Notes on Complexity NEST meeting May 7, 2003 Sorin Solomon

Molecules chemistry reactions Cells biology life functions COMPLEXITY EMERGENCE ?

Chemicals almost free particles DNA chains, proteins reproduction,evolution,synthesis Cells chemotaxis, metabolism Systems, Organisms health, perception self-non-self recognition

Neuronssimple I/O Nets of Neurons memory, perception, information processing Mindconcepts, feelings, meaning Communitieslanguage, meaningful communication

Phil Anderson (1972) "More is Different". Science 177, (1972) 293 COMPLEXITY: Not just a new language / grammar: New interrogative forms The Microscopic Representation of Complex Macroscopic Phenomena, S. Solomon, Annual Reviews of Computational Physics II pp , editor D. Stauffer, World Scientific S Solomon and E Shir, Complexity; A Science at 30 Europhysics News, 34/2, 2003 Mar-Apr, p54. -Old real life =hardware => applicative science = experimental sci -New real life=information=> applicative science = also theoretical

MOBILE Networks Computer Arrays Traffic Internet SOCIO Crowds Markets Companies Percolation Institutions (humans, ants) Colonies BIO (co)evolution; innovation COGN Immune Genetics; Proteomics Behavioral Finance Auctions Games ECONO MATH Multiscale Ren. Group Stochastic Processes Scaling GLASS Combinatorial NP-complete Non-Lin Chaos Reaction Diffusion AGENTS Spatially extended Systems Localization, Emergence Statistical Mechanics And Phase Transitions percolation Swarms, bots Language;brain Computer Science;

The Microscopic Representation Method. MICRO - the relevant microscopic degrees of freedom INTER - their fundamental interactions MACRO - the macroscopic emerging collective objects Intrinsically interdisciplinary: -Micro belongs to one science -Macro to another science -Mechanisms: statistical mechanics (?) phase transitions, scale invariance, spontaneous symmetry breaking etc At C nothing special happens to one or two H 2 O molecules! or 100 or 1000! How come that 1 Kg of them behave so dramatically?

Microscopic Links, Macroscopic Networks MICRO – Nodes, connections INTERACTIONS - Local changes (node / link (dis-) appearance) MACRO- Global connectivity, K-cores, percolation, topology G Weisbuch and S Solomon, In Handbook of Graphs and Networks: From the Genome to the Internet, Wiley-VCH, Berlin, p113 eds. S. Bornholdt and H. G. Schuster, Global connectivity => percolation, K-cores; Scale invariance => power laws Topological invariance => metastability, long time-scale processes

- 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 demarketing Social Percolators and Self-Organized Criticality Gerard Weisbuch, Sorin Solomon and Dietrich Stauffer in: Economics with heterogeneous interacting agents, ed. by A.Kirman and J.B. Zimmermann, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin- Heidelberg 2001 page

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 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 YLouzoun S Solomon, H Atlan and I R. Cohend Bulletin of Mathematical Biology Volume 65, Issue 3, May 2003, P

Yet the agents b always win ! b. = ( a -  )  b + D b  b => b (x,t) ~ e ( a 0 –  ) t b-> 0; a+b-> b+a+b

Individual wealth and global power laws MICRO – individual investments INTER – returns proportional (through stochastic factors) to investments MACRO – social wealth distribution; market returns distribution S Solomon, P Richmond, O Biham and O Malcai Co-Evolutionist Stochastic Dynamics: Emergence of Power-LawsPower-laws in stochastic Lotka-Volterra-Eigen-Schuster Systems in Towards Cognitive Economics; Eds P Bourgine and J-P Nadal Springer 2003 to appear. Pioneers on a New continent: on Physics and Economics, S Solomon and M Levy, Quantitative Finance, 3/ Feb, C12

- Microscopic Immune Cells and Macroscopic Health MICRO - Cells, Enzimes, Antigens, Antibodies INTER - producing, destroying, changing state of a cell/enzime, 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 ; Modeling complexity in biology Yoram Louzoun, Sorin Solomon, Henri Atlan and Irun. R. Cohen Physica A, 297 (1-2) (2001) pp

New strains appear and are destroyed within weeks. Many new small strains accumulate and destroy many immune system cells. The system collapses The strains of the first invasion are completely wiped out REALITY SIMULATION

Mediterranean; uniform Desert; uniform 200mm 500mm Semi-arid; patchy s Measurements of organic matter distribution - 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)

Desert uniform Mediterranean uniform Semi-arid patchy

Levy, Solomon and Levy's Microscopic Simulation of Financial Markets points us towards the future of financial economics." Harry M. Markowitz, Nobel Laureate in Economics - 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)

L.Muchnick and S.Solomon Physica Scripta, in press

- 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

-Microscopic Concepts and Macroscopic Ideas MICRO - concepts, connections between concepts INTER - creating/deleting/activating 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

Figure 2b: General scheme underlying the replacement version of the pictorial analogy template

NY Times Herald Tribune Communication at the speed of sound

Table 2: Idea Ratings for the Four Sources Creativity RatingsMeanS.D. Winning Ads Magazine Ads Routine-Generated Ads Laymen-Generated Ads Originality RatingsMeanS.D. Winning Ads Magazine Ads Routine-Generated Ads Laymen-Generated Ads

Microscopic words and Macroscopic Stories MICRO – characters, relations INTER – change in relations ; acting MACRO –plot, story, meaning What Are Stories Made Of? Quantitative Categorical Deconstruction of Creation Y. Stolov, M. Idel, S. Solomon, IJMPC 11 (2000) 1

EVENT EVENT NO EVENT TOTAL DENSITY but and NO LINK LENGTH NO LINK LINK RAVEN % PRINCESS % (Lost Princess story has no end) 21 commentators, 29 events Ordered in nr of commentators. Highest one diagonal was only rank 14 Only one non-link below it.

-Microscopic Drivers / police and Macroscopic Jams MICRO - cars INTER - go ahead/give way at intersections. MACRO - traffic flow, jamming; self-organization; useless police E. Mar Or, E. Shir and S. Solomon. Solving Traffic Jams: Human Intervention or Self-Organization? To appear in International Journal of Modern Physics. - Microscopic Seers and Macroscopic Sight MICRO - motion visual sensors for points and line elements. INTER - time and space local data integration. MACRO - Perception of 3 Dimensional global structure. Restricted Ability to Recover 3D Global Motion from 1 D Motion Signals: Restricted Ability to Recover 3D Global Motion from 1 D Motion Signals: N. Rubin, S. Hochstein and S. Solomon, Vision Research 35 (1995)