Notes on Complexity

NEST meeting May 7 , 2003

Sorin Solomon

Molecules chemistry reactions

Cells biology life functions

COMPLEXITY

EMERGENCE ?

Chemicals almost free particles

DNA chains, proteins reproduction,evolution,synthesis

Cells chemotaxis, metabolism

Systems, Organisms health, perception self-non-self recognition

Neurons simple I/O

Nets of Neurons memory , perception, information processing

Mind concepts, feelings, meaning

Communities language, meaningful communication

Phil Anderson (1972) "More is Different". Science 177, (1972) 293

COMPLEXITY: Not just a new language / grammar:

New interrogative forms

The Microscopic Representation of Complex Macroscopic Phenomena,

S. Solomon, Annual Reviews of Computational Physics II pp 243-294, editor D. Stauffer, World Scientific 1995.

S Solomon and E Shir, Complexity; A Science at 30Europhysics News, 34/2, 2003 Mar-Apr , p54.

-Old real life =hardware => applicative science = experimental sci

-New real life=information=> applicative science = also theoretical

MOBILE Networks

Computer Arrays

Traffic

Internet

SOCIOCrowds

Markets

CompaniesPercolationInstitutions

(humans, ants)Colonies

BIO

(co)evolution; innovation

COGN

Immune

Genetics; Proteomics

Behavioral Finance

Auctions Games

ECONOMATHMultiscale

Ren. Group

Stochastic Processes

Scaling

GLASSCombinatorial NP-complete

Non-LinChaos

Reaction DiffusionAGENTS

Spatially extended Systems

Localization, Emergence

Statistical Mechanics

And

Phase Transitions

percolation

Swarms, bots

Language;brain

Computer Science;

http://complexity.cogniview.com/MapIndex.html

The Microscopic Representation Method.

MICRO - the relevant microscopic degrees of freedom        

INTER - their fundamental interactions        

MACRO - the macroscopic emerging collective objectsIntrinsically interdisciplinary:

-Micro belongs to one science

-Macro to another science

-Mechanisms: statistical mechanics (?) phase transitions, scale invariance, spontaneous symmetry breaking etc

At 1000 C nothing special happens to one or two H2O molecules! or 100 or 1000!

How come that 1 Kg of them behave so dramatically?

Microscopic Links, Macroscopic Networks

MICRO – Nodes, connections

INTERACTIONS - Local changes (node / link (dis-) appearance)

MACRO- Global connectivity, K-cores, percolation, topology

G Weisbuch and S Solomon, In Handbook of Graphs and Networks: From the Genome to the Internet, Wiley-VCH, Berlin, 2002. p113 eds. S. Bornholdt and H. G. Schuster,

Global connectivity => percolation, K-cores;

Scale invariance => power laws

Topological invariance => metastability, long time-scale processes

- 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

Social Percolators and Self-Organized Criticality Gerard Weisbuch , Sorin Solomon and Dietrich Stauffer in: Economics with heterogeneous interacting agents, ed. by A.Kirman and J.B. Zimmermann, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin- Heidelberg 2001 page 43. http://shum.huji.ac.il/~sorin/wehia.ps

Individual Losers and Collective Winners MICRO – individuals with arbitrary high death rateINTER – arbitrary low birth rate; arbitrary low density of catalisersMACRO –always resilient collective patches

The importance of being discrete: Life always wins on the surface N M. Shnerb, Y Louzoun, E Bettelheim, and S Solomon Proc. Natl. Acad. Sci. USA, 97/ 19, 10322-10324, Sep 12, 2000 http://xxx.lanl.gov/abs/adap-org/9912005

Proliferation and Competition in Discrete Biological Systems YLouzoun S Solomon, H Atlan and I R. Cohend Bulletin of Mathematical Biology Volume 65, Issue 3 , May 2003, P 375-396

Yet the agents b always win !

b.

= ( a - )b + Db b

=> b (x,t) ~ e (a0 – ) t

b-> 0; a+b-> b+a+b

Individual wealth and global power laws MICRO – individual investments INTER – returns proportional (through stochastic factors) to investments MACRO – social wealth distribution; market returns distribution

S Solomon, P Richmond, O Biham and O MalcaiCo-Evolutionist Stochastic Dynamics: Emergence of Power-LawsPower-laws in stochastic Lotka-Volterra-Eigen-Schuster Systems in Towards Cognitive Economics; Eds P Bourgine and J-P NadalSpringer 2003 to appear.

Pioneers on a New continent: on Physics and Economics,S Solomon and M Levy, Quantitative Finance, 3/1 2003 Feb, C12

  - Microscopic Immune Cells and Macroscopic Health

MICRO  - Cells, Enzimes, Antigens, Antibodies          INTER  - producing, destroying, changing state of a cell/enzime,          MACRO  - immunity, health, infection, sickness, inflamation.

Losing All Battles and Wining the War; HIV time hierarchy: U Hershberg, Y Louzoun, H Atlan and S Solomon Physica A: 289 (1-2) (2001) pp.178-190 ; http://xxx.lanl.gov/abs/nlin.AO/0006023

Modeling complexity in biology Yoram Louzoun, Sorin Solomon, Henri Atlan and Irun. R. Cohen Physica A , 297 (1-2) (2001) pp. 242-252

New strains appear and are destroyed within weeks.

Many new small strains accumulate and destroy many immune system cells. The system collapses

The strains of the first invasion are completely wiped out

REALITY

SIMULATION

Mediterranean; uniform

Desert; uniform

200mm500mmSemi-arid; patchy

s

Measurements of organic matter distribution

- Microscopic seeds and Macroscopic Oases    MICRO –individual plants     INTER –growth, water fixation, MACRO – bushes, vegetation patches

N.M. Shnerb, P. Sarah, H. Lavee, and S. Solomon Reactive glass and vegetation patterns Phys. Rev. Lett. 90, 38101 (2003)

Desert

uniform

Mediterranean

uniform

Semi-arid

patchy

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

- Microscopic Investors and Macroscopic Crashes       MICRO - Investors, individual capital ,shares         INTER - sell/buy orders, gain/loss          MACRO - social wealth distribution, market price fluctuations (cycles, crushes, booms, stabilization by noise)

9 9.5 10 10.5 11 11.53750

3800

3850

3900

3950

4000

4050

4100

L.Muchnick and S.Solomon

Physica Scripta, in press

- Microscopic Draws and Macroscopic Drawings

MICRO - local line / motion features, mental states, mental eventsINTER - line breaks and mind events vs line/mind inertia.MACRO - drawing shapes, emergence of meaning

Emergence of Representation in Drawing: The Relation Between Kinematic and Referential Aspects E Adi-Japha, I Levin and S. Solomon, Cognitive Development 13 (1998) 25

Breaks are correlated with a posteriori representation

-Microscopic Concepts and Macroscopic Ideas

MICRO - concepts, connections between concepts

INTER - creating/deleting/activating connections between concepts

MACRO –Novel products, creative ideas, real-life problem solving

Creative Sparks, J Goldenberg, D Mazursky, and S Solomon , Science 285: 1495-1496, 1999;

Templates of original innovation: Projecting original incremental innovations from intrinsic information Goldenberg J. Mazursky D. Solomon S., (1999) Technological Forecasting and Social Change, May, Vol. 61/1 P. 1-12.

Figure 2b: General scheme underlying the replacement version of the pictorial analogy template

Symbols set

Symbol 1 Symbol 2 Symbol 3

Product Message

Product space

P1

P2

P3 Matching by a linking operator

?

P4

NY Times Herald Tribune

Communication at the speed of sound

 

Table 2: Idea Ratings for the Four SourcesCreativity Ratings Mean S.D.Winning Ads 3.26 .49Magazine Ads 2.88 .55Routine-Generated Ads 2.89 .48Laymen-Generated Ads 2.22 .43 

Originality Ratings Mean S.D.Winning Ads 3.33 .55Magazine Ads 2.85 .58Routine-Generated Ads 2.89 .54Laymen-Generated Ads 2.22 .46

Microscopic words and Macroscopic Stories

MICRO – characters, relationsINTER – change in relations ; actingMACRO –plot, story, meaning

What Are Stories Made Of? Quantitative Categorical Deconstruction of Creation Y. Stolov, M. Idel, S. Solomon, IJMPC 11 (2000) 1

EVENT EVENT NO EVENT TOTAL DENSITY

but and NO LINK LENGTH

NO LINK LINK

RAVEN 9 8 1 1652 0.7 %

PRINCESS 12 3 1312 1.4 %

(Lost Princess story has no end)

21 commentators, 29 events

Ordered in nr of commentators.

Highest one diagonal was only rank 14

Only one non-link below it.

-Microscopic Drivers / police and Macroscopic Jams

MICRO - carsINTER - go ahead/give way at intersections.MACRO - traffic flow, jamming; self-organization; useless policeE. Mar Or, E. Shir and S. Solomon. Solving Traffic Jams: Human Intervention or Self-Organization? To appear in International Journal of Modern Physics.

- Microscopic Seers and Macroscopic Sight

MICRO - motion visual sensors for points and line elements.

INTER - time and space  local data integration.

MACRO - Perception of 3 Dimensional global structure.

Restricted Ability to Recover 3D Global Motion from 1 D Motion Signals: N. Rubin, S. Hochstein and S. Solomon, Vision Research 35 (1995) 569-578.