Complexity Sorin Solomon, Racah Institute of Physics HUJ Israel Complex Multi-Agent Systems Division, ISI Turin Lagrange Interdisciplinary Lab for Excellence In Complexity MORE IS DIFFERENT (Anderson 72) (more is more than more) Complex “Macroscopic” properties may be the collective effect of many simple “microscopic” components (and independent on their details) 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. ”

95 0 C 1Kg 1cm 97 1cm 1Kg 99 1Kg 101 The breaking of macroscopic linear extrapolation ? Extrapolation?

Statistical Physics Phase Transitions, clusters, scaling Biology Social Science Cognition Economics and Finance Business Administration Computers Semiotics and Ontology Chemicals Cells Bits Information items Neurons Brain Words Meaning Individuals Society Customer Market Traders Herds Atoms Drops

Instead of temperature: Exchange rate/ interest rate Value At Risk / liquid funds Equity Price / Dividends Equity Price / fundamental value Political Activity Education …

Chemicals almost free particles DNA chains, proteins reproduction,evolution,synthesis Cells chemotaxis, metabolism Systems, Organisms health, perception self-non-self recognition CONCEPTUAL AND DISCIPLINARY JUMPS of the MORE IS DIFFERENT type

The Multi-Agent Complex Systems Paradigm MICRO - the relevant microscopic degrees of freedom INTER - their fundamental interactions MACRO - the macroscopic emerging collective objects Intrinsically (3x) interdisciplinary: -MICRO belongs to one science -MACRO to another science -Mechanisms: statistical mechanics (?) phase transitions, scale invariance, The challenge : transcend traditional disciplinary research Complexity Research: More than a juxtaposition of expertises: a new grammar with new interrogative forms allowing the formulation of new questions. Grow a new generation of bi- or multi-lingual scientists.

Microscopic Links, Macroscopic Networks MICRO – Nodes, connections INTERACTIONS - Local changes (node / link (dis-) appearance) MACRO- Global connectivity, percolation, topology New generation of network studies: Instead of study generic properties that are not specific to any particular system, Study specific macroscopic collective properties implied by specific elementary interactions.. site links Copied site /gene links site Transitive link browse Gene activation WWW linking

- 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. Losing All Battles and Wining the War; HIV time hierarchy : U Hershberg, Y Louzoun, H Atlan and S Solomon Physica A: 289 (1-2) (2001) pp ; 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

- Microscopic Investors and Macroscopic Crashes MICRO - 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'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

Realistic macroscopic simulations require a new causal framework: discrete / delayed/ conditional / nested causality instead of the usual Markov infinitesimal one New mathematical concept : Markov Webs

“Stock market shock explained Physicists model recent trading frenzy” 1 October 2002 Realistic Continuous Time Simulation Platform

- Microscopic Draws and Macroscopic Drawings MICRO - local line / motion features, mental states, mental events INTER - line breaks and mind events vs line/mind inertia. MACRO - drawing shapes, emergence of meaning Emergence of Representation in Drawing: The Relation Between Kinematic and Referential Aspects E Adi-Japha, I Levin and S. Solomon, Cognitive Development 13 (1998) 25 Breaks are correlated with a posteriori representation EMPTY SHELLS “looking for representation al content”

-Microscopic Concepts and Macroscopic Ideas MICRO - concepts, connections between concepts INTER - creating/deleting connections between concepts MACRO – Novel products, creative ideas, real-life problem solving Creative Sparks, J Goldenberg, D Mazursky, and S Solomon Science 285: , 1999; Templates of original innovation: Projecting original incremental innovations from intrinsic information Goldenberg J. Mazursky D. Solomon S., (1999) Technological Forecasting and Social Change, May, Vol. 61/1 P Communication at the speed of sound

Individual Losers and Collective Winners MICRO – individuals with arbitrary high death rate INTER – arbitrary low birth rate; arbitrary low density of catalisers MACRO –always resilient collective patches (THEOREM) The importance of being discrete: Life always wins on the surface N M. Shnerb, Y Louzoun, E Bettelheim, and S Solomon Proc. Natl. Acad. Sci. USA, 97/ 19, , Sep 12, Proliferation and Competition in Discrete Biological Systems Y Louzoun S Solomon, H Atlan and I R. Cohend Bulletin of Mathematical Biology Volume 65, Issue 3, May 2003, P continuum density distributions  - uniform distribution - population extinction discrete individuals  - self-organize in - localized adaptive patches - survival and development SAME SYSTEM

Nowak Prediction by Logistic Differential Equation  < 0 Logistic Multi-Agent Prediction     Economy (89-92) vs. EDUCATION ( ‘ 88) note complete correspondence to education AFTER (‘92) but NOT BEFORE(‘89) liberalization 1989

Fractal Wealth Distribution: Scaling; Power laws Zipfplot of thewealthsof the investors in the Forbes 400 of 2003 vs. their ranks. The corresponding model results are shown in the inset. Dell Buffet 20 ALLEN GATES WALMART 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

Distribution of individual wealth ~ (by MACS Prediction) Distribution of global financial fluctuations Social equity is good for the financial stability ! Levy

- Microscopic Customers and Macroscopic Sales MICRO – Customers, products / ideas / information INTER – purchase, inform, learn, hear-say MACRO – global trends, waves of sales (e.g. Tamaguchi), hits, flops, market fluctuations, anomalous diffusion Percolation transition From non-sales at all to a lot of sales Social Percolators and Self-Organized Criticality Gerard Weisbuch, Sorin Solomon in: Economics with heterogeneous interacting agents, page 43. eds A.Kirman and J.B. Zimmermann, Lecture Notes in Economics and Mathematics, Springer, %sales 55% 60% 59.3 Theorem 60% potential buyers 55% potential buyers Sales Potential buyers

55% 60%

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

CAR SALES in USA Sales extrapolation formula vs microscopic representation New Generation of Models: Take into account negative reaction to the propagation: -Negative word-of-mouth: unsatisfied customers influence their contacts in non-buying: anti-percolation. -anti-viruses propagating on “almost” the same network: role of additional links: antivirus arrives first. -Timing of transmission: not all contacts are always active Extrapolation

Conclusions No Doctrina Complexity May be Unifying Language Simple “Microscopic Agents” Dynamics => Macroscopic Complexity