Complexity as Theoretical Applied Science

1. Complexity as TheoreticalApplied 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.”

2. “MORE IS DIFFERENT” Complex Systems Paradigm MICRO - the relevant elementary agents INTER - their basic, simple interactions MACRO - the emerging collective objects Traders, investors transactions herds,crashes,booms Decision making, psychology economics statistical mechanics, physicsmath, game theory, info • Intrinsically (3x) interdisciplinary: • MICRO belongs to one science • MACRO to another science • Mechanisms: a third science

3. 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) Yet with a strong collective identity and common motivation.

4. Complexity Induces a New relation Theoretical Science  Real Life Applications:Traditional Applied Scienceappliedhardware devices (results ofexperimental science)to material / physical reality. Modern Complexity rather appliestheoretical methods e.g.- new (self-)organization concepts and - (self-)adaptation emergence theoriesto reallife, but not necessarily material / physical items: - social and economic change, - individual and collective creativity, - the information flow in life

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

6. 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.

7. Malthus : autocatalitic proliferation/ returns :B+AB+B+Adeath/ consumption B  Ødw/dt = awa =(#A x birth rate - death rate)a=(#A x returns rate - consumption /losses rate) exponential solution: w(t) = w(0)e a t w= #B birth rate > death rate a > 0 birth rate > death rate a < 0 TIME

8. Solution: exponential==========saturation Verhulst way out of it: B+B BThe LOGISTIC EQUATIONdw/dt = a w – c w2c=competition / saturation w = #B

9. 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

10. SAME SYSTEM Reality Models Discrete Individuals ContinuumDensity Complex ----------------------------------Trivial Localized patches-----------------------Spatial Uniformity Adaptive ----------------------------------Fixed dynamical law Development -----------------------------Decay Survival -----------------------------------Death Misfit was always assigned to the neglect of specific details. 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

11. Logistic Equation usually ignored spatial distribution,Introducediscretenessandrandomeness ! w. = ( conditionsx birth rate - death) xw+diffusion w - competition w2 conditions is a function ofmany spatio-temporal distributed discrete individual contributionsrather then totally uniform and static

12. 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.”

13. Shnerb, Louzoun, Bettelheim, Solomon,[PNAS (2000)] proved by (FT,RG) that the continuum , differential logistic equation prediction: Multi-Agent a << 0prediction Differential Equations(continuum a<< 0approx) Time Instead: emergence of singularspatio-temporal localizedcollective islands with adaptive self-serving behavior Is ALWAYS wrong ! resilience and sustainabilityeven for a << 0!

14. 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 δand a B-particle at x at time ssplits 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.

15. 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 constantPd=the probability for anA to return to originP1=P2=1

16. 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 . in terms of the Master Equation:d Pnm / dt =death of B’s:- m[ m Pnm – (m+1) P n,m+1]birth of B’sin the presence of n A’s- ln[ m P nm – (m-1) P n,m-1]+ diffusion to and from neighbors Interpret it as aSchroedinger Equationwith imaginary time where and +diffusion etc. (second quantization creation/anihilation operators) and

17. 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

18. w. = a w –c w2 Logistic Diff Eq prediction: Multi-Agent stochastic<a> << 0prediction Differential Equationscontinuum<a><< 0approx) Time GDP Poland Nowak, Rakoci, Solomon, Ya’ari

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

20. Movie By Gur Ya’ari

21. Nowak, Rakoci, Solomon, Ya’ari

22. Number of Economic Enterprizes per capita1989 B= Number of Economic Enterprizes per capita1994 “A”= education 1988 Nowak, Rakoci, Solomon, Ya’ari

23. 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 EDU IGN IGN

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

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

26. Other predictions • 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 reinvestmentis enough to insure growth. Very few localized growth centers (occasionally efficient but unequal and unstable) Uniform distribution (inefficient but stable)

27. Poland Russia Ukraine Latvia

28. Instability of over-localized economies

29. Predictionthe economic inequality (Pareto exponent)and the economic instability (index anomalous fluctuations exponent) a b 400 Forbes 400 richest by rank Levy, Solomon,2003

30. What next?

31. 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 PIEMONTE MAP

32. 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.