The Interesting In Between: Why Complexity Exists Scott E Page University of Michigan Santa Fe Institute

Background Reading

Outline Attributes Properties The Interesting In Between Why Complexity Conclusions

Complex Adaptive Systems: Attributes

Complex Adaptive Systems Networks Source: MIT

Complex Adaptive Systems Networks Adaptation Source: Exploring Nature

Complex Adaptive Systems Networks Adaptation Interactions Source: Uptodate.com

Complex Adaptive Systems Networks Adaptation Interactions Diversity Source: Scientific American

Complex Adaptive Systems: Properties

Complex ≠ Complicated

Complex ≠ Equilibrium (w/ Shocks)

Complex ≠ Chaos Source: Andrew Russell

Complex ≠ Difficult Source: Biology-direct

Complex = Dancing Landscapes Source: Chris Lucas

Epi-Phenomena Emergence Structures and Levels Source: Boortz.com

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)

Diffusion Limited Aggregation seed walker

Diffusion Limited Aggregation

Conway’s Game of Life X 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

Examples X

Bigger Space

A New Kind of Science - Wolfram Binary state objects arranged in a line using simple rules can create - “perfect’’ randomness - chaos - patterns - computation

Epi-Phenomena Emergence Structures and Levels Emergent Functionalities Source: Biology-direct

Wolfram’s 256 Automata N X

Rule 90 N X Sum = 90

Rule 90 N X Sum = 90

Four Classes of Behavior

Emergent Computation Source: U of Indiana

Epi-Phenomena Emergence Structures and Levels Emergent Functionalities Innovation F5EB3891.jpg

Epi-Phenomena Emergence Structures and Levels Emergent Functionalities Innovation Large Events

A Long Tailed Distribution

A Long Tailed Distribution cities size words citations web hits book sales phone calls earthquakes moon craters wars net worth family names

Large Events Source: www2002

Per Bak’s Sandpile sand table floor

Per Bak’s Sandpile sand table floor

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.

Epi-Phenomena Emergence Structures and Levels Emergent Functionalities Innovation Large Events Robustness Source: NBC

“Imagine how difficult physics would be in electrons could think.” -Murray Gell-Mann

Robustness: The World of Thinking (or adapting) Electrons

The Langton Graph

The Langton Graph

A Thought Play A Simple Model of Forest Fires & Bank Failures

The Bank Model Banks choose to make a risky loan each period with probability p

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

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

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

Example Period 1: 00R00R000RR0R Period 2: R0R00R00RRRRR

Example Period 1: 00R00R000RR0R Period 2: R0R00R00RRRRR Period 3: R0R00R00FRRRR Period 4: R0R00R00FFFFFF Period 5: R0R00R

Key Insight Revisited Bank managers should be smarter than trees!

Forest Fire Model Results Yield increases in p up to a point and then falls off rather dramatically Physicists call this a ``phase transition’’

Poised at the ‘edge of chaos’ rate of risky loans p* yield

Smarter Banks Let each bank learn (using a standard learning rule from psychology called Hebbian learning) whether or not to make risk loans.

Emergent Robustness rate of risky loans p* yield

Emergence of Firewalls

The Interesting In Between

The Barn Mutation/Adaptation Network Big Area Real Novelty InteractionDiversity

Tuning Complexity

Rates of Adaptation/Learning 0: - rule aggregation 11: - rational expectations

Interdependencies 0: - decision theory 11: - mangle

Network/Connectedness Mathematically tractable models: N = 2 -game theory N = Infinity -averaging - random mixing

Rock, Paper, Scissors Rock: All DToxic E Coli Paper:TFTResistant E Coli Scissors:All CSensitive E Coli

Rock, Paper, Scissors Rock: All DToxic E Coli Paper:TFTResistant E Coli Scissors:All CSensitive E Coli Simulations: we get “ stone soup” but diversity on a lattice or a line

Rock, Paper, Scissors Rock: All DToxic E Coli Paper:TFTResistant E Coli Scissors:All CSensitive E Coli Real Experiments: we get one type E Coli in a flask but diversity on a slide Kerr, Riley, Feldman, Bohannan (Nature 2002)

alone lattice network soup complexity complexity

Diversity 0: - representative agent model 11: - statistical averaging

A complex adaptive system requires the right amount of “interplay” between our agents.

The Small Barn Mutation Network Equilibrium InteractionDiversity

The Big Barn Mutation Network Lack of Structure: Limiting Distributions Interaction Diversity

The Interesting in Between Mutation Network Complex InteractionDiversity

Why Complexity?

Emergent Complexity A lurking theory of homeocomplexus: learning rates, interaction effects, networks, and diversity adjust to maintain complexity.

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.

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.

Dali’s Barn Mutation Network Big Area Real Novelty Interaction Diversity

Conclusions

Big Successes Crowds and Panics Spatial Segregation Residential Location Transportation Networks Internet Structure Scaling Laws

We Have No Choice Global Warming Global Financial Markets Disease Transmission Transportation Internet Terrorism Networks Crime

Normal Science Step 1: Construct a Model Step 2: Produce Hypotheses Step 3: Test the Hypotheses

All New Non Analytic Ensembles of Models Interactions of disciplines in same model