Complexity as Theoretical Applied Science Sorin Solomon,

Racah Institute of Physics HUJ Israel Director, Complex Multi-Agent Systems Division, ISI Turin

Head, Lagrange Interdisciplinary Laboratory for Excellence In Complexity Coordinator of EU General Integration Action in Complexity Science (GIACS)

Chair of the EU Expert Committee for Complexity Science

MORE IS DIFFERENT (Anderson 72)Complex “Macroscopic” properties may be the collective effect of many simple “microscopic” componentsPhil Anderson “Real world is controlled …

• by the exceptional, not the mean; • by the catastrophe, not the steady drip; • by the very rich, not the ‘middle class’.

…thus, we need to free ourselves from ‘average’ thinking.”

“MORE IS DIFFERENT” Complex Systems Paradigm

MICRO - the relevant elementary agents        

INTER - their basic, simple interactions        

MACRO - the emerging collective objects

Intrinsically (3x) interdisciplinary:

-MICRO belongs to one science

-MACRO to another science

-Mechanisms: a third science

Traders, investors

transactions

herds,crashes,booms

Decision making, psychology

economics

statistical mechanics, physicsmath, game theory, info

Yet with a strong collective identity and common motivation.

A science without a fixed area, moving with the frontier , much like fundamental high energy physics used to be (atoms->quarks)

In the present case feeding on the frontiers (and consuming them)

Complexity Induces a New relation Theoretical Science Real Life Applications: Traditional Applied Science applied hardware devices (results of experimental science)

to material / physical reality. Modern Complexity rather applies theoretical methods e.g. - new (self-)organization concepts and - (self-)adaptation emergence theories

to real life, but not necessarily material / physical items: - social and economic change,

- individual and collective creativity, - the information flow in life

Applications of Complexity are thus of a new brand: "Theoretical Applied Science" and should be recognized as such when evaluating their expected practical impact

I present in the sequeldata and theoretical study of Poland's 3000 counties over 15 years following the 1990 liberalization of the economy.

The data tells a very detailed story of application of multi-agents complexity to real life.

To understand it we have to go back in time more then 200 years ago in Holland.

Malthus : autocatalitic proliferation/ returns :B+AB+B+Adeath/ consumption B Ødw/dt = aw

a =(#A x birth rate - death rate)

a =(#A x returns rate - consumption /losses rate)

exponential solution: w(t) = w(0)e a t

a < 0

w= #B

a

TIME

birth rate > death rate

birth rate > death rate

Verhulst way out of it: B+B B The LOGISTIC EQUATION

dw/dt = a w – c w2 c=competition / saturation Solution: exponential ==========saturation

w = #B

almost all the social phenomena, except

in their relatively brief abnormal times obey the logistic growth. “Social dynamics and quantifying of social forces” Elliott W. Montroll US National Academy of Sciences and American Academy of Arts and Sciences 'I would urge that people be introduced

to the logistic equation early in their education…

Not only in research but also in the

everyday world of politics and economics …” Nature

Robert McCredie, Lord May of Oxford, President of the Royal Society

SAME SYSTEM Reality Models

Complex ----------------------------------Trivial

Adaptive ----------------------------------Fixed dynamical law

Localized patches -----------------------Spatial Uniformity

Survival -----------------------------------Death

Discrete Individuals Continuum Density

Development -----------------------------Decay

We show it was rather due to the neglect of the discreteness.

Once taken in account => complex adaptive collective objects. emerge even in the worse conditions

Misfit was always assigned to the neglect of specific details.

Logistic Equation usually ignored spatial distribution, Introduce discreteness and randomeness !

w.

= ( conditions x birth rate - deathx w + diffusion w - competition w2

conditions is a function of many spatio-temporal distributed discrete individual contributions rather then totally uniform and static

Phil Anderson

“Real world is controlled …

– by the exceptional, not the mean;

– by the catastrophe, not the steady drip; – by the very rich, not the ‘middle class’

we need to free ourselves from ‘average’ thinking.”

that the continuum , differential logistic equation prediction:

Time

Differential Equations

(continuum a << 0 approx)

Multi-Agent a

prediction

Is ALWAYS wrong !

Shnerb, Louzoun, Bettelheim, Solomon,[PNAS (2000)] proved by (FT,RG)

Instead: emergence of singular spatio-temporal localized collective islands with adaptive self-serving behavior

resilience and sustainability

even for a << 0!

Electronic Journal of Probability Vol. 8 (2003) Paper no. 5, pp 1–51.Branching Random Walk with Catalysts Harry Kesten, Vladas Sidoravicius

Shnerb, Louzoun, Betteleim, Solomon (2000), (2001) studied the following system of interacting particles on Zd: There are two kinds of particles, called A-particles and B-particles.

The A-particles perform continuous time simple random walks, independently of each other. The jump rate of each A-particle is DA.

The B-particles perform continuous time simple random walks with jump rate DB,

but in addition they die at rate δ and

a B-particle at x at time s splits into two particles at x during the next ds time units with a probability βNA(x, s)ds+o(ds),

where NA(x, s) (NB(x, s)) denotes the number of A-particles (respectively B-particles) at x at time s.

Using Kesten, Sidoravicius (2003) techniques, we proved (2005) that: in d dimensions, the condition for B growth is: δ / DA> 1-Pd where, the Polya constant

Pd= the probability for an A to return to origin

P1=P2=1

in terms of the Master Equation:d Pnm / dt = death of B’s: - [ m Pnm – (m+1) P n,m+1 ]

birth of B’s in the presence of n A’s - n [ m P nm – (m-1) P n,m-1] + diffusion to and from neighbors

Original Field Theory analysis: express the dynamics of Pnm (x) = the probability that there are m B’s and n A’s at the site x .

Interpret it as a Schroedinger Equation with imaginary time

and

and

+diffusionetc. (second quantization creation/anihilation operators)

where

Renormalization Group results: The systems made out of autocatalytic discrete agents (B+A B+B+A)present “Anderson” localization (in 2D, ALWAYS).

This invalidates the naïve, classical continuum differential logistic-type equation results.i-1 localization implies localized exponential growth

Interpretations of the logistic localization phase transition[conductor isolator] death life extinction survival economic decay capital autocatalytic growth

Logistic Diff Eq prediction:

Time

Differential Equations continuum

a << 0 approx)

Multi-Agent stochastic

a

prediction

w.

= a w – c w2

GDP Poland

Nowak, Rakoci, Solomon, Ya’ari

The GDP rate of Poland, Russia and Ukraine (the 1990 levels equals 100 percent) 

Poland

Russia

Ukraine

Movie By Gur Ya’ari

Nowak, Rakoci, Solomon, Ya’ari

Nowak, Rakoci, Solomon, Ya’ari

“A”= education 1988

B= Number of Economic Enterprizes

per capita1994

Number of Economic Enterprizes

per capita1989

Other details of the Predicted Scenario:

First the singular educated centers WEDU develop while the others WIGN decay

Then, as WEDU >> WIGN , the transfer becomes

relevant and activity spreads from EDU to IGN and all develop with the same rate but preserve large inequality

EDU

IGN

IGN

EDU

Nowak, Rakoci, Solomon, Ya’ari

simulation

real dataEDU

EDU

IGN

IGN

Nowak, Rakoci, Solomon, Ya’ari

simulation

real data

IGN

IGN

EDU

EDU

• Case 1: low level of capital redistribution -high income inequality -outbreaks of instability (e.g. Russia, Ukraine).•Case2: high level of central capital redistribution - slow growth or even regressing economy (Latvia) but quite - uniform wealth in space and time.•Case 3 :Poland - optimal balance : - transfers enough to insure adaptability and sustainability - yet the local reinvestment is enough to insure growth.

Other predictions

Very few localized growth centers

(occasionally efficient but unequal and unstable)

Uniform distribution (inefficient but stable)

PolandRussia Ukraine

Latvia

Instability of over-localized economies

Predictionthe economic inequality (Pareto exponent) and the economic instability (index anomalous fluctuations exponent)

Forbes 400 richest by rank

400

Levy, Solomon,2003

What next?

PIEMONTE MAPPiemonte

Belarus

Piemonte

Romania

Future and on-going studies Measure chain of

changes in capital growth and transfer due to Fiat plant closure.

Enterprises creation and disappearance, etc

With Prof Terna’s group

Check alternatives

Conclusions• The logistic dynamics was believed for 200 years to be capable

to describe a very wide range of systems in biology, society, economics, etc

• The naïve continuous differential equations expression of this dynamics lead often to predictions incompatible with the empirical evidence

• We show that taking properly into account the multi-agent character of the system one predicts generically the emergence of adaptive, collective objects supporting development and sustainability.

• The theoretical predictions are validated by the confrontation with the empirical evidence and are relevant for real life economic, social and biological applications.