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.