Complexity Sorin Solomon, Multi-Agent Division ISI and Racah Institute of Physics HUJ 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)

Statistical Physics Phase Transitions, clusters, scaling Biology Social Science Cognition Economics and Finance Business Administration Computers Semiotics and Ontology

Could it be that common mechanisms lead to the emergence of life from many molecules, of meaning from simple sensors, of societies from individuals, of health from simple immune cells? The challenge : transcend traditional disciplinary research Complexity Research: More than a juxtaposition of expertises: a new grammar with new interrogative forms grow a new generation of bi- or multi-lingual scientists. The emergent collective objects belong to one science The elementary objects generating them to another science

Phase Transitions, clusters, scaling Biology Social Science Cognition Economics and Finance Business Administration Semiotics and Ontology Atoms Drops Computers Statistical Physics Micro Macro

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 Micro Macro

95 0 C 1Kg 1cm 2

95 0 C97 1Kg 1cm 1Kg

95 0 C Kg 1cm 1Kg

? 95 0 C Kg 1cm 1Kg Extrapolation?

95 0 C Kg 1cm 1Kg The breaking of macroscopic linear extrapolation

Microscopic view of a water drop: a network of linked water molecules From Gene Stanley

The water drop becomes vapors: the network splits in small clusters From Gene Stanley

Boiling is not a physical property of the molecules but a generic property of the clusters. 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

Instead of temperature (energy / matter): Exchange rate/ interest rate Value At Risk / liquid funds Equity Price / Dividends Equity Price / fundamental value

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

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

IN THIS TALK: Examples –from economics –connected to the boiling and –without mathematics But at the Multi-Agent Division at ISI also: –social science, biology, cognition, ontology –applications to Scaling, Criticality, autocataliticity and other physics/ statistical mechanics originating ideas. –Theorems, Renormalization group,etc.

Propagation effects: - product propagation - spread of ideas - epidemics - Internet viruses - Social ills: drugs, terror - Credit networks and bankruptcy avalanches

Product Propagation BASS VCR SALES Bass extrapolation formula vs microscopic representation VCR Extrapolation Actual sales

Reality curves DVD VCR CARS in USA Extrapolation Product Propagation Bass extrapolation formula vs microscopic representation Actual sales

Potential Buyers Rejectors The Square Lattice is just for clarity The effects demonstrated are much more general

Density of potential adopters/ buyers: 26/48>50% What Percent will actually buy?

The Buyers are split in small clusters

Density of potential adopters/ buyers: 26/48>50% What Percent will actually buy?

The epidemics, bankruptcy avalanche, idea, product spread is limited to one cluster

Density of potential adopters/ buyers: 26/48>50% What Percent will actually buy? 7/48 < 15 %

Only 15 % will actually buy! But what if add one more potential buyer?

If adds one more potential buyer 22 out of 27 potential buyers buy. 22/48 ~ 46%

Buyers Density 55% This is not just a fortuitous case; for larger systems the effect is even more dramatic

55%

If lowering the price, or increasing quality, etc one gains 5% more potential buyers Then density of potential buyers = 60% How much will this increase the actual sales?

55%

60%55%

60%55%

60%55%

60% potential buyers 55% potential buyers

60% potential buyers 55% potential buyers 0%sales 55% 60% 59.3 Theorem

Small changes in product quality, price, external conditions can produce large effects (e.g. large market fluctuations) Small deterioration in credit market can trigger large waves of bankruptcies Market 'spikes' are seen by traders as freak events. Physicists expect them Stock market shock explained Physicists model recent trading frenzy.

ECONOMIC Clustering Development after economic liberalization of Poland: year 0 Andrzej Nowak

ECONOMIC Clustering Development after economic liberalization of Poland: year 1

ECONOMIC Clustering Development after economic liberalization of Poland: year 2

ECONOMIC Clustering Development after economic liberalization of Poland: year 3

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 Micro Macro

Community Research Boiling

My papers I am here Community Research Boiling New (Dynamic, Distributed, Open, Free, Self-Org, Ontology

Stock Index Stability in time Time Interval (seconds) Probability of “No significant fluctuation” Time Interval Time Interval (s) Probability of “no significant fluctuation” Stock Index Stability in time

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph Ln RANK Ln WEALTH

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph Walton Ln 90

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph GatesWalton Ln 2 Ln 90 Ln 48

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph GatesBuffettWalton Ln 2 Ln 3 Ln 90 Ln 48 Ln 41

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph GatesBuffett Allen Walton Ln 2 Ln 4Ln 3 Ln 90 Ln 48 Ln 41 Ln 20

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph GatesBuffett Allen Walton Dell Ln 2 Ln 4Ln 5Ln 3 Ln 90 Ln 48 Ln 41 Ln 20 Ln 14.2

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph GatesBuffett Allen Walton DellEllison Ln 2 Ln 4Ln 5Ln 6Ln 3 Ln 90 Ln 48 Ln 41 Ln 20 Ln 14.2 Ln 13.7

1 Gates, William Henry III 48,000, MicrosoftGates, William Henry III 2 Buffett, Warren Edward 41,000, BerkshireBuffett, Warren Edward 3 Allen, Paul Gardner 20,000, Microsoft,Allen, Paul Gardner 4-8Walton 5X18,000, Wal-MartWalton 9 Dell, Michael 14,200, DellDell, Michael 10 Ellison, Lawrence Joseph 13,700, OracleEllison, Lawrence Joseph GatesBuffett Allen Walton DellEllison Ln 2 Ln 4Ln 5Ln 6Ln 3 Ln 90 Ln 48 Ln 41 Ln 20 Ln 14.2 Ln 13.7 

~ population growth rate ~ average family size fixed income (+redistribution) / market returns volatility economic stability; Wealth Social Distribution Forbes 400 richest by rank 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 Log INDIVIDUAL WEALTH Rank in Forbes 400 list 400 Wealth Social Distribution 

~ population growth rate ~ average family size fixed income (+redistribution) / market returns volatility economic stability; Wealth Social Distribution Stock Index Stability in time Forbes 400 richest by rank Time Interval (seconds) 400 Probability of “No significant fluctuation” Time Interval 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 Log INDIVIDUAL WEALTH Rank in Forbes 400 list 400 Time Interval (s) Probability of “no significant fluctuation” ~ population growth rate ~ average family size fixed income (+redistribution) / market returns volatility Stock Index Stability in time  

M. Levy S.S  

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 Some economist colleagues teach already from it Not yet mainstream economics but: