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: