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## The Interesting In Between: Why Complexity Exists

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**The Interesting In Between: Why Complexity Exists**Scott E Page University of Michigan Santa Fe Institute scottepage@gmail.com**Outline**Attributes Properties The Interesting In Between Why Complexity Conclusions**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 ≠ 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**Conway’s Game of Life**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 2 3 1 4 X 5 8 6 7**Examples**X**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 N X**Rule 90**N X N X 2 8 16 64 Sum = 90**Rule 90**N X N X 2 8 16 64 Sum = 90**Emergent Computation**Source: U of Indiana**Epi-Phenomena**Emergence Structures and Levels Emergent Functionalities Innovation http://media-2.web.britannica.com/eb-media/54/4054-004-F5EB3891.jpg**Epi-Phenomena**Emergence Structures and Levels Emergent Functionalities Innovation Large Events**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**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: R0R00R00000000**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’’