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Complexity Emergence

Complexity Emergence. Sorin Solomon, Racah Institute of Physics HUJ Israel Scientific Director of Complex Multi-Agent Systems Division, ISI Turin and of the Lagrange Interdisciplinary Laboratory for Excellence In Complexity Coordinator of EU General Integration Action in Complexity Science.

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Complexity Emergence

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  1. Complexity Emergence Sorin Solomon, Racah Institute of Physics HUJ Israel Scientific Director of Complex Multi-Agent Systems Division, ISI Turin and of the Lagrange Interdisciplinary Laboratory for Excellence In Complexity Coordinator of EU General Integration Action in Complexity Science MORE IS DIFFERENT (Anderson 72)(more is more than more)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’. we need to free ourselves from ‘average’ thinking.”

  2. Simplest Example of a “More is Different” Transition Extrapolation? ? 1cm The breaking of macroscopic linear extrapolation 1Kg 1Kg 101 97 99 Water level vs. temperature 1cm 1Kg 950C BOILING PHASE TRANSITIONMore is different: a single molecule does not boil at 100C0

  3. Example of “MORE IS DIFFERENT” transition in Finance: Instead of Water Level: -economic index(Dow-Jones etc…) 97 99 101 95 Crash = result of collective behavior of individual traders

  4. - Microscopic Investors and Macroscopic CrashesMICRO - Investors, individual capital ,shares         INTER - sell/buy orders, gain/loss          MACRO - social wealth distribution, market price fluctuations (cycles, crushes, booms, stabilization by noise) “Levy, Solomon and Levy'sMicroscopic Simulation of Financial Markets points us towards the future of financial economics. If we restrict ourselves to models which can be solved analytically, we will be modeling for our mutual entertainment, not to maximize explanatory or predictive power."HARRY M. MARKOWITZ, Nobel Laureate in Economics

  5. The Importance of Being Discrete; Life Always Wins on the Surface Irun Cohen (immunology), Henri Atlan (biology), J Goldenberg (marketing), Hanoch Lavee (desert/ecology) H and M Levy (financeecono), D Mazursky (Soc. Sci.,Bus. Adm.) The emergence of Macroscopic Complex Adaptive Objects from Microscopic Noise

  6. Cells biology teleological causalitylife functions COMPLEXITY EMERGENCE ? Moleculeschemistry past-to future causality reactions

  7. 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

  8. Size a > 0 a < 0 WELL KNOWN Logistic Equation(but usually ignored spatial distribution, discreteness and randomeness b. = ( a l- m)b + Db D b – c b 2 almost all the social phenomena, …. obey the logistic growth. “Social dynamics and quantifying of social forces”E. W. Montroll 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 … Lord Robert May TIME

  9. surprize Surprize!

  10. Multi-Agent Complex Systems Implications: one can prove rigorously that the DE prediction: Multi-Agent stochastic<a> << 0prediction Differential Eqations(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!

  11. one can prove rigorously(Renormalization Group (2000) , Branching Random Walks Theorems (2002))that: • On a large enough 2 dimensional surface, the B populationalways grows! No matter how fast the death rate m, how low the A density, how small the proliferation rate l - In all dimensions d: l/Da > 1-Pdalways sufficesPd = Polya’s constant ; P2= 1

  12. Angels and Mortals movie by Gur Ya’ari

  13. Movie By Gur Ya’ari

  14. EXAMPLE of Theory Application GNP Education 88 89 90 91 92 THEOREM (RG, RW) one of the fundamental laws of complexity APPLICATION: Liberalization Experiment Poland Economy after 1989 MACRO decay 1990 MACRO decay(90) +MICRO growth 1991 MICRO growth(91) ___________________ => MACRO growth 1992MACRO growth (92) Complexity prediction Global analysis prediction Maps Andrzej Nowak’s group (Warsaw U.), CO3 collaboration

  15. TIME Emergent Collective Dynamics:B-islands search, follow, adapt to, and exploit fortuitous fluctuations in A density. lnb (A location and b distribution) E C A This is in apparent contradiction to the “fundamental laws” where individual B don’t follow anybody P TIME S The strict adherence of the elementary particles A and B to the basic fundamental laws and the emergenceof complex adaptive entities with self-serving behavior do not interfere one with another.Yet they determine one another. Is this a mystery? Not in the AB model where all is on the table !

  16. Movie by Gur Ya’ari

  17. Effect of competition: Islands are of limited height

  18. Fractal Wealth Distribution: Scaling; Power laws No one however, has yet exhibited a stable social order, ancient or modern, which has not followed the Pareto pattern…Davis; Cowles Commission for Research in Economics Pareto’s curve … great generalizations of human knowledge.Snyder 1939 WALMART GATES Buffet ALLEN 20 Dell 1/a Zipf plot of the wealths of the investors in the Forbes 400 of 2003 vs. their ranks. The corresponding model results are shown in the in set.

  19. Number of sites with that B occupation number Number of B’s on the site

  20. Rigorous Result: Even in non-stationary, arbitrarily varying conditions(corresponding to wars, revolutions, booms, crashes, draughts) The Theorempredicts: that stable Pareto Laws emerge generically from stochastic logistic systems Indeed it is verified: the list of systemspresenting scaling ~list of systems modeled in the past by logistic equations ! The 100year oldPareto puzzle is solved by combiningthe 100 year old logistic Lotka-Volterraequation with the 100 year old Boltzmann Statistical Mechanics

  21. 1 3 10 Mantegna and Stanley The distribution of price variations as a function of the time interval t The relative probability of the price being the same after t as a function of the time interval t : P(0,t) ~ t –1/b

  22. 1 a b M. Levy S.S 3 10 -1/b -1/b -1/ a Prediction of the Lotka-Volterra-Boltzmann model: b = a

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