Executive Abstract • Logistic dynamics has been recognized since 200 years to govern a wide range of social, economic, biological and cognitive systems. • In the past the predictions of the logistic equation have been invalidated almost systematically in many occasions. • In particular they predicted often falsely the decay of the dynamics in adverse conditions. • We show that the correct accounting for the discrete character of the elementary components of the system leads to dramatically different predictions: – In particular the emergence of adaptive collective objects that insure survival and development in conditions in which the naïve continuous/ global treatment would predict complete and uniform decay. – The emergence of stable Pareto-Zipf power laws even in very non-stationary conditions. • We review a series of applications, predictions and their validation.
Transcript
Executive Abstract• Logistic dynamics has been recognized since 200 years to govern a
wide range of social, economic, biological and cognitive systems.• In the past the predictions of the logistic equation have been
invalidated almost systematically in many occasions.• In particular they predicted often falsely the decay of the dynamics in
adverse conditions.• We show that the correct accounting for the discrete character of the
elementary components of the system leads to dramatically different predictions:– In particular the emergence of adaptive collective objects that insure survival
and development in conditions in which the naïve continuous/ global treatment would predict complete and uniform decay.
– The emergence of stable Pareto-Zipf power laws even in very non-stationary conditions.
• We review a series of applications, predictions and their validation.
Complexity Sorin Solomon,
Racah Institute of Physics HUJ Israel Director, Complex Multi-Agent Systems Division, ISI Turin
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)
Director, Lagrange Interdisciplinary Lab for Excellence In Complexity
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.
SAME SYSTEM Reality Models
Complex ----------------------------------Trivial
Adaptive ----------------------------------Fixed dynamical law
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
“MORE IS DIFFERENT” Complex Systems Paradigm
MICRO - the relevant elementary agents
INTER - their basic, simple interactions
MACRO - the emerging collective objects
Intrinsically (3x) interdisciplinary:
-MICRO belongs to one science
-MACRO to another science
-Mechanisms: a third science
traders
orders, transactions
herds,crashes,booms
Decision making, psychology
Financial economics
statistical mechanics, physicsmath, game theory, info
950C
1Kg
1cm
97
1cm
1Kg
99
1Kg
101
The breaking of macroscopic linear extrapolation
?Extrapolation?
BOILING PHASE TRANSITIONMore is different: a single molecule does not boil at 100C0
Simplest Example of a “More is Different” Transition
Water level vs. temperature
95 97 99 101
Example of “MORE IS DIFFERENT” transition in Finance:
Instead of Water Level: -economic index(Dow-Jones etc…)
Crash = result of collective behavior of individual traders
Statistical Mechanics
Phase Transition
Atoms,Molecules
Drops,Bubbles
Anderson abstractization
Complexity MICRO
MACRO More is different
BiologySocial Science
Brain ScienceEconomics and
Finance
BusinessAdministration ICT
Semiotics and Ontology
Chemicals
E-pages
Neurons
Words
people
Customers
Traders
Cells,lifeMeaning
Social groups
WWW
Cognition, perception
Markets
Herds, Crashes
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
Reality curves
DVD
VCR
CARS in USA 1895-1930
Product Propagation
Bass extrapolation formula vs
microscopic representation
Actual sales
Extrapolation
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
Microscopic view of a water drop: a network of linked water molecules
The water drop becomes vapors: the network splits in small clusters
The water drop becomes vapors: the network splits in small clusters
The water drop becomes vapors: the network splits in small clusters
The water drop becomes vapors: the network splits in small clusters
The water drop becomes vapors: the network splits in small clusters
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
Product Propagation
BASS
VCR
SALES
Bass extrapolation formula vs
microscopic representation
VCR
Extrapolation
Actual sales
Product Propagation
BASS
VCR
SALES
Bass extrapolation formula vs
microscopic representation
VCR
Extrapolation
Actual sales
Also Belief Propagation
Reality curves
DVD
VCR
CARS in USA 1895-1930
Extrapolation
Product Propagation
Bass extrapolation formula vs
microscopic representation
Actual sales
Also Belief Propagation
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
PotentialAdopters
RejectorsThe Square Lattice is
just for clarityThe effects demonstrated
are much more general
Density of potential adopters: 26/48>50% What Percent will actually adopt?
The Buyers are split in small clusters
The epidemics, bankruptcy avalanche, idea, product spread is limited to one cluster
Density of potential adopters: 26/48>50% What Percent will actually adopt? 7/48 < 15 %
Density of potential adopters: 26/48>50% What Percent will actually adopt? 7/48 < 15 %
Only 15 % will actually adopt! But what if add one more potential adopter?
If adds one more potential adopter 22 out of 27 potential adopters adopt 22/48~46%
Adopters 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, or decreasing taxes or subsidizing adopters
(or affecting credit rate) etc
one gains 5% more potential adopters Then
density of potential adopters = 60%
How much will this increase the actual adoption?
55%
60%55%
60%55%
60%55%
60% potential adopters
55% potential adopters
60% potential adopters
55% potential adopters 0%adoption55%
60%
59.3
Theorem
55%density
61%
Potential Adopters
Adopters fraction
0% salesPercolation transition
infin
itely
sha
rp
at in
finite
siz
e
Fractal Sales: Prediction Tool for product success (15/17)
fractal space distributionPrediction of campaign success (15/17) Goldenberg
Air-view of a sub-urban neighborhood;
crosses on the roofs indicate air-conditioner purchase
Stock market shock explainedPhysicists model recent trading frenzy.
Market 'spikes' are seen by traders as freak events.Physicists expect them
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
points us towards the future of financial economics.
If we restrict ourselves to models which can be solved analytically, we will be modeling for our mutual entertainment, not to maximize explanatory or predictive power."
--HARRY M. MARKOWITZ, Nobel Laureate in Economics
-emergence of High-Tech communities-start-ups connections to previous businesses-entrepreneurs emerging from old businesses-partners having previous common institutions
-emergence of High-Tech communities-start-ups connections to previous businesses-entrepreneurs emerging from old businesses-partners having previous common institutions
- map the interdisciplinary cooperation network(- people are nodes - cooperations andcommon papers, are links).
- give priority to people with high interdisciplinarity
rather then high rank / disciplinary authority
Discipline 2
Discipline 1
Subjects that need synthesis
Objective Algorithm to Evaluate Interdisciplinary researchers relevance
Discipline3
• nphys177-s1.mov
• nphys177-s2.avi
This was a Particular case of Logistics dynamics (with Corrections!!); Other:
![The Logistic Function - mygeodesy.id.au Logistic Function.pdf · courbe logistique [the logistic curve]. The properties of the logistic curve are derived and a general equation developed](https://static.documents.pub/doc/80x56/5b95cda609d3f2c2678cb9ab/the-logistic-function-logistic-functionpdf-courbe-logistique-the-logistic.jpg)
