Complexity Research; Why and How

1. Complexity Research; Why and How Sorin SolomonRacah Institute of Physics HUJ Israel Director, Complex Multi-Agent Systems Division, ISI TurinDirector, Lagrange Interdisciplinary Laboratory for Excellence In Complexity

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

3. 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

4. Complexity Sorin Solomon, Racah Institute of Physics HUJ Israel andDirector of the Complex Multi-Agent Systems Division, ISI Turin Lagrange Laboratory for Excellence In Complexity at ISI Torino support for students and researchers General Integration Action in Complexity Science + 12 Specific Targeted Research Projects in Complexity (CO3) 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)

5. 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 researchComplexity 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.

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

7. Complexity Sorin Solomon, Racah Institute of Physics HUJ Israel Complex Multi-Agent Systems Division, ISI TurinLagrange 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.”

8. 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

9. 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

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

11. Semiotics and Ontology Social Science Biology MACRO More is different MICRO BusinessAdministration Complexity ICT Drops,Bubbles Atoms,Molecules Economics and Finance Brain Science Meaning Cells,life Social groups Words people Chemicals Markets WWW Customers E-pages Anderson abstractization Herds, Crashes Cognition, perception Traders Neurons Statistical Mechanics Phase Transition

12. Instead of temperature (energy / matter): • Exchange rate/interest rate • Value At Risk / liquid funds • Equity Price / Dividends • Equity Price / fundamental value • Taxation (without representation)/ Tea

13. Product Propagation Bass extrapolation formulavs microscopic representation VCR Actual sales Extrapolation CARS in USA 1895-1930 DVD Reality curves

14. Microscopic view of a water drop: a network of linked water molecules

15. Microscopic view of a water drop: a network of linked water molecules

16. Microscopic view of a water drop: a network of linked water molecules

17. Microscopic view of a water drop: a network of linked water molecules

18. Microscopic view of a water drop: a network of linked water molecules

19. Microscopic view of a water drop: a network of linked water molecules

20. Microscopic view of a water drop: a network of linked water molecules

21. Microscopic view of a water drop: a network of linked water molecules

22. Microscopic view of a water drop: a network of linked water molecules

23. Microscopic view of a water drop: a network of linked water molecules

24. Microscopic view of a water drop: a network of linked water molecules

25. Microscopic view of a water drop: a network of linked water molecules

26. Microscopic view of a water drop: a network of linked water molecules

27. Microscopic view of a water drop: a network of linked water molecules

28. Microscopic view of a water drop: a network of linked water molecules

29. The water drop becomes vapors: the network splits in small clusters

30. The water drop becomes vapors: the network splits in small clusters

31. The water drop becomes vapors: the network splits in small clusters

32. The water drop becomes vapors: the network splits in small clusters

33. The water drop becomes vapors: the network splits in small clusters

34. Boiling is not a physical property of particular molecules but a generic property of the cluster geometry To understand, one does not need the details of the interactions. Rather one can prove theorems on what is the density of links that ensures the emergence or disintegration of clusters Phase Transition

35. Product Propagation Bass extrapolation formulavs microscopic representation VCR VCR Actual sales Extrapolation SALES BASS

36. Product Propagation Bass extrapolation formulavs microscopic representation VCR VCR Actual sales Extrapolation SALES BASS Also Belief Propagation

37. Product Propagation Bass extrapolation formulavs microscopic representation VCR Actual sales Extrapolation Also Belief Propagation CARS in USA 1895-1930 DVD Reality curves

38. - 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

39. Propagation effects: - product propagation - spread of ideas - epidemics - Internet viruses - Social ills: drugs, violence, terror - Credit networks and bankruptcy avalanches - production / trade practices - real estate valuation - tax paying habits

40. The Square Lattice is just for clarityThe effects demonstrated are much more general PotentialAdopters Rejectors

46. Density of potential adopters: 26/48>50% What Percent will actually adopt?