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” components 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’. …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, physics math, 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 sequel data 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+A  B+B+A death/ consumption B  Ø dw/dt = a  w 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

Verhulst way out of it: B+B  B The LOGISTIC EQUATION dw/dt = a w – c w 2 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 RealityModels 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 - death  x w + diffusion w - competition w 2 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 Z d : 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 D A. The B-particles perform continuous time simple random walks with jump rate D B, 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 βN A (x, s)ds+o(ds), where N A (x, s) (N B (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 / D A > 1-P d where, the Polya constant P d = the probability for an A to return to origin P 1 =P 2 =1

in terms of the Master Equation: d P nm / dt = death of B’s: -  [ m P nm – (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 P nm (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 +diffusion etc. ( 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 w 2 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

“A”= education 1988 B= Number of Economic Enterprizes per capita 1994 Number of Economic Enterprizes per capita 1989

Other details of the Predicted Scenario: First the singular educated centers W EDU develop while the others W IGN decay Then, as W EDU >> W IGN, the transfer becomes relevant and activity spreads from EDU to IGN and all develop with the same rate but preserve large inequality EDU IGN EDU

Nowak, Rakoci, Solomon, Ya’ari simulation real data EDU IGN

Nowak, Rakoci, Solomon, Ya’ari simulation real data IGN 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)

Poland Russia Ukraine Latvia

Instability of over-localized economies

Prediction the economic inequality (Pareto exponent) and the economic instability (index anomalous fluctuations exponent) Forbes 400 richest by rank 400   Levy, Solomon,2003

What next?

PIEMONTE MAP 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.