UNIVERSAL SCIENCE UNIVERSAL SCIENCE OF COMPLEXITY OF COMPLEXITY - - PowerPoint PPT Presentation
Andrei P. Kirilyuk Andrei P. Kirilyuk Institute of Metal Physics, Kiev, Ukraine Institute of Metal Physics, Kiev, Ukraine http://myprofile.cos.com/mammoth http://myprofile.cos.com/mammoth UNIVERSAL SCIENCE UNIVERSAL SCIENCE OF COMPLEXITY OF
UNIVERSAL SCIENCE UNIVERSAL SCIENCE OF COMPLEXITY OF COMPLEXITY
Consistent Understanding of Consistent Understanding of Ecological, Ecological, Living Living and Intelligent and Intelligent System Dynamics System Dynamics
Andrei P. Kirilyuk Andrei P. Kirilyuk
Institute of Metal Physics, Kiev, Ukraine Institute of Metal Physics, Kiev, Ukraine http://myprofile.cos.com/mammoth http://myprofile.cos.com/mammoth
Can real real, higher , higher-
complexity system dynamics be understood at the be understood at the level of rigour level of rigour of
Newtonian science? Newtonian science?
The problem of unreduced unreduced many many-
body interaction interaction ( (unsolved unsolved in Newtonian science) in Newtonian science)
The unique possibility for a new progress of fundamental science fundamental science (otherwise (otherwise “ “ending ending” ”) )
Universal Science of Complexity
Escaping Complexity Escaping Complexity
http://books.google.com/books?ie=UTF http://books.google.com/books?ie=UTF-
8&hl=en&vid=ISBN9660001169&id=V1cmKSRM3EIC
Universal Science of Complexity
Cosmos
Nano ICT Bio
Unreduced Interaction Unreduced Interaction
Dynamic Complexity Dynamic Complexity
http://arxiv.org/find/quant http://arxiv.org/find/quant-
ph,gr-
qc,physics/1/au:+Kirilyuk/0/1/0/all/0/1
Brain
Arbitrary many Arbitrary many-
body interaction process:
The unreduced (nonperturbative) general solution is always The unreduced (nonperturbative) general solution is always probabilistic probabilistic (phenomenon of (phenomenon of dynamic multivaluedness dynamic multivaluedness = = i intrinsic chaoticity ntrinsic chaoticity): ): Dynamically determined probability Dynamically determined probability
( ) ( ) ( ) ( )
( )
1 2,
, , ,...,
N
N N k k kl k l k l k
h q V q q Ψ Q EΨ Q Q q q q
= >
+ = =
∑ ∑
( ) ( ) ( ) ( ) ( ) ( )
, 1
, , , ,
N N k k k k kl k l k l k
h h q V q V q q Ψ Q EΨ Q q ξ ξ ξ ξ ξ
+ = >
+ + = ≡
∑ ∑
( ) ( )
1, ,
r r
N
Q Q ρ ξ ρ ξ
ℜ=
⊕
=∑
1 r r r r
N N α α
= ℜ
= , ∑
Multivalued Dynamics of Unreduced Interaction Multivalued Dynamics of Unreduced Interaction
Unreduced Interaction Dynamics Unreduced Interaction Dynamics
Arbitrary interaction process in terms of (free) component eigen Arbitrary interaction process in terms of (free) component eigenvalues: values: where the total system state where the total system state-
function is obtained as Usual Usual perturbative (mean perturbative (mean-
field) approximations: approximations:
( ) ( ) ( ) ( ) ( )
n nn n n n n
h V ξ ψ ξ ξ ψ ξ η ψ ξ
′ ′ ′
+ =
∑
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
,
nn n n n n n nn nh V V V V V ξ ξ ξ ψ ξ η ψ ξ ξ ξ ξ
′ ′ + + = < <
∑
ɶ ɶ
( ) ( )
( )
( ) ( ) ( ) ( ) ( )
1 2 1 2 1 1 2 2, ,...,
, ...
N N N Nn n n n n n n n n n n
Ψ Q q q q q Φ Q ξ ψ ϕ ϕ ϕ ψ ξ
≡
= ≡
∑ ∑
Unreduced general solution Unreduced general solution of the same problem:
where where are are solutions solutions of the
effective potential (EP) equation equation
( ) ( ) ( ) ( ) ( )
2 2 1
, , , , , ,
r r r r
N
Q Ψ Q Q Q Ψ Q ρ ξ ξ ρ ξ ρ ξ ξ
ℜ =
⊕
≡ = =
∑
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
*,
,
r n ni ni n i r r r i i r i ni nn i
Q d V Ψ Q c Q i
ξ ΩΦ ψ ξ ξ ψ ξ ξ ψ ξ ξ Φ ψ ξ η η ε
′ ′ ′′
′ ′ ′ ′ = + − −
∫
( )
{ , }
r r i iψ ξ η
( ) ( ) ( ) ( ) ( )
eff
; h V ξ ψ ξ ξ η ψ ξ ηψ ξ + =
( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
00 eff*
,
;
r n ni ni n i r r r i i i r i ni nn i
V d V V V
ξ Ωξ ψ ξ ξ ψ ξ ξ ψ ξ ξ η ψ ξ ξ ψ ξ η η ε
′ ′ ′′
′ ′ ′ ′ = + − −
∫
Elementary length time action
r ix t x V t λ η Δ = = Δ , Δ = Δ , Δ = Δ
A
v
Unreduced Interaction: Dynamic Multivaluedness (Chaos) Unreduced Interaction: Dynamic Multivaluedness (Chaos)
First
Second
INTERACTION INTERACTION N points N points
( (modes
modes)
)
N points N points
( (modes
modes)
)
combinations combinations
(N N)
×
( (a a1 1, ,a a2 2, ,a a3 3, ,b b1 1, ,b b2 2,etc.) ,etc.)
⇓ ⇓
N N-
fold redundance
a b c
1 2 3
a3 b3 c3 a2 b2 c2 a1 b1 c1
First Second Third Dynamically redundant interaction result: incompatible system realisations Permanent Permanent realisation change realisation change in in causally (dynamically) random causally (dynamically) random order
Unreduced Interaction Complexity Unreduced Interaction Complexity
where is the (dynamically derived) where is the (dynamically derived) system realisation number system realisation number for example: for example: with the with the dynamically determined probability dynamically determined probability
( ) ( )
, 0, 1 dC C C N C dN
ℜ ℜ
= > = ( ) ( )
1, ,
r r
N
Q Q ρ ξ ρ ξ
ℜ=
⊕
=∑
1 r r r r
N N α α
= ℜ
= , ∑
Nℜ
( ) ( )
ln , 1 , etc. C C N C C N
ℜ ℜ
= = −
Universal dynamic complexity Universal dynamic complexity includes includes intrinsic intrinsic chaoticity chaoticity due to the due to the dynamically probabilistic dynamically probabilistic problem solution: problem solution: UNIVERSAL DEFINITION OF DYNAMIC (INTERACTION) COMPLEXITY: UNIVERSAL DEFINITION OF DYNAMIC (INTERACTION) COMPLEXITY:
Unreduced Complexity Measures Unreduced Complexity Measures
Two universal, Two universal, emerging emerging forms of complexity, forms of complexity, space space and and time time Generalised Generalised action action is the simplest combination of space & time: is the simplest combination of space & time: is a universal is a universal integral integral complexity measure complexity measure Differential Differential complexity measures: complexity measures: momentum momentum ( (spatial spatial rate of realisation emergence) rate of realisation emergence) energy energy/ /mass mass ( (temporal temporal rate of realisation emergence) rate of realisation emergence) Dispersion relation Dispersion relation: :
causal relativity
,
r r i
x t x λ η Δ = = Δ Δ = Δ v p x E t Δ = Δ − Δ A
A
pdx Nℜ = ∝
∫
A
const t
p x x
=
∂ Δ = = ∂ Δ A A
2 const x
E m t t
=
∂ Δ = = − = − ∂ Δ v A A
2, = x p E m t c Δ = = Δ v v v
Generalised wavefunction (distribution function) Generalised wavefunction (distribution function)
Total number of unreduced EP eigenvalues: Total number of unreduced EP eigenvalues: N Nmax
max =
= N Nξ
ξ(
(N Nξ
ξ N
Nq
q + 1) = (
+ 1) = (N Nξ
ξ)
)2
2N
Nq
q +
+ N Nξ
ξ
N
Nℜ
ℜ =
= N Nξ
ξ “
“regular regular” ” realisations realisations
Nξ
ξ N
Nq
q eigen
eigen-
solutions each + “ “incomplete incomplete” ” set of set of N Nξ
ξ eigen
eigen-
solutions = transitional realisation transitional realisation, , generalised wavefunction generalised wavefunction, or , or distribution function distribution function ⇓ ⇓ causal extension causal extension of usual quantum
mechanical wavefunction Ψ
Ψ (
(x x) ) transiently weak EP, disentangled components, system restructuri transiently weak EP, disentangled components, system restructuring ng
Causally generalised Born probability rule Born probability rule: : α αr
r =
= ⏐
⏐Ψ
Ψ (
(X Xr
r)
)⏐
⏐
2 2
Generalised Hamilton-
Jacobi equation for action for action-
complexity A
A (
(x x) ) + + causal quantisation rule causal quantisation rule, , Δ
ΔA A =
= ̶̶ A
A0
0 Δ
ΔΨ Ψ /
/Ψ
Ψ
universal Schrö ödinger equation dinger equation
( )
const const
ˆ = , , ,
x t
H x t x t t x Ψ Ψ
= =
Δ Δ Δ Δ
A
Universal Regimes of Complex Dynamics Universal Regimes of Complex Dynamics
1 κ ≫
Two limiting regimes of complex dynamics: multivalued self multivalued self-
and uniform (global) chaos uniform (global) chaos Universal criterion of global (strong) chaos:
resonance of the main system motions Criterion of quasi-regularity (self-organisation): (or ) Highly complicated interaction networks cannot be close to regul Highly complicated interaction networks cannot be close to regularity arity Ordinary, unitary dynamic models and approaches are inapplicable Let’s transform the unitary approach defect defect (system failure) into the unreduced, complex-dynamic operation advantage advantage : superior power and qualities 1 κ ≪ As network intensity grows one cannot avoid resonance cannot avoid resonance (“jam”): and therefore essential essential dynamic dynamic randomness becomes inevitable randomness becomes inevitable
1 κ ∼
1
i n Q ξ
ω η κ η ω Δ ≡ = Δ ≃ 1 κ ≫
Dynamically probabilistic fractal Dynamically probabilistic fractal
Unreduced general solution Unreduced general solution of a problem:
are are solutions to a truncated problem: solutions to a truncated problem: treated by the same generalised EP method: treated by the same generalised EP method:
( ) ( ) ( ) ( ) ( )
2 2 1
, , , , , ,
r r r r
N
Q Ψ Q Q Q Ψ Q ρ ξ ξ ρ ξ ρ ξ ξ
ℜ =
⊕
≡ = =
∑
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
*,
,
r n ni ni n i r r r i i r i ni nn i
Q d V Ψ Q c Q i
ξ ΩΦ ψ ξ ξ ψ ξ ξ ψ ξ ξ Φ ψ ξ η η ε
′ ′ ′′
′ ′ ′ ′ = + − −
∫
( )
{ }
,
ni ni
ψ ξ η
( ) ( ) ( ) ( ) ( ) ( )
nn n nn n n n n n
h V V ξ ξ ψ ξ ξ ψ ξ η ψ ξ
′ ′ ′≠
+ + =
∑
( ) ( ) ( ) ( )
eff
;
n n n n n
h V ξ ξ η ψ ξ η ψ ξ + =
Dynamically probabilistic fractal Dynamically probabilistic fractal
Unreduced EP of the second level Unreduced EP of the second level describes second describes second-
level splitting into incompatible realisations The The unreduced general solution unreduced general solution is the is the dynamically probabilistic fractal dynamically probabilistic fractal: : with with dynamic entanglement dynamic entanglement ( (ξ
ξ,
,Q Q) ) and and dynamic probabilities dynamic probabilities: :
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
eff
*
,
;
n n nnn n i n i n n n n n n nn n n n i n n
n n i
V d V V V
ξΩ
ξ ψ ξ ξ ψ ξ ξ ψ ξ ξ η ψ ξ ξ ψ ξ η η ε ε
′ ′ ′ ′ ′ ′
′≠
′ ′ ′ ′ = + − + −
∫
( ) ( ) ( ) ( )
... exp ... ...
, , ... , , ...
, , , , ,
rr r rr r rr r
r r r r r r
N N
Q Q Q Q ρ ξ ρ ξ ρ ξ α ρ ξ
ℜ ℜ
′ ′′ ′ ′′ ′ ′′
′ ′′ ′ ′′
⊕
= =
∑ ∑
... ... ...
...
, 1
rr r rr r rr r
rr r
N N α α
′ ′′ ′ ′′ ′ ′′ ℜ
′ ′′
= =
∑
Complex Complex-
Dynamic Interaction Network Properties
N N
Huge efficiency growth Huge efficiency growth of
dynamically chaotic ( chaotic (multivalued multivalued) networks: ) networks:
Chaotic network efficiency is determined by the number of all combinations of links
where the number of links N is very large itself Unitary (regular) dynamic efficiency grows only as . The huge advantage in efficiency expresses intrinsic creativity/adaptability
INTELLIGENCE, CONSCIOUSNESS, AUTONOMIC COMMUNICATION INTELLIGENCE, CONSCIOUSNESS, AUTONOMIC COMMUNICATION Particular aspects and applications Particular aspects and applications
N β β ( 1) ∼
! 2π ( ) (unreduced dynamic complexity)
N N
N N N e N C ∝ ≃ ∼
(1) Knowledge Knowledge-
based structure of intelligent communication networks (2) Holistic, two-layer dynamics of advanced advanced intelligent network (“superbrain”)
Complex Complex-
dynamic meaning of true true intelligence/consciousness intelligence/consciousness (physics/0409140)
(3) Intelligent network and its users automatically become more intelligent
Intrinsically suited to complex Intrinsically suited to complex-
dynamic problem solution →
→ revolution of complexityrevolution of complexity
(4) Universal symmetry/development of complexity Universal symmetry/development of complexity: unified guiding principle
Transformation of Transformation of dynamic information dynamic information ( (“ “interaction potential interaction potential” ”) into ) into dynamic entropy dynamic entropy
Evolution as complexity development
System evolution System evolution as a result of the as a result of the symmetry of complexity symmetry of complexity: :
qualitative, irreversible, qualitative, irreversible, dynamically discrete dynamically discrete (quantized) (quantized) change change (event): transformation of (event): transformation of dynamic information dynamic information, , I
I,
, into into dynamic entropy dynamic entropy, , S
S, while the sum,
, while the sum, total complexity total complexity, ,
C C = = I I + + S S, remains
, remains unchanged unchanged: :
Δ ΔC C = 0 = 0 ,
,
Δ ΔS S = = -
ΔI = I = -
ΔA
A > 0
> 0 ,
, where the extended, nonlinear action where the extended, nonlinear action A
A =
= I I is a unified
is a unified measure of measure of complexity complexity-
information, Δ
ΔA
A
~
~
V
Veff
eff
Δ
Δt t
time arrow
time arrow ( (E
E, , L L > 0 > 0)
)
Generalised Hamilton Generalised Hamilton-
Jacobi and Schrö ödinger equations: dinger equations:
, , The universal The universal meaning meaning and and purpose purpose of any system
evolution, , progress progress, and , and existence existence: : complexity development complexity development as a result of as a result of the the symmetry of complexity symmetry of complexity → → teleological, purposeful dynamics teleological, purposeful dynamics
const const
, ,
x t
H x t t x
= =
Δ Δ + = Δ Δ
A A
( ) ( )
const
ˆ ,
t
H x x E x x Ψ Ψ
=
Δ = Δ
UNIVERSAL MEANING AND CRITERION OF PROGRESS UNIVERSAL MEANING AND CRITERION OF PROGRESS
Progress by complexity steps
dynamic entropy change Complexity levels, n n n n = 1 n n = 2 n n = 3 Fractal hierarchy of complexity time, t t
ΔI, I, Δ ΔS S Any Any structure creation is a structure creation is a growth growth of complexity
entropy DYNAMICALLY DISCRETE COMPLEXITY DEVELOPMENT DYNAMICALLY DISCRETE COMPLEXITY DEVELOPMENT
“progress” vs “decline”
time, t t dynamic entropy change, Δ ΔS S, Hamiltonian (energy), Δ ΔS S/ /Δ Δt t = = H, E H, E Δ ΔS S H H period of period of progress progress period of period of decline decline moments of happiness moments of happiness moments of ennui moments of ennui For For both both “ “progress progress” ” and and “ “decline decline” ”: : H H = = ∂ ∂S S/ /∂ ∂t t > 0 > 0 Progressive development (creation) Progressive development (creation): : W W = = ∂ ∂H H/ /∂ ∂t t = = ∂ ∂2
2SS/ /∂ ∂t t2
2 > 0> 0 Decline (decay, degradation) Decline (decay, degradation): : W W = = ∂ ∂H H/ /∂ ∂t t = = ∂ ∂2
2SS/ /∂ ∂t t2
2 < 0< 0 Max Max progress results ( progress results (“ “happiness happiness” ”): ): ∂ ∂H H/ /∂ ∂t t = = ∂ ∂2
2SS/ /∂ ∂t t2
2 = 0,= 0, ∂ ∂2
2HH/ /∂ ∂t t2
2 < 0< 0 Max Max decay results ( decay results (“ “ennui ennui” ”): ): ∂ ∂H H/ /∂ ∂t t = = ∂ ∂2
2SS/ /∂ ∂t t2
2 = 0,= 0, ∂ ∂2
2HH/ /∂ ∂t t2
2 > 0> 0 Transition Transition max max ( (“ “moment of truth moment of truth” ”): ): ∂ ∂2
2HH/ /∂ ∂t t2
2 = 0,= 0, ∂ ∂3
3HH/ /∂ ∂t t3
3 < 0< 0 Decline crisis ( Decline crisis (“ “moment of sin moment of sin” ”): ): ∂ ∂2
2HH/ /∂ ∂t t2
2 = 0,= 0, ∂ ∂3
3HH/ /∂ ∂t t3
3 > 0> 0 death branch
Unified mathematics of complexity
Non-uniqueness of any real problem solution: universal dynamic multivaluedness dynamic multivaluedness
emergence, origin of events events and time time: A A ≠ ≠ A A for any real A A
dynamic entanglement: rigorous rigorous expression of material quality material quality
randomness, nonintegrability nonintegrability, noncomputability noncomputability, etc.
Dynamic discreteness (causal quantisation causal quantisation), nonunitarity nonunitarity, dynamic origin of space space
DYNAMIC FRACTAL: DYNAMIC FRACTAL: UNREDUCED PROBLEM SOLUTION UNREDUCED PROBLEM SOLUTION http://arXiv.org/abs/physics/0502133 http://arXiv.org/abs/physics/0502133 UNIVERSAL SYMMETRY OF COMPLEXITY UNIVERSAL SYMMETRY OF COMPLEXITY
Science Progress Diagram
Mechanistic discreteness: Numbers Classical figures No interaction No change No quality Mechanistic Mechanistic discreteness: discreteness: Numbers Numbers Classical figures Classical figures No interaction No interaction No chan No chang ge e No quality No quality
Unitary 1 Unitary 1 Unitary 1 Unitary 2 Unitary 2 Unitary 2 USciCom USciCom USciCom
Unitary science: Unitary science: only one
from many real system realisations Universal Science of Complexity (USciCom): Universal Science of Complexity (USciCom): all all system realisations system realisations NEW MATHEMATICS OF COMPLEXITY NEW MATHEMATICS OF COMPLEXITY Mechanistic continuity: Calculus Deformable shapes Trivial interaction Formal change No quality Mechanistic Mechanistic continuity: continuity: Calculus Calculus Deformable shapes Deformable shapes Trivial interaction Trivial interaction Formal chan Formal chang ge e No quality No quality Dynamic discreteness: Multivaluedness Dynamical fractal Full interaction Intrinsic change Full quality Dynamic Dynamic discreteness: discreteness: Multivaluedness Multivaluedness Dynamical fractal Dynamical fractal Full interaction Full interaction Intrinsic chan Intrinsic chang ge e Full quality Full quality http://arXiv.org/abs/physics/9806002 http://arXiv.org/abs/physics/9806002
Unreduced complexity features
Unreduced complexity >> usual imitations of complexity imitations of complexity
Fundamental difference of unreduced complexity unreduced complexity (dynamic multivaluedness) from any dynamically single-valued (unitary) imitations of complexity imitations of complexity
Usual science = zero-
dimensional projection of reality projection of reality
The whole whole usual, unitary science, including scholar “science of complexity” (“chaos”, “self-organisation”, “nonlinear dynamics”, etc.), is the simplest simplest possible, zero zero-
dimensional, point-
like projection of real, multivalued multivalued world dynamics
Unreduced complexity = natural completion natural completion of usual science
Universal science of complexity (unreduced unreduced interaction problem solution solution) is the explicit, causally complete extension extension of the unitary science (from one system realisation to their complete set)
Problem-
solving power of the universal science of complexity
Unreduced complexity (dynamically multivalued solution) solves solves stagnating stagnating problems problems of unitary science (quantum physics, particles, field theory, gravity, cosmology, solid state, biology, etc.) and completes completes it up to the humanities (consciousness, ethics, aesthetics, development, etc.)
Complex system creation by unreduced complexity understanding by unreduced complexity understanding
Only the unreduced unreduced dynamic complexity is suitable for real real-
world applications involving new system design new system design (like autonomic communication networks, intelligent software, AI, machine consciousness)
UNIVERSAL CONCEPT AND SCIENCE OF COMPLEXITY UNIVERSAL CONCEPT AND SCIENCE OF COMPLEXITY
http://arXiv.org/abs/physics/9806002 http://arXiv.org/abs/physics/9806002
Today’ ’s knowledge s knowledge development is development is not not sustainable: sustainable:
quickly quickly growing problems growing problems of intensity, content, efficiency, creativity
( (e.g. usual ecological problems) e.g. usual ecological problems)
we need
we need always more always more
Illusion of regularity: :
regular, regular, “ “industrial industrial” ” operation mode
inevitably leads to leads to degradation degradation at a at a high intensity high intensity stage (the case of usual stage (the case of usual developed developed industry) industry)
Illusion of power:
power power cannot cannot increase increase quality quality by itself: increasing power capacities by itself: increasing power capacities need another, need another, qualitatively qualitatively different dynamics different dynamics
complexity
complexity
Only complex complex-
dynamic creation can be sustainable: can be sustainable:
– – system freedom system freedom to change its own structure ( to change its own structure (true autonomy true autonomy) ) – – efficient management of efficient management of creation result creation result ( (intelligence intelligence) ) – – complex complex-
dynamic (chaotic) control (chaotic) control genuine genuine security security and and progress progress – – permanent, natural permanent, natural user user-
machine-
network complexity coevolution coevolution
Today’ ’s s bifurcation bifurcation of
knowledge/civilisation development: :
Complexity Transition = Sustainability Transition = Creative Eco Complexity Transition = Sustainability Transition = Creative Ecology logy
Sustainable knowledge
http://arXiv.org/abs/physics/0509234 http://arXiv.org/abs/physics/0509234