads to an equation externally resembling a mod-
el description of Eq. (3),
( ) ( ) ( ) ( ) ξ + ξ η ψ ξ = ηψ ξ eff0 0 0;h V , (4)
but where the effective potential (EP) ξ η
eff
( ; )V contains the unreduced
interaction complexity in the form of its (nonlinear) dependence on the
eigenvalues and eigenfunctions to be found:
( ) ( ) ( ) ( ) ξ η ψ ξ = ξ ψ ξ +
0 0eff 00;V V
( ) ( ) ( ) ( ) ( )
ξ
∗
Ω
′ ′ ′ ′ξ ψ ξ ξ ψ ξ ξ ψ ξ
+
η − η − ε
0 0
00 0
0
0,
n ni ni n
ni nn i
V d V
, (5)
where ε = ε − ε0 0n n , η ≡ η
0 is the eigenvalue to be found and ψ ξ0{ ( )}
ni ,
η0{ }
ni are the complete sets of (a priori unknown) eigenfunctions and
eigenvalues for a system of equations of smaller dimensionality re-
duced from the full system of Eq. (2) [1—11].
Whereas usual applications of the optical potential method proceed
with perturbative reduction of this always nonintegrable EP expres-
sion, Eq. (5), inevitably implying the same fundamental deficiency, the
unreduced EP formalism analysis [1—12] reveals indeed a qualitatively
new phenomenon of interaction result splitting into many intrinsically
complete and therefore incompatible system configurations, or realisa-
tions, just giving rise to intrinsic time flow and dynamic origin of evo-
lutionary changes. This dynamic multivaluedness, or redundance,
phenomenon can be detected by directly counting the number of eigen-
values η for the characteristic equation of Eq. (4) with the unreduced
EP of Eq. (5). It results from the nonlinear EP dependence on η reflect-
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 5
ing the full complexity of interaction feedback loops in a real many-
body system. We thus discover that the total number of incompatible
system realisations Nℜ is determined by the number of its interacting
eigenmodes, ℜ ξ=N N , where ξN is the number of terms in summation
over i in Eq. (5). This algebraic analysis result is totally confirmed and
further supported by its geometric version [1, 14] clearly demonstrat-
ing the eigenvalue distribution dynamics.
The fundamental importance of this new, intrinsic quality of dy-
namic redundance of any real (unreduced) interaction process is that it
provides the desired universal origin of physically real, irreversibly
flowing time, evolutionary change and (new) structure formation (or
‘self-organisation’). Indeed, being dynamically equal and physically
incompatible, those multiple system realisations are forced, by the
same driving interaction, to replace each other permanently and irre-
versibly, in a dynamically random order thus defined. In other words,
realisation plurality implies fundamental dynamic instability of each
individual realisation that follows its physically transparent cycles of
emergence, saturation and inevitable replacement by a next emerging,
randomly (dynamically) chosen realisation [1—12, 14]. In this process,
the system incessantly repeats the cycles of dynamic entanglement of
its interacting degrees of freedom (at the realisation formation stage)
and their further disentanglement during transition to the next reali-
sation through a special, intermediate realisation of the generalised
wavefunction with transiently quasi-free components [1—11] (it gener-
alises the now causally understood quantum-mechanical wavefunction
at the lowest interaction levels to the distribution function at any in-
teraction/complexity level [1, 2, 11, 15]). Universally defined system
change in that realisation rotation process corresponds to well-defined
leaps of physically real time (see Sec. 3) of a given complexity level,
which thus unstoppably flows simply due to the driving (multivalued!)
interaction process and cannot be reversed even artificially because of
the dynamically random choice of each next system realisation.
As a result, the observed system density ρ ξ( , )Q ( = Ψ ξ 2| ( , ) |Q or
Ψ ξ( , )Q , depending on complexity level) or any other quantity is ob-
tained as a dynamically probabilistic sum of this quantity for all reali-
sations implying their permanent dynamically random change:
( ) ( ) ( ) ( )
= =
ℜ ℜ⊕ ⊕ρ ξ = Ψ ξ = ρ ξ = Ψ ξ
2 2
1 1
, , , ,
r r
r r
N N
Q Q Q Q , (6)
where Ψ ξ( , )
r
Q is the r-th regular (non-intermediate) realisation state
function obtained from solution of the unreduced EP formalism, Eqs.
(4), (5), ⊕ sign stands for the dynamically probabilistic sum character,
and the dynamically determined (a priori) probability value for the r-th
realisation emergence, αr, is attached:
6 A. P. KIRILYUK
,
ℜ
α = α =1
1r r
rN
. (7)
It becomes clear why any usual, dynamically single-valued, either
statistical or dynamical-model description cannot reveal any intrinsic
origin of time and evolutionary change. Although the former statisti-
cal (or stochastic) analysis formally postulates an imitation of random
changes (without revealing their dynamic origin), it is forced then to
deal only with their averaged description just at the level of distribu-
tion function (our intermediate realisation), perfectly reproducing
thus the dynamically single-valued reduction scheme. The same is true
for all other dynamically single-valued imitations of ‘complexity’ and
emergence in usual theory, including ‘(strange) attractors’, ‘multista-
bility’ and ‘exponentially diverging trajectories’ (or ‘Lyapunov expo-
nents’) as they all deal with formally postulated system ‘evolution’ in
mathematical ‘time’ within one and the same realisation, with totally
compatible structure parts (some of these approaches, in particular,
attractors, also deal with system evolution in abstract, ‘phase’ spaces,
which deforms essentially the meaning of ‘change’). One can say that
any such dynamically single-valued, or unitary, description actually
deals with a point-like, zero-dimensional projection of the unreduced,
dynamically ‘multi-dimensional’ (multivalued) evolution of real sys-
tem, the former reproducing only the respective strongly limited scope
of essential properties of the latter.
These conclusions are confirmed by the universal definition of dy-
namic complexity within our dynamically multivalued description of
arbitrary interaction process (in any real system). Dynamic complexi-
ty, C, of a system or interaction process (thus, any object) is universal-
ly defined as a function of the number of its realisations (or rate of
their change) equal to zero for the (unrealistic) case of one system real-
isation [1—11, 14]:
( ) ℜ ℜ= > =, 0, (1) 0C C N dC dN C , (8)
where, for example, ℜ ℜ=
0
( ) ln( )C N C N or ℜ ℜ= −
0
( ) ( 1)C N C N . As for
any real system 1Nℜ > and for macroscopic systems the total ℜN is a
huge number, any real system complexity has a positive (and usually
relatively great) value. Correspondingly, all unitary, dynamically sin-
gle-valued models of usual description, including their imitations of
‘complexity’, correspond to strictly zero value of this universal dy-
namic complexity. The unreduced dynamic complexity, genuine dy-
namic randomness, essential evolutionary change (emergence) and
physically real, irreversibly flowing time come thus all together as
unified manifestations of fundamental dynamic multivaluedness of
any real interaction process. It implies that system realisations enter-
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 7
ing the unreduced complexity definition of Eq. (8) should not be con-
fused or tacitly substituted with any loosely defined or empirically ob-
served system ‘states’ or ‘structure elements’, but should instead be
explicitly derived as those internally complete results of real interac-
tion development, as shown by the above unreduced EP method. On the
other hand, for each particular problem, one can often ignore realisa-
tions of certain lower (e.g., quantum) levels of complexity that prova-
bly do not directly influence the higher-level (e.g., classical) dynamics
under consideration.
The hierarchical, multilevel structure of world complexity thus de-
fined is implied already by the basic EP formalism of Eqs. (4), (5). In-
deed, the same analysis can be applied to the reduced system of equa-
tions giving rise to eigensolutions { }ψ ξ0
( )ni ,{ }η0
ni , leading to their dy-
namical splitting by the same mechanism and so on for a series of all
lower-dimension solutions. As a result, one obtains the causally com-
plete final solution and system structure in the form of dynamically
probabilistic fractal, containing many levels of permanently randomly
changing realisations of progressively decreasing scale, which gives
rise to the rigorous and universal definition of life [1, 2, 6, 7, 10]. It
extends essentially the simplified, abstract and dynamically single-
valued model of ordinary fractals, with their limited, always practical-
ly broken scale symmetry being now replaced by the externally irregu-
lar but always exact symmetry of complexity underlying thus real evo-
lution dynamics (see Sec. 3) [1, 2, 5—11, 15].
This most complete, dynamically fractal general solution to the
starting unreduced interaction problem of Eq. (1) can be presented as
the multilevel extension of one-level version of Eqs. (6), (7):
( ) ( )′ ′′
′ ′′
ℜ ⊕
ρ ξ = ρ ξ ...
, , ...
, ,rr r
r r r
N
Q Q , (9)
where ′ ′′, , , ...r r r enumerate respective fractal level realisations, while
the dynamically determined probability ′ ′′α
...rr r of realisation emergence
is
′ ′′
′ ′′ ′ ′′
′ ′′ℜ
α = α =...
... ...
, , ...
, 1rr r
rr r rr r
r r r
N
N
, (10)
with ′ ′′...rr rN being the number of empirically inseparable elementary
realisations within the corresponding observed composite realisation.
The permanent ‘horizontal’ realisation change at any level is complet-
ed here by ‘vertical’ structure development to other levels, which has
the transparent physical interpretation of progressive emergence of
new structures as a result of interaction of structures formed at neigh-
bouring levels. This ‘evident’ interaction process development and real
8 A. P. KIRILYUK
structure creation would be impossible, however, without much less
evident dynamic multivaluedness at each interaction level. Even the
average expectation value ρ ξ
ex
( , )Q (for long enough observation time)
hides in it a very complicated, multivalued and multilevel interaction
development process:
( ) ( )′ ′′ ′ ′′
′ ′′
ℜ
ρ ξ = α ρ ξex ... ...
, , ...
, ,
rr r rr r
r r r
N
Q Q . (11)
3. SPACE, TIME, EVOLUTION, AND THE UNIVERSAL SYMMETRY
OF COMPLEXITY
We can now provide the above physical origin of time (emergence) and
evolution (structure formation) in the multivalued interaction dynam-
ics (Sec. 2) with a rigorous expression. We first note that what actually
emerges in such real, dynamically multivalued interaction process is
different, permanently mutually replaced system realisations forming
its evolving structure. Therefore, one can start with universal defini-
tion of elementary space (structure) element xΔ , as characteristic ei-
genvalue separation for the unreduced EP formalism, Eqs. (4), (5),
Δ = Δηr
i
x , where r enumerates realisations and i eigenvalues within the
same realisation. One should distinguish here between the elementary
length of system jump between realisations, λ = Δ = Δ ηr
r r i
x (neigh-
bouring r-values, fixed i), determining the dimension of observed dy-
namic structures, and the minimum size of effective space point,
= Δ = Δ η
0
r
i i i
r x (fixed r, neighbouring i values), reflecting the smallest
system dimension at a given complexity level. Based exclusively on the
unreduced (multivalued) interaction development, we obtain thus the
totally consistent and universal definition of intrinsically discrete and
physically tangible space structure resulting from that interaction.
As physically real time (and evolution) originates from system reali-
sation change (Sec. 2), one obtains now universal time definition as in-
tensity specified as frequency ν of realisation change, with elementary
time interval (period) Δt for that frequency being Δ = τ = ν = λ
0
1t v ,
where λ = Δ
r
x is the above elementary length of system jump between
realisations and 0
v is the signal propagation speed in the material of
interacting components (known from lower complexity levels). Thus,
defined real time is permanently flowing due to unstoppable transitions
between system realisations driven by its interaction and this time
flow is irreversible because of the dynamically random choice of each
next realisation.
Note that in usual, dynamically single-valued interaction models
there is only one realisation and therefore λ = Δ = 0
r
x , Δ = λ =
0
0t v ,
so that there can be no either genuine structure formation or real time
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 9
flow, both of them being inserted only artificially (postulated), includ-
ing conventional ‘self-organisation’ and ‘chaos’ theories. By contrast,
in our unreduced, dynamically multivalued description, there is a mul-
tilevel, fractally structured hierarchy of real space and time corre-
sponding to the hierarchy of developing interaction complexity [1, 5,
8, 10, 11, 15]. Whereas each individual (big enough) level of complex
dynamics is observed and characterised as stationary system mechan-
ics, transitions between essentially different complexity levels appear
as explicit evolution phenomena, even though in both cases one deals
with the same process of dynamically multivalued interaction devel-
opment. We shall specify now both these cases within a unified de-
scription in terms of suitable complexity measures.
As the elementary space and time intervals introduced above are de-
termined by system transitions between realisations, a major physical
measure of complexity determined by the number of realisations (Eq.
(8)) emerges as the generalised action as the simplest quantity pro-
portional to both time and space (increments) and now extended to any
level of complex world dynamics [1, 5, 8, 10, 11]:
Δ = Δ − Δp x E t (12)
with coefficients, p and E, recognised as (now generalised) momentum
and (total) energy:
=
Δ=
Δ λ
0
const ;tp
x
, (13)
=
Δ= −
Δ τ
0
const ;xE
t
, (14)
where 0 is a characteristic action value at a given complexity level,
while x and p should be properly understood as vectors where neces-
sary. We see thus that these omnipresent quantities, momentum and
energy, are also universal differential measures of complexity, whereas
action is its integral measure, which extends essentially the meaning
and importance of these originally mechanical quantities. We can see
also that, following space and time discreteness, action is a dynamical-
ly discrete, or naturally quantised, quantity at any level of complexity,
leading to fundamental quantum-mechanical discreteness at the lowest
complexity levels (with elementary action increment = 0 , Planck
constant) [1, 2, 11, 15] but also to discrete structures and evolutionary
transitions at higher complexity levels (Sec. 4).
For irreversibly growing time and always-positive total energy,
complexity-action as determined by Eq. (12) will always decrease
with time, irrespective of interaction development details. It is but an-
other expression of dynamically random realisation choice underlying
10 A. P. KIRILYUK
time irreversibility [1, 5, 8, 10, 11, 15]. On the other hand, there is cer-
tainly also a growing form of complexity in the same (arbitrary) inter-
action process development that describes emergence of ever growing
number of its fractally structured realisations (in agreement with the
universal complexity definition of Eq. (8)). It generalises traditional
entropy to any (real) interaction process, and, therefore, we call this
growing complexity form dynamic entropy, S. As both decreasing
complexity-action and growing complexity-entropy account for one
and the same process of interaction-driven structure emergence, with
the same underlying universal definition of dynamic complexity of Eq.
(8), it becomes clear that one of them, complexity-entropy, grows ex-
actly at the expense of the dual form of complexity-action, so that the
decrease of action, also called dynamic information I [1, 2, 5, 7—11,
15], produces just the same quantity of dynamic entropy. Whereas dy-
namic information expressed as action accounts for system (interac-
tion) potentiality to produce new structures (realising thus the univer-
sal integral extension of ‘potential energy’), dynamic entropy de-
scribes the irreversibly produced tangible result of that potential pow-
er, in the form of real-structure complexity.
In summary, any interaction process can be universally described as
conservation and transformation, or symmetry, of the total dynamic
complexity C defined as the sum of dynamic information (action)
= I and dynamic entropy S (measured in the same units of general-
ised action), = + = +C I S S , where the first summand permanently
decreases to the exact amount of simultaneous growth of the second
summand:
Δ = Δ + Δ = Δ = −Δ > 0, 0C S S . (15)
Dynamic complexity-entropy of real emerging structures thus simp-
ly realises their ‘plan’ described by dynamic complexity-action, while
the entire process is a result of the exact symmetry (conservation) of
total complexity, rather than any conventional extremum principle
(e.g., maximum entropy or often-evoked maximum or minimum entro-
py growth rate, etc.). Symmetry of complexity is derived thus as the
absolutely universal law eventually underlying all (correct) particular
laws and ‘principles’ always only empirically postulated in usual theo-
ry [1, 5, 8—11, 15] (see also below). Contrary to regular, always limited
and somewhere broken symmetries of unitary theory, the universal
symmetry of complexity remains always exact but relating externally
irregular structures and sequences. As it simply connects system con-
secutive dynamical states, it also represents the most precise expres-
sion of any system evolution understood now as the necessary result of
dynamic conservation by inevitable transformation of total dynamic
complexity. Internally irregular and chaotic change is seen now as a
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 11
result of a perfect and universal symmetry, contrary to opposite ideas
of unitary (dynamically single-valued) science, where change is rather
a (conceivably small) deviation from (always-inexact) particular sym-
metry due to its explicit violation by an extraneous influence.
If we consider now manifestations of the universal symmetry of
complexity for the case of system mechanics (see above), i.e., relatively
small changes at a given complexity level, then we can produce its more
convenient, differential form by dividing Eq. (15) by a small real time
increment = Δ constxt (consistently defined above):
= =
Δ Δ + = Δ Δ
const const
, , 0x tH x t
t x
, = > 0H E , (16)
where the generalised Hamiltonian, = ( , , )H H x p t , is the differential
expression of complexity-entropy, == Δ Δ
const
( )
x
H S t , in agreement
with the definition of generalised (total) energy E ( = H ) through com-
plexity-action, Eq. (14), and generalised momentum definition, Eq.
(13). We obtain thus the discrete complex-dynamic extension of the
well-known Hamilton—Jacobi equation provided now with a new, es-
sentially generalised meaning and time-flow direction towards grow-
ing dynamic entropy and decreasing dynamic information (complexity-
action). The latter condition can be further amplified, if we introduce
the generalised Lagrangian, L, as the (generally discrete) total time
derivative of complexity-action:
= =
Δ Δ Δ Δ= = + = − = −
Δ Δ Δ Δconst constx t
x
L p E p H
t t x t
v v , (17)
where = Δ Δx tv is the (global) motion speed and the scalar product of
vectors is implied if necessary. The same fundamental feature of dy-
namically random choice among multiple incompatible realisations
implies permanently decreasing dynamic information of action:
< > ≥0, , 0L H E pv , (18)
that is the generalised and stronger version of the extended second law
of Eqs. (15), (16) determining the time arrow direction.
The generalised Hamilton—Jacobi formalism of Eq. (16) describing
the evolution of ‘regular’, localised and entangled, system realisations
can be completed with the equally universal Schrödinger equation for
the generalised wavefunction, or distribution function, Ψ, of interme-
diate, delocalised and disentangled, realisation (Sec. 2) [1, 5, 8—11]:
( ) = =
ΔΨ Δ = Ψ Δ Δ const const0
ˆ , , ,
x t
H x t x t
t x
, (19)
12 A. P. KIRILYUK
where 0
is a characteristic action value from the generalised quanti-
sation rule (see below) that may include a numerical constant ( =
0
i
for quantum complexity levels), while the Hamiltonian operator,
ˆ ˆ( , , )H x p t , is obtained from its ordinary form of Eq. (16) by replace-
ment of momentum variable = = Δ Δ const( / ) |tp x with the respective
‘momentum operator’, = = Δ Δ
0 constˆ ( / ) |tp x . The generalised Schrö-
dinger equation, Eq. (19), is related to the generalised Hamilton—
Jacobi equation, Eq. (16), by the dynamic quantisation rule,
( )Δ Ψ = 0 ,
ΔΨΔ = −
Ψ0
, (20)
which results from the same dynamic complexity conservation law of
Eq. (15) (first equality) implying here that each regular realisation is
obtained by intermediate realisation (generalised wave-function) ‘re-
duction’ due to entanglement of interaction components, with further
disentanglement back to intermediate realisation [1, 5, 8—11, 15]. The
same multivalued dynamics for the case of measurement process leads
to the generalised Born’s rule [1, 5, 8—11, 15] providing another, ex-
tremely convenient expression for regular realisation probabilities (cf.
Eqs. (7), (10)):
α = Ψ 2
( )r rX , (21)
where r
X is the r-th realisation configuration and α
r its probability.
This extension of respective relation of usual quantum mechanics
(simply postulated but never causally derived there) to arbitrary sys-
tem dynamics explains the importance of the generalised Schrödinger
equation, especially for cases of sufficiently ‘smeared’ dynamics with
many close realisations.
The resulting Hamilton—Schrödinger formalism, Eqs. (16)—(21),
expresses thus the universal symmetry of complexity, Eq. (15), espe-
cially for cases of relatively smooth system evolution within the same
(big) complexity level. We can see now the origin of universality of the
starting Hamiltonian description, Eq. (1), referred to at the beginning
of Sec. 2. Moreover, we can see how the symmetry of complexity and its
Hamilton—Schrödinger formalism underlies (and now unifies) many
popular, actually postulated dynamic equations and principles. For ex-
ample, if we consider generalised Hamiltonian expansion in powers of
its momentum variable,
( ) ( )
∞
=
=
0
, , ,
n
n
n
H x p t h x t p , (22)
with generally arbitrary functions ( , )
n
h x t , then its substitution into
the generalised Hamilton—Jacobi and Schrödinger equations gives re-
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 13
spectively (for ordinary, continuous versions of derivatives):
( )
∞
=
∂ ∂ + = ∂ ∂
0
, 0
n
n
n
h x t
t x
, (23)
( )
=
∞
=
∂Ψ ∂ Ψ
∂ ∂
0
0 ,
n
n n
n
h x t
t x
. (24)
For various ( , )
n
h x t and series truncations, one can obtain here many
particular model equations. Other models result from simplification of
dynamically nonlinear dependence of unreduced EP, Eqs. (4), (5), on ei-
genfunctions and eigenvalues to be found. In addition to universal con-
servation and transformation of complexity (including generalised first
and second laws of thermodynamics), one can derive other fundamental
laws and principles from this universal description of multivalued dy-
namics, including now causally substantiated quantum behaviour and
elementary particle properties intrinsically unified with equally dynam-
ically explained laws of special and general relativity [1, 11, 15].
If we consider now the situation of very uneven, ‘revolutionary’
transformation of complexity-action to complexity-entropy between
big enough complexity levels (complementary to the above mechanics
within each level), then the universal Hamilton—Schrödinger formal-
ism of Eqs. (16)—(21) will be much less useful because of ‘singular’,
relatively great complexity (and structure formation) leap involved.
One may analyse such transitions in more detail applying other, more
qualitative approach to manifestations of the same symmetry of com-
plexity of Eq. (15).
A general scheme of evolutionary complexity transformation pro-
cess is shown in Fig. 1 [8]. Here, the characteristic increment, ΔS, of
dynamic complexity-entropy during system ‘revolutionary’ transition
from i-th to j-th complexity level is much greater than its maximum
variations, Δ Δ,i jS S , in each level dynamics, Δ Δ Δ 0 0: , : ,i j i jS S S ,
where 0 0,i j are characteristic (absolute) action values for respective
levels. Therefore, complexity evolution analysis in terms of differen-
tial equations, Eqs. (16), (19), becomes inefficient on this global scale.
However, we can clearly specify the fundamental origin of both system
evolution as such, and its strongly uneven, step-wise dynamics clearly
seen in Fig. 1. It is reduced to dynamic multivaluedness of any real in-
teraction process (Sec. 2) giving rise to permanent, irreversible (dy-
namically random) realisation change and new structure formation, as
well as inevitable realisation discreteness (related to dynamic entan-
glement of interacting system components) taking relatively huge
proportions at those greater, revolutionary transitions (involving pro-
portionally greater system volumes and dynamical depth).
Note once again the related important feature of permanent dynam-
ic entropy growth during evolutionary process in our dynamically mul-
14
tivalued
of therm
in usual
new exte
ond law (
greater e
valued d
evolution
as any n
multiplic
thus to e
Note t
ing!) con
recogniti
istic scie
liefs, suc
erning a
clearly s
science p
duced m
proximat
the unred
urally le
down to
rectly de
er, withi
Fig. 1. Sc
of its dyn
description
modynamics
dynamical
ernally orde
(usually ‘so
environmen
description)
n possibilit
new, howev
city of new
ssential en
that the m
ntradictions
ion of fund
ence metho
ch as the al
arbitrary, c
ee now, th
paradigm t
many-body i
tions negle
duced, dyn
ads to gene
respective
erived) dyna
in a dynam
cheme of un
namic compl
A.
n (in full ag
s), as oppos
lly single-v
ered struct
olved’ by in
nt becomin
). We obta
ty (and eve
ver externa
w, chaotical
tropy grow
entioned a
s of usual,
damental f
od, with st
lleged abse
complex en
his is only
that replace
interaction
ecting all b
namically m
eral evolut
particular
amic model
mically mult
niversal syst
lexity-inform
P. KIRILYU
greement w
sed to the w
valued the
tures enters
ncorrect ref
ng unnecess
ain thus th
en necessity
ally ‘ordere
ly changin
wth [1, 2, 4,
and other e
dynamical
failure of r
triking con
ence of any
nough syst
an artefac
es the (abs
n problem w
but one-sys
multivalued
tion law, Eq
r laws, Eqs
ls that shou
tivalued de
tem evolutio
mation (I) i
UK
with the gen
well-known
ory, where
s in contrad
ference to s
sary in our
he totally c
y) in a tota
ed’ structu
g realisatio
5, 7—11].
evident, pe
ly single-v
respective t
nclusions a
scientifica
em evoluti
t of conven
sent) correc
with its in
tem realisa
d problem s
q. (15), wh
s. (16)—(21)
uld always
escription,
on by perma
into complex
neralised se
n persisting
e the appea
diction with
system open
dynamical
correct (and
ally isolated
ure contain
ons and cor
rsisting (a
alued theor
traditional
nd far-reac
ally certain
ion [16]. A
ntional, po
ct solution
ncorrect ‘m
ations. By
olution (Se
hich can be
), or even (
be analysed
such as th
anent trans
xity-entropy
econd law
g problem
arance of
h the sec-
nness to a
lly multi-
d strong)
d system,
ns a huge
rresponds
and press-
ry lead to
l, positiv-
ching be-
n law gov-
As we can
ositivistic
n of unre-
model’ ap-
contrast,
ec. 2) nat-
specified
(now cor-
d, howev-
he univer-
sformation
y (S).
DYN
sal EP m
its versio
tainty/p
4. THE S
AND SO
Let us no
transitio
tem tran
solutely u
This g
entropy
tive time
= ∂ ∂H S
right, hig
importan
(and easi
big comp
Fig. 2. Un
between t
Δ = −ΔS ,
higher de
NAMIC ORIGI
method appl
ons includ
robability a
STRUCTU
OCIAL TRA
ow conside
on illustrat
nsformation
universal a
graphical i
growth (ev
e dependen
∂t or energ
gher time d
nt role in p
ily recognis
plexity tran
niversal per
them in ter
, generalised
rivatives.
IN OF EVOLU
ied above. T
e dynamica
and irrever
RE OF CO
ANSFORM
r the detai
ed in Fig.
n [8] (altho
and applica
illustration
volutionary
nce of its (p
gy = − ∂E
derivatives
practical ten
sable) mom
nsition [8].
riods of a re
rms of dyna
d Hamilton
UTION AND
The obtain
ally specifi
rsibility as
MPLEXIT
MATION
iled structu
2, with exp
ough the an
able to any s
n shows a
y) curve of
partial) tim
∂ = t H . A
s of dynami
ndency ana
ments in soci
It should b
eal system p
amic comple
nian = ∂H S
SOCIAL TRA
ed universa
ied (true) r
its integra
Y TRANS
ure of such
plicit refer
nalysis rem
system evol
part of st
Fig. 1 com
me derivativ
As shown i
ic complexi
alysis mark
ial system e
e emphasiz
progress, de
exity-entrop
∂t or energ
ANSFORMATI
al evolution
randomnes
l constituen
ITION
greater co
ence to a s
mains, of co
lution).
tep-like com
mpleted wit
ve, the Ham
in the inse
ty-entropy
king variou
evolution a
zed that the
ecline and t
py (or actio
gy = − ∂ ∂E
ION 15
n law and
ss, uncer-
nts.
omplexity
social sys-
ourse, ab-
mplexity-
th respec-
miltonian
ert on the
y also play
us critical
around its
e underly-
transitions
on) change
∂ =t H and
16 A. P. KIRILYUK
ing definition of dynamic complexity, Eq. (8), takes into account all
system interactions, in our case all social interactions in all their real
economic, political, psychological and other aspects, rather than their
various severely limited ‘models’ emphasizing separate (e.g., economi-
cal) aspects. The resulting social complexity development laws illus-
trated in Fig. 2 and having clearly observable, strong manifestations
possess therefore totally objective, (new) exact-science nature liberated
from usual social-science uncertainties, which implies complete relia-
bility of conclusions derived from those observable manifestations.
A major feature of this universal complexity development curve in
Fig. 2 is the complexity transition, or revolution, which is a sharp and
high step-wise rise on the temporal dependence of dynamic entropy-
complexity ( ΔS ) corresponding to a narrow maximum on the temporal
dependence of generalised energy ( = = ∂ ∂E H S t ) and separating
neighbouring periods of progress and decline. If we start at the end of
the last decline period, at the ‘moment of ennui’ where
∂ ∂ = ∂ ∂ = ∂ ∂ >2 2 2 20, 0H t S t H t , then we enter in a very short period
of bifurcation of system’s dynamic selection between creative (rising)
tendency of complexity transition and destructive tendency of the
‘death branch’, which is simply the default continuation of the previ-
ous decline tendency in the absence of complexity revolution.
Complexity revolution leading to the superior complexity level oc-
curs if the system has a high enough potential (stock) of hidden inter-
action complexity-action, or dynamic information, which is to be
transformed into explicit complexity-entropy of the emerging higher
level of system structure. In the opposite case, for example, in the case
of too ‘old’ and ‘tired’ social system, there is no enough (potential) en-
ergy in the system to perform that big structure transformation and it
is condemned to a rapid degradation of the death branch. In this con-
nection, we emphasize again the highly uneven, discrete, or ‘nonline-
ar’ character of this specific phase of complexity transition con-
trasting with previous smooth evolution, where the former contrary to
the latter cannot proceed in a gradual regime of ‘small steps’. That
‘sudden’ (and practically often ‘unexpected’) switch to a qualitatively
different regime of change is deeply rooted in the unreduced, holistic
interaction dynamics, where the entirely formed system structure of
existing levels (attained precisely at that time and not before) consti-
tutes itself the main obstacle for its further ‘smooth’ development. It
is related to the physical origin of system realisation discreteness (e.g.,
quantum-mechanical discreteness at the lowest complexity levels [1—3,
11, 15]), where a system can only ‘jump’ to another realisation or high-
er complexity level as a whole, through its complete restructuring
(disentanglement and new entanglement of interacting components)
occurring necessarily in a step-wise manner (Secs. 2, 3). That is why
the necessity, origin and dynamics of complexity transition cannot be
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 17
adequately described within usual, dynamically single-valued theory
framework, irrespective of its model sophistication (including com-
puter simulations). Note also the equally important implication of the
symmetry (transformative conservation) of interaction complexity
that constitutes the underlying integral, genuine reason of system
(complexity) development, as opposed to any particular tendency (in-
cluding falsely understood entropy growth in the unitary theory).
Based on that universal complexity transition dynamics and cur-
rently observed economic, social, psychological and bio-ecological
tendencies (cf. Fig. 2), we can state therefore that the entire planetary
human civilisation (acquiring right now the characteristically unified,
‘globalised’ structure of a ‘phase transition’) is situated just at that
critical bifurcation point of selection between the ‘revolution of com-
plexity’ (transition to the superior level of its dynamic complexity) and
the ‘death branch’ of mere irreversible destruction (inevitably ending
at a much lower complexity level) [8—10, 17]. The unprecedented and
actually historically unique scale of (very rapid) divergence between
those two incompatible (and the only real) possibilities certainly neces-
sitates equally unprecedented efforts in order to realise the progres-
sive development tendency and avoid the only alternative of self-
destruction, the more so that the latter corresponds to the default, ‘in-
herited’ tendency of previous ‘natural’ (not anymore!) smooth growth.
Those extraordinary efforts can only be based on the unreduced under-
standing of complexity transition and its manifestations (see below)
within the holistic description of all real social-system interactions
uniquely provided by our analysis.
Let us emphasize once more two key, practically important results
of this causally complete description of modern critical state of global
civilisation development. The first is the fact of unique, unavoidable
choice between two qualitatively big changes, those of global progress
by complexity revolution and equally rapid degradation within the
dominating (default) death branch. Contrary to various, especially
economic ‘models’ of dynamically single-valued imitation of real in-
teraction processes, there is no other possibility somewhere ‘in be-
tween’ those two extreme, quickly diverging choices. In particular, one
cannot separate, especially near this critical point, any particular, e.g.,
economical aspects of development from other, equally important (e.g.,
‘human’) dimensions. Therefore, after the complete (unprecedented,
including technological) saturation of the current complexity level,
the system cannot simply find its way out of today ‘economic crisis’ by
analogy to previous economic difficulties occurring within yet unsatu-
rated complexity level development.
The second particularly important result uniquely provided by the
present analysis is that the necessary progressive change cannot be
smaller than the qualitatively big growth of unreduced complexity of
18 A. P. KIRILYUK
civilisation dynamics up to its superior level, which implies a qualita-
tive change of the entire social system structure, including its ‘human’
(intellectual and spiritual) dimensions. This feature strongly limits
the scope of suitable changes and provides the indispensable general
direction of their realisation. Thus, all partial, ‘technical’ system mod-
ifications at existing complexity level become now fundamentally,
qualitatively insufficient, irrespective of efforts applied (including
any resource/effort redistribution and amplification of particular de-
velopment aspects such as ‘education’, ‘computerisation’, or ‘ecology’,
often evoked as the necessary ‘revolutionary’ change within the uni-
tary development concepts). By contrast, based on our unreduced in-
teraction complexity understanding, we can specify changes objective-
ly necessary and sufficient in order to realise the revolution of civilisa-
tion complexity towards its superior levels.
5. COMPLEXITY REVOLUTION AND THE NEXT-LEVEL
CIVILISATION
Referring to our more detailed description [8], we can specify now es-
sential features of the superior level of social system complexity de-
termining also the direction of complexity transition towards that
next-level civilisation. As various ideas of a necessary social transfor-
mation become increasingly popular in this very special epoch of
change and uncertainty, one should emphasize, first of all, that the
sustainable new level of complexity cannot be, in order to avoid easy
but misleading imitations of that important transition. Namely, one
should exclude from consideration any modification of existing, Uni-
tary System of social organisation, with its centralised and obligatory
(linear) power dynamics and eventually equally linear economic and
human relations. The latter may seem to possess greater freedom and
complexity than political system as such, at least, within any basically
liberal version of Unitary System (‘market economy’, ‘democracy’,
etc.). However, eventually every aspect and dimension of such social
system dynamics is forced to follow the same unitary, centralised and
characteristically limited (artificially and mechanically ‘enforced’)
dynamics inevitably ending up in self-destructive saturation.
We can see that this mechanically fixed system of orders cannot
overcome its fundamental complexity limits and becomes saturated and
obsolete just at the stage of its highest possible perfection correspond-
ing to all tried and imaginable technological applications. Thus, today
‘financial’ problems are not caused by limited power of available com-
puter calculations and they can hardly be solved by any increase or
‘stronger’ application of that power. By contrast, in terms of a popular
biological analogy of social system, one can say that what is definitely
missing is social system (conscious) intelligence considered as a proper-
DYNAMIC ORIGIN OF EVOLUTION AND SOCIAL TRANSFORMATION 19
ty of the entire social organism (starting, of course, from any national
or even smaller scale). It is easy to see indeed that any most allegedly
‘advanced’ version of unitary social system, with all its ‘scientific’ and
‘intellectual’ departments, still represents nothing more than a version
of the same primitive tribal organisation, with the eventually dominat-
ing ‘power of the crowd’ devoid of any real (collective) mind by defini-
tion and only formally delegated to and realised by respective ‘central
units’. The limits of complexity development of any such unitary sys-
tem are simply due to its highest possible empirically driven use of
available resources that inevitably attains (right now) its evident tech-
nical limitation due to physically complete (empirical) comprehension
and quantitatively limited stock. At that point, any version of Unitary
System loses any further (general) purpose and thus meaning of exist-
ence and becomes inevitably unstable against dissociative degradation.
The only possible alternative to resulting Unitary System destruc-
tion and the unique way of further progress can therefore be attained
at a superior level of social conscious intelligence, or genuine ‘social
mind’, with its respective social and individual realisation. This fun-
damental conclusion is in perfect agreement with our description of
(any) consciousness as a high enough (and well-specified) level of the
same unreduced dynamic complexity [18]. It is thus the right moment
now for any real social organism to acquire this higher level of con-
scious dynamics or, in other words, to become a truly conscious adult
organism, after previous stages of social ‘childhood’ with essentially
limited consciousness and basically only empirically driven, animal
intelligence. As with any kind of conscious behaviour, it practically
implies the prerequisite genuine, causally complete understanding of
any real situation and way of development or problem solution, here at
the level of entire society, which is driven thus by such power of ideas,
rather than unitary power of individuals (or practical needs). Natural-
ly, this essentially new quality implies serious social structure change
and progress towards the one explicitly guided by respective (new) or-
gans and priorities.
This superior level of social structure and thus human civilisation
development provided with the ensuing solutions of known major
problems of the degrading Unitary System can be called the Harmoni-
ous System, in agreement with its intrinsic sustainability [8]. The su-
perior possibilities of Harmonious System are well illustrated by the
phenomenon of exponentially huge power of unreduced complex dy-
namics with respect to any unitary model, related to the dynamically
multivalued fractal structure of the former (Sec. 2) [2, 3, 7—11, 17,
18]. This enormous, practically ‘magic’ efficiency jump is the unique
way to span the current equally impressive and always growing gap be-
tween practical development needs and failing unitary system stagna-
tion. We can only mention here major aspects of qualitatively new,
20 A. P. KIRILYUK
harmonious social organisation and dynamics after the jump (all of
them rigorously substantiated by progressive complexity growth cri-
terion; cf. Sec. 4), including emerging (rather than fixed) decision pow-
er and social structure, complexity-increasing production ways, new
kind of settlement and infrastructure and the underlying new kind of
understanding (and organisation of science) of the universal science of
complexity (with its unreduced, multivalued dynamics) [8, 19]. The
latter inevitably becomes thus an integral (and major) part of this true
knowledge-based society, contrary to now dominating but strongly lim-
ited unitary, dynamically single-valued science ‘models’ fundamental-
ly separated from any real system dynamics and its consistent under-
standing, as well as from any technologically ‘advanced’ society dy-
namics and government. Essential knowledge development from uni-
tary imitative models to causally complete understanding of unre-
duced, dynamically multivalued real-system complexity is therefore
inseparable from, and thus can only occur together with, the necessary
social system progress from its ending unitary to the forthcoming
harmonious level.
The emerging new civilisation of harmonious level automatically
overcomes the tragic destructive purposelessness of the ending unitary
civilisation and acquires the universal superior Purpose of now unlim-
ited and dominating progressive growth of complexity-entropy (guid-
ed by its superior conscious levels), which corresponds to vanishing
depressions on the ( )H t curve in Fig. 2. Contrary to old and new uni-
tary religious and ideological imitations, the unified Purpose of har-
monious levels is naturally integrated into any practical activity, so
that there is no more contradiction between the end and the means and
no blind domination of the latter. In particular, the Purpose is indis-
tinguishable from the clearly specified ‘entailing law’ (cf. Ref. [16]) of
the universal symmetry of complexity, provided with all necessary
emergence and uncertainly aspects of exact dynamic origin (Sec. 2, 3).
Note finally that, as any kind of higher-level ‘phase transition’, this
social revolution of complexity can occur as a locally great but spatial-
ly gradual, self-propagating process of qualitative change, which es-
sentially simplifies its practical realisation. By contrast, it cannot oc-
cur in a locally gradual way implied by any unitary development con-
cept inevitably related to the dominating Unitary System and its way
of thinking, which just determines today critically high evolution bar-
rier and the necessity of complexity revolution in both knowledge and
society development.
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