The emergence of Self-Organized Sustainable Ecologies from Individual random interactions D Mazursky (Soc. Sci., Bus. Adm.) Henri Atlan (biology), Irun Cohen (immunology), Hanoch Lavee (desert/ecology) H and M Levy (finance econo), J Goldenberg (marketing), The Importance of Being Discrete; Life Always Wins on the Surface

COMPLEXITY EMERGENCE ? Individual plants Self-organized Resilient Ecological patterns

Simplest model: A water ; B plants A+B-> A+B+B proliferation B->.  death B+B-> B  competition WELL KNOWN Logistic Equation (Malthus, Verhulst. Lotka, Volterra, Eigen) b. = ( a -  )  b + D b  b –  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  < 0 #b#b 

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.

Instead: emergence of singular spatio-temporal localized collective islands with adaptive self-serving behavior => resilience and sustainability even for << 0 ! Multi-Agent Complex Systems Implications: one can prove rigorously that the DE prediction: Time Differential Eqations ( continuum << 0 approx ) Multi-Agent stochastic  a   prediction Is ALWAYS wrong !

Discrete Individuals  microscopic noise Autocatalytic proliferation  amplification Collective Macroscopic Objects -Emergent Properties : Adaptability -Life “always” wins

APPLICATION: Liberalization Experiment Poland Economy after MACRO decay (90) 1992 MACRO growth (92) 1991 MICRO growth (91) GNP Global analysis prediction Complexity prediction

fractal space distribution Prediction of campaign success (15/17) Goldenberg Air-view of a sub-urban neighborhood; crosses on the roofs indicate air-conditioner purchase Innovations Refuse to Die:-The Unforeseen Longevity of Society Fundamental Ideas. Mazurski. D., Goldberg. J. Barak.L. Louzoun. Y. Solomon. S. (2003) Technological forecasting and Social Change

Individual fluctuations of b between different sites  Time fluctuations in the total b M. Levy S.S   “ Levy, Solomon and Levy's Microscopic 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

- Microscopic Immune Cells and Macroscopic Health MICRO - Cells, Enzimes, Antigens, Antibodies INTER -producing, destroying, changing state of cells/enzymes MACRO - immunity, health, infection, sickness, inflamation. Proliferation and competition in discrete biological systems. Louzoun, Y., Atlan, H., Solomon. S., Cohen, I.R (2003) Bulletin of mathematical biology 65(3) Antigen-receptor degeneracy and immunological paradigms Irun R. Cohen,, Uri Hershberg, Sorin Solomon Molecular Immunology 40 (2004) 993–996 REALITY Agents SIMULATION HIV Acute Phase T-cells

- Microscopic seeds and Macroscopic Oases MICRO –individual plants INTER –growth, water fixation, MACRO – bushes, vegetation patches N.M. Shnerb, P. Sarah, H. Lavee, and S. Solomon Reactive glass and vegetation patterns Phys. Rev. Lett. 90, (2003) Mediterranean; uniform Semi-arid; patchy Desert; uniform

Two coupled reaction-diffusion systems with slow and fast reactants may support an instability at finite wavelength. TURING PATTERNS Vegetation in semi-arid zones

When the average naïve growth rate is negative -> discreteness effects -> still survival But no PDE

NO!

Picture Radel Ben-Av