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

CognitionEconomics

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 SocialScience

CognitionEconomicsand Finance

BusinessAdministration

Semiotics and Ontology

AtomsDrops

Computers

Statistical Physics

MicroMacro

Statistical Physics

Phase Transitions, clusters, scaling

Biology SocialScience

CognitionEconomicsand Finance

BusinessAdministration

Computers

Semiotics and Ontology

ChemicalsCells

BitsInformation items

NeuronsBrain

WordsMeaning Individuals

Society

CustomerMarket

TradersHerds

AtomsDrops

MicroMacro

950C

1Kg

1cm2

950C 97

1Kg

1cm

1Kg

950C 97 99

1Kg

1cm

1cm

1Kg 1Kg

?

950C 97 99 101

1Kg

1cm

1cm

1Kg 1Kg 1Kg

Extrapolation?

950C 97 99 101

1Kg

1cm

1cm

1Kg 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

95 97 99 101

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 SocialScience

CognitionEconomicsand Finance

BusinessAdministration

Computers

Semiotics and Ontology

ChemicalsCells

BitsInformation items

NeuronsBrain

WordsMeaning

IndividualsSociety

CustomerMarket

TradersHerds

AtomsDrops

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 1895-1930

Extrapolation

Product Propagation

Bass extrapolation formula vs

microscopic representation

Actual sales

PotentialBuyers

RejectorsThe Square Lattice is

just for clarityThe effects demonstrated

are much more general

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

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

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

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

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

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

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

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?

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

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

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

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 %

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?

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

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

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

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

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

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

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

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%

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 explainedPhysicists 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 SocialScience

CognitionEconomicsand Finance

BusinessAdministration

Computers

Semiotics and Ontology

ChemicalsCells

BitsInformation items

NeuronsBrain

WordsMeaning Individuals

Society

CustomerMarket

TradersHerds

AtomsDrops

MicroMacro

Clusters automatically formed by elastic

connectionsand repelling forces

Community Research Boiling

Clusters automatically formed by elastic

connectionsand repelling forces

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 IntervalTime Interval (s)

Pro

bab

ilit

y o

f “

no

sig

nif

ican

t fl

uct

uat

ion

” Stock Index Stability in time

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Ln RANK

Ln WEALTH

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Walton

Ln 90

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

GatesWaltonLn 2

Ln 90Ln 48

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Gates BuffettWaltonLn 2 Ln 3

Ln 90Ln 48

Ln 41

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Gates Buffett AllenWaltonLn 2 Ln 4Ln 3

Ln 90Ln 48

Ln 41Ln 20

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Gates Buffett AllenWalton Dell

Ln 2 Ln 4 Ln 5Ln 3

Ln 90Ln 48

Ln 41Ln 20

Ln 14.2

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Gates Buffett AllenWalton Dell Ellison

Ln 2 Ln 4 Ln 5 Ln 6Ln 3

Ln 90Ln 48

Ln 41Ln 20

Ln 14.2Ln 13.7

1 Gates, William Henry III 48,000, Microsoft

2 Buffett, Warren Edward 41,000, Berkshire

3 Allen, Paul Gardner 20,000, Microsoft,

4-8Walton 5X18,000, Wal-Mart

9 Dell, Michael 14,200, Dell

10 Ellison, Lawrence Joseph 13,700, Oracle

Gates Buffett AllenWalton Dell EllisonLn 2 Ln 4 Ln 5 Ln 6Ln 3

Ln 90Ln 48

Ln 41Ln 20

Ln 14.2Ln 13.7

~ population growth rate ~ average family size fixed income (+redistribution) / market returns volatility

economic stability;

Wealth Social Distribution

Forbes 400 richest by rank

Dell

Buffet

20ALLEN

GATES

WALMART

Lo

g IN

DIV

IDU

AL

WE

AL

TH

Rank in Forbes 400 list400

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

Dell

Buffet

20ALLEN

GATES

WALMART

Lo

g IN

DIV

IDU

AL

WE

AL

TH

Rank in Forbes 400 list400

Time Interval (s)

P

rob

abil

ity

of

“n

o s

ign

ific

ant

flu

ctu

atio

n”

~ 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: