Deep Simplicity - Chapter 5

Earthquakes, Extinctions, and Emergence

• Complex system are made up of simple components
• The way component interact is very important (creates complexity)

• Earthquakes - Richter scale is logarithmic; each unit = factor of 30
• Follows power-law in frequency-size
• 10:1 ratio of size-1 to size-2 earthquakes (so on)
• Power-law is present in fractals (coast of Normandy)
• Scale-free: no difference b/w small & large earthquake except for size
• Property of fractals
• Causes are the same, only difference is magnitude & frequency
• Ubiquity: Why Catastrophes Happen

• Throwing rock or frozen potatoes at a wall - scalefree
• Power-law relationship b/w frequency of large and small fragments
• Landscape of Moon - created by impacts, which imply meteor impacts are scale-free
• 1/f Law - size of an even is proportional to 1/(power of frequency f)
• Soundwaves
• White noise (completely random) - useless
• 1/f - provides information
• Mononote (completely uniform) - useless (ie one single musical note in perpetuity)
• "Hundred Year Droughts" - can be followed by another "drought", or a "freeze" next year
• Memory-less

•  Traffic Jams - frequency and size follow power-law
• There are jams within jams (fractals)
• Large jams can be caused by large triggers (crashes) or small triggers (braking)
• As density of cars increase, lowering the speed limit will decrease traffic
• Function of time it takes to slow down (less) & speed up (more)

• Commodity & stock prices follow 1/f & power-law (p.160-161)
• Relatively unpredictable - small changes in interest rates can have no or much effect

• Extinctions - KT event refers to extinction of dinosaurs (end of Cretaceous)
• Big Five - global extinction events in past 600M years
• Are mass extinctions 'special' or just large versions of small extinctions (scalefree)
• Jack Sepkoski & David Raup - proved that extinctions occur with 1/f noise
• Life is a complex system, self-organizing, with energy source, at edge of chaos

•  Per Bak - Sandpile Model
• On a tabletop, slowly add grains of sand one at a time (source)
• Pile slowly forms
• Avalanche(s) eventually appear (edge of chaos)
• Sand falls off (sink) - 'equilibrium'
• Amount of sand stay relatively constant - self-organized criticality
• Each grain can trigger an avalanche or do nothing
• Earthquakes: crusts slide against each other, strain builds (like sand), rocks deform, energy may be stored or released, marginally or heavily
• How Nature Works: The Science of Self-Organized Criticality
• Sandpile model can be simulated on chess board
• Randomly stack/drop blocks on squares
• Once a stack reach 4-high, dispense 1 block to each neighbor
• Some will eventually begin to fall off the board
• Creates system at precipice of chaos, with energy source and sink (self-organized)
• Sand/rice obeys power-law (frequency and size) in avalanches
• It also displays fractal patterns
• Use red to denote 'energetic' grains (more chaotic)
• Initial stages show little red
• As red grows, density also grows
• Density determines likelihood of large avalanche
• Even after large avalanche, not all energy is removed
• System remains at edge of chaos

• Stuart Kauffman (Santa Fe Institute) - button analogy
• Initially unconnected (uncomplex)
• Use string to randomly connect one button to another randomly (button = node)
• Each cluster of connected buttons is a network
• Size of largest cluster network determines complexity of the system
• Growth of largest cluster is slow at first
• At approximately (# of buttons)/2, cluster grows exponentially (super cluster)
• Phase transition

• Grain/sand connection (thread) - gravity, friction, angles
• Asteroid connection - Sun, planets, moons, other asteroids
• Kauffman - developed theory on origin of life describing chemicals engaged in autocatalytic reactions
• Form network
• With sufficient connections, life emerges
• Phase transition
• Either/or (no ambiguity)
• Kauffman - DNA cell theory
• 30K to 100K genes in humans - 256 different kinds of specialized cells
• Despite every cell having the same DNA
• With 2 connections per node (DNA)
• Sqrt(nodes) as number of cycles
• Sqrt(nodes) as number of steps
• 1 connection freezes
• >2 connections lead to chaos (butterfly effect)