the science of man-made systems gábor vattay physics of complex systems eötvös university
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The Science of Man-made systems
Gábor Vattay
Physics of Complex Systems
Eötvös University
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Advent of quantitative science
• 5 July 1686
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
In the last 300 years
• Reductionist strategy was very successful
• Elementary parts: electron, photon, atoms and molecules, proton, neutron, quarks, gluons …
• Almost complete understanding of how these interact (attract, repel, kick …) and affect each other in general
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Understanding the arrow of time
• Ludwig Boltzmann• Rudolf Clausius• Entropy• 2nd law of
thermodynamics
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
During the last 150 years
• Statistical mechanics/physics was very successful
• Laws of physics do not distinguish between past and future
• Yet, we see that past and future are different
• Things go from order to disorder
• Coffee cools, sugar dissolves …
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Wait a second!
• Formation of atoms from nucleons and electrons.• More and more complicated atoms…• Formation of molecules from atoms.• More and more complicated molecules …• Formation of condensed matter from molecules.• More and more complicated forms of condensed
matter …• …• Formation of cells, tissues …
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
The science of complexity
• Ilya Prigogine• 1977 Nobel Prize in
Chemistry• Entropy can decrease• Makes life possible• Order Out of Chaos
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
In the last 40 years
• I can increase my order if I can export my mess to you …
• Entropy inside can decrease if the system is open and can pump it out into the environment
• Understanding open dissipative structures
• Understanding the complexity of nonlinear dynamics, bifurcations, chaos.
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Evolution
• Ok! We understand that it is physically possible to increase the complexity of systems
• Ok! We understand how this happens technically
• But, why the hell is this happening? • Any law of evolution?• Darwinian selection is a good start, but not
enough
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Cooperation
• Robert Axelrod• Evolution of
cooperation 1981• Competition of agents• Fundamentally selfish
agents will spontaneously cooperate
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Post human aspects of evolution
• Humans form societies• Humans create, design, build man-made
systems • Start their own human assisted evolution
• Emergence of language• Evolution of communication starts • Communication is a special MMS
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Evolution via design
• John Doyle 1999• The human assisted
evolution of different man-made systems share some common features
• Robustness• Fragility• Highly Optimized
Tolerance
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• Robustness is more important than– materials– energy– entropy– information– computation
• Extreme robustness: “robust yet fragile.”• Developing new theories of complexity that focus
on robustness• (slides borrowed from Doyle)
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Power outages
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104 105 106 10710-2
10-1
100
101
N= # of customers affected by outage
Frequency(per year) of outages > N
1984-1997
August 10, 1996
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Square site percolation or simplified “forest fire” model.
The simplest possible toy model of cascading failure.
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connected
notconnected
Connected clusters
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A “spark” that hits a cluster causes loss of that cluster.
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yield =
density- loss
Assume: one randomly located spark
(average)
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yield =
density- loss
Think of (toy) forest fires.
(average)
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0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(avg.)yield
density
“critical point”
N=100
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Critical point
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criticality
This picture is very generic.
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100
101
102
103
104
10-1
100
101
102
Power laws Criticality
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100
101
102
103
104
10-1
100
101
102
Power laws: only at the critical point
low density
high density
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Life, networks, the brain, the universe and everything are at “criticality” or the “edge of chaos.”
Does anyone really believe this?
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Self-organized criticality:dynamics have critical point as global attractor
Simpler explanation: systems that reward yield will naturally evolve to critical point.
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Would you design a
system this way?
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Maybe random networks aren’t
so great
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High yields
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0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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isolated
critical
tolerant
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Why power laws?Why power laws?
Almost any distribution
of sparks
OptimizeYield
Power law distribution
of events
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0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
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random
“optimized”
density
yield
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5 10 15 20 25 30
5
10
15
20
25
30
Probability distribution (tail of normal)
High probability region
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Optimal “evolved”
“Evolved” = add one site at a time to maximize incremental (local) yield
Very local and limited optimization, yet still gives very high yields.
Small events likely
large events are unlikely
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0 0.2 0.4 0.6 0.8 10
0.1
0.2
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0.4
0.5
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random
“optimized”
density
High yields.
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Optimized gridSmall events likely
large events are unlikely
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Optimized grid
0 0.2 0.4 0.6 0.8 10
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random
grid
High yields.
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This source of power This source of power laws is quite universal.laws is quite universal.
Almost any distribution
of sparks
OptimizeYield
Power law distribution
of events
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Tolerance is very different from criticality.
• Mechanism generating power laws.• Higher densities.• Higher yields, more robust to sparks. • Nongeneric, won’t arise due to random fluctuations. • Not fractal, not self-similar.• Extremely sensitive to small perturbations that were not designed for, “changes in the rules.”
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Extreme robustness and extreme hypersensitivity.
Small flaws
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Evolution of Communication
humans and beyond …
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Evolution beyond humans
• Communication networks are man-made systems: we think we evolve them
• Yet, they are special: • Structural changes happen the way we work• Changes our collaboration pattern• Restructures our time• Restructures human sexuality• We are part of the system: they strongly shape our
own evolution
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Evolution of communication
• More information further and faster:• Voice: short range~ 10 m• Courier (on horse)• Light and smoke signaling• Post service (horse based)• Steam engine, railroad, post (railroad based) • Electricity, copper wire, telegraph, telephone• For 100 years …
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Telephone exchange and network
Puskás Tivadar
1878
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Computer appears
ENIAC 1946
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Internet
Growth of the ARPANET (a) December 1969. (b) July 1970.• (c) March 1971. (d) April 1972. (e) September 1972.
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
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The Beast
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Evergrow, ETOMIC, CNDA
• Understanding the future of the Internet
• Understanding the evolution of computer communication
• Understanding how computers compete and cooperate
• Power laws of Internet
roboust yet fragile
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Robust yet fragile topology
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Roboust yet fragile traffic
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One day in Europe
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Gábor Vattay Center for Network Data Analysis, Collegium Budapest
Thank you!