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06-04-09
The Interesting In Between: Why Complexity Exists
Scott E Page
University of Michigan
Santa Fe Institute
scottepage@gmail.com
06-04-09
Background Reading
06-04-09
Outline
Attributes
Properties
The Interesting In Between
Why Complexity
Conclusions
06-04-09
Complex Adaptive Systems: Attributes
06-04-09
Complex Adaptive Systems
Networks
Source: MIT
06-04-09
Complex Adaptive Systems
NetworksAdaptation
Source: Exploring Nature
06-04-09
Complex Adaptive Systems
NetworksAdaptationInteractions
Source: Uptodate.com
06-04-09
Complex Adaptive Systems
NetworksAdaptationInteractionsDiversity
Source: Scientific American
06-04-09
Complex Adaptive Systems: Properties
06-04-09
Complex ≠ Complicated
06-04-09
Complex ≠ Equilibrium (w/ Shocks)
06-04-09
Complex ≠ Chaos
Source: Andrew Russell
06-04-09
Complex ≠ Difficult
Source: Biology-direct
06-04-09
Complex = Dancing Landscapes
Source: Chris Lucas
06-04-09
Epi-Phenomena
Emergence Structures and Levels
Source: Boortz.com
06-04-09
Diffusion Limited Aggregation
Start with a seed on a plane.
Create drunken walkers who start from a random location and walk in random directions until touching the seed, at which point the walkers become immobilized.
Witten and Sander (1981)
06-04-09
Diffusion Limited Aggregation
seed
walker
06-04-09
Diffusion Limited Aggregation
06-04-09
Conway’s Game of Life
X 5
76
41 2 3
8
Cell has eight neighbors
Cell can be alive
Cell can be dead
Dead cell with 3 neighbors comes to life
Live cell with 2,3 stays alive
06-04-09
Examples
X
06-04-09
Bigger Space
06-04-09
A New Kind of Science - Wolfram
Binary state objects arranged in a line using simple rules can create- “perfect’’ randomness- chaos- patterns- computation
06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent Functionalities
Source: Biology-direct
06-04-09
Wolfram’s 256 Automata
N X N X
06-04-09
Rule 90
N X N X
2
8
16
64
Sum = 90
06-04-09
Rule 90
N X N X
2
8
16
64
Sum = 90
06-04-09
Four Classes of Behavior
06-04-09
Emergent Computation
Source: U of Indiana
06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent FunctionalitiesInnovation
http://media-2.web.britannica.com/eb-media/54/4054-004-F5EB3891.jpg
06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent FunctionalitiesInnovation Large Events
06-04-09
A Long Tailed Distribution
06-04-09
A Long Tailed Distribution
cities size words citations web hits book sales phone calls earthquakes moon craters wars net worth family names
06-04-09
Large Events
Source: www2002
06-04-09
Per Bak’s Sandpile
sand
table
floor
06-04-09
Per Bak’s Sandpile
sand
table
floor
06-04-09
Self Organized Criticality
Systems may self organize into critical states. If so “events” may not be normally distributed. They may instead have long tails. Small events could have enormous consequences.
06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent FunctionalitiesInnovationLarge Events Robustness
Source: NBC
06-04-09
“Imagine how difficult physics would be in electrons could think.”
-Murray Gell-Mann
06-04-09
Robustness: The World of Thinking (or adapting)
Electrons
06-04-09
The Langton Graph
06-04-09
The Langton Graph
06-04-09
A Thought Play
A Simple Model of Forest Fires & Bank Failures
06-04-09
The Bank Model
Banks choose to make a risky loan each period with probability p
06-04-09
The Bank Model
Banks choose to make a risky loan each period with probability p
Risky loans fail with probability q but have a higher yield
06-04-09
The Bank Model
Banks choose to make a risky loan each period with probability p
Risky loans fail with probability q but have a higher yield
Failures spread to neighboring banks only if those banks have a risky loan outstanding
06-04-09
The Forest Fire Model
Trees choose to make a grow each period with probability p
Trees get hit by lightening with probability q
Fire spreads to neighboring locations only if those locations have a tree
06-04-09
Example
Period 1: 00R00R000RR0RPeriod 2: R0R00R00RRRRR
06-04-09
Example
Period 1: 00R00R000RR0RPeriod 2: R0R00R00RRRRR Period 3: R0R00R00FRRRRPeriod 4: R0R00R00FFFFFFPeriod 5: R0R00R00000000
06-04-09
Key Insight Revisited
Bank managers should be smarter than trees!
06-04-09
Forest Fire Model Results
Yield increases in p up to a point and then falls off rather dramatically
Physicists call this a ``phase transition’’
06-04-09
Poised at the ‘edge of chaos’
rate of risky loans p*
yield
06-04-09
Smarter Banks
Let each bank learn (using a standard learning rule from psychology called Hebbian learning) whether or not to make risk loans.
06-04-09
Emergent Robustness
rate of risky loans p*
yield
06-04-09
Emergence of Firewalls
11101101110111100111
06-04-09
The Interesting In Between
06-04-09
The Barn
Mutation/Adaptation Network
Big Area Real Novelty
InteractionDiversity
06-04-09
Tuning Complexity
06-04-09
06-04-09
Rates of Adaptation/Learning
0: - rule aggregation
11: - rational expectations
06-04-09
Interdependencies
0: - decision theory
11: - mangle
06-04-09
Network/Connectedness
Mathematically tractable models: N = 2
-game theory N = Infinity
-averaging- random mixing
06-04-09
Rock, Paper, Scissors
Rock: All D Toxic E ColiPaper: TFT Resistant E ColiScissors: All C Sensitive E Coli
06-04-09
Rock, Paper, Scissors
Rock: All D Toxic E ColiPaper: TFT Resistant E ColiScissors: All C Sensitive E Coli
Simulations: we get “ stone soup” but diversity on a lattice or a line
06-04-09
Rock, Paper, Scissors
Rock: All D Toxic E ColiPaper: TFT Resistant E ColiScissors: All C Sensitive E Coli
Real Experiments: we get one type E Coli ina flask but diversity on a slide
Kerr, Riley, Feldman, Bohannan (Nature 2002)
06-04-09
alone lattice network soup
complexity
06-04-09
Diversity
0: - representative agent model
11: - statistical averaging
06-04-09
A complex adaptive system requiresthe right amount of “interplay” between our agents.
06-04-09
The Small Barn
Mutation Network
Equilibrium
Interaction Diversity
06-04-09
The Big Barn
Mutation Network
Lack of Structure: Limiting Distributions
Interaction Diversity
06-04-09
The Interesting in Between
Mutation Network
Complex
InteractionDiversity
06-04-09
Why Complexity?
06-04-09
Emergent Complexity
A lurking theory of homeocomplexus: learning rates, interaction effects, networks, and diversity adjust to maintain complexity.
06-04-09
Enlarging the Barn
If the barn is small, the system is often both stable predictable. These two properties create an opportunity for faster adaptation – this can mean a new action (diversity), a new connection, or a new interdependency.
06-04-09
Shrinking the Barn
If the barn is big, the system tends to be either a mangle or random. Either state creates an incentive for simple strategies, fewer connections, less diversity, and reducing interdependencies.
06-04-09
Dali’s Barn
Mutation Network
Big Area Real Novelty
Interaction
Diversity
06-04-09
Conclusions
06-04-09
Big Successes
Crowds and PanicsSpatial SegregationResidential LocationTransportation NetworksInternet StructureScaling Laws
06-04-09
We Have No Choice
Global WarmingGlobal Financial MarketsDisease TransmissionTransportationInternet Terrorism NetworksCrime
06-04-09
Normal Science
Step 1: Construct a ModelStep 2: Produce HypothesesStep 3: Test the Hypotheses
06-04-09
All New
Non Analytic
Ensembles of Models
Interactions of disciplines in same model
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