06-04-09 the interesting in between: why complexity exists scott e page university of michigan santa...
TRANSCRIPT
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06-04-09
The Interesting In Between: Why Complexity Exists
Scott E Page
University of Michigan
Santa Fe Institute
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06-04-09
Background Reading
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06-04-09
Outline
Attributes
Properties
The Interesting In Between
Why Complexity
Conclusions
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06-04-09
Complex Adaptive Systems: Attributes
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06-04-09
Complex Adaptive Systems
Networks
Source: MIT
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06-04-09
Complex Adaptive Systems
NetworksAdaptation
Source: Exploring Nature
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06-04-09
Complex Adaptive Systems
NetworksAdaptationInteractions
Source: Uptodate.com
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06-04-09
Complex Adaptive Systems
NetworksAdaptationInteractionsDiversity
Source: Scientific American
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06-04-09
Complex Adaptive Systems: Properties
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06-04-09
Complex ≠ Complicated
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06-04-09
Complex ≠ Equilibrium (w/ Shocks)
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06-04-09
Complex ≠ Chaos
Source: Andrew Russell
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06-04-09
Complex ≠ Difficult
Source: Biology-direct
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06-04-09
Complex = Dancing Landscapes
Source: Chris Lucas
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06-04-09
Epi-Phenomena
Emergence Structures and Levels
Source: Boortz.com
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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)
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06-04-09
Diffusion Limited Aggregation
seed
walker
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06-04-09
Diffusion Limited Aggregation
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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
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Examples
X
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Bigger Space
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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
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06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent Functionalities
Source: Biology-direct
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06-04-09
Wolfram’s 256 Automata
N X N X
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06-04-09
Rule 90
N X N X
2
8
16
64
Sum = 90
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06-04-09
Rule 90
N X N X
2
8
16
64
Sum = 90
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06-04-09
Four Classes of Behavior
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Emergent Computation
Source: U of Indiana
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06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent FunctionalitiesInnovation
http://media-2.web.britannica.com/eb-media/54/4054-004-F5EB3891.jpg
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06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent FunctionalitiesInnovation Large Events
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A Long Tailed Distribution
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A Long Tailed Distribution
cities size words citations web hits book sales phone calls earthquakes moon craters wars net worth family names
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Large Events
Source: www2002
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06-04-09
Per Bak’s Sandpile
sand
table
floor
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06-04-09
Per Bak’s Sandpile
sand
table
floor
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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.
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06-04-09
Epi-Phenomena
Emergence Structures and LevelsEmergent FunctionalitiesInnovationLarge Events Robustness
Source: NBC
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06-04-09
“Imagine how difficult physics would be in electrons could think.”
-Murray Gell-Mann
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Robustness: The World of Thinking (or adapting)
Electrons
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The Langton Graph
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06-04-09
The Langton Graph
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A Thought Play
A Simple Model of Forest Fires & Bank Failures
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The Bank Model
Banks choose to make a risky loan each period with probability p
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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
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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
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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
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Example
Period 1: 00R00R000RR0RPeriod 2: R0R00R00RRRRR
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Example
Period 1: 00R00R000RR0RPeriod 2: R0R00R00RRRRR Period 3: R0R00R00FRRRRPeriod 4: R0R00R00FFFFFFPeriod 5: R0R00R00000000
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Key Insight Revisited
Bank managers should be smarter than trees!
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Forest Fire Model Results
Yield increases in p up to a point and then falls off rather dramatically
Physicists call this a ``phase transition’’
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Poised at the ‘edge of chaos’
rate of risky loans p*
yield
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Smarter Banks
Let each bank learn (using a standard learning rule from psychology called Hebbian learning) whether or not to make risk loans.
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Emergent Robustness
rate of risky loans p*
yield
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Emergence of Firewalls
11101101110111100111
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The Interesting In Between
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The Barn
Mutation/Adaptation Network
Big Area Real Novelty
InteractionDiversity
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Tuning Complexity
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Rates of Adaptation/Learning
0: - rule aggregation
11: - rational expectations
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Interdependencies
0: - decision theory
11: - mangle
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Network/Connectedness
Mathematically tractable models: N = 2
-game theory N = Infinity
-averaging- random mixing
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Rock, Paper, Scissors
Rock: All D Toxic E ColiPaper: TFT Resistant E ColiScissors: All C Sensitive E Coli
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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
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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)
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alone lattice network soup
complexity
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Diversity
0: - representative agent model
11: - statistical averaging
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A complex adaptive system requiresthe right amount of “interplay” between our agents.
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The Small Barn
Mutation Network
Equilibrium
Interaction Diversity
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The Big Barn
Mutation Network
Lack of Structure: Limiting Distributions
Interaction Diversity
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The Interesting in Between
Mutation Network
Complex
InteractionDiversity
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Why Complexity?
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Emergent Complexity
A lurking theory of homeocomplexus: learning rates, interaction effects, networks, and diversity adjust to maintain complexity.
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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.
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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.
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Dali’s Barn
Mutation Network
Big Area Real Novelty
Interaction
Diversity
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Conclusions
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Big Successes
Crowds and PanicsSpatial SegregationResidential LocationTransportation NetworksInternet StructureScaling Laws
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We Have No Choice
Global WarmingGlobal Financial MarketsDisease TransmissionTransportationInternet Terrorism NetworksCrime
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Normal Science
Step 1: Construct a ModelStep 2: Produce HypothesesStep 3: Test the Hypotheses
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All New
Non Analytic
Ensembles of Models
Interactions of disciplines in same model