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Endogenous vs. Exogenous Causality. Dr. Green. Extreme Events. Mass Biological Extinctions occurred 65 million years ago when 75% of the species went extinct Exogenous—meteor or volcano Endogenous—cascade of collapse from interdependencies. Extreme Events. Immune Deficiencies

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extreme events
Extreme Events
  • Mass Biological Extinctions occurred 65 million years ago when 75% of the species went extinct
    • Exogenous—meteor or volcano
    • Endogenous—cascade of collapse from interdependencies
extreme events1
Extreme Events
  • Immune Deficiencies
    • Exogenous—virus
    • Endogenous—regulatory failure
  • Discoveries
    • Exogenous—unpredicted and discontinuous
    • Endogenous—result of previous build up of knowledge
thing ontology
Thing Ontology
  • Things are lumpy
  • To be cut off from other things it has to have an identity constituted by some internal traits
normal distribution
Normal Distribution
  • Values cluster around a central or “typical” value
  • This assumes that many small, independent effects are additively contributing to each observation.
normal distribution1
Normal Distribution
  • A sequence is independent and identically distributed if
    • each has the same probability distribution as the others
    • all are mutually independent.
  • Serious of random shocks
  • Each random shock
    • Abrupt peak
    • Power law relaxation as a fast rate
random walk
Random Walk
  • an individual walking on a straight line who at each point of time either takes one step to the right with probability p or one step to the left with probability 1 − p.
  • The individual is subject to a series of random, external shocks
random walk2
Random Walk
  • http://www.rpi.edu/dept/materials/MEG/Java_Modules_files/RandomWalk/RandomWalkApplet.html
process ontology
Process Ontology
  • Processes can vary from minutely small to tremendously large
  • There need be no typical size
endogenous causality and an interconnected world
Endogenous Causality and an Interconnected World
  • Many aspects of reality do not follow a normal distribution, i.e., there is no central hump
  • There is no typical
    • Earthquake size
    • Forest fire size
    • Avalanche size in a sand pile
power law2
Power Law
  • Fingers of instability of all possible lengths
  • Even the greatest event have no exceptional cause
    • The same causes can cause small or larger avalanches
  • Size of the avalanche has to do not with the original cause but with the unstable organization of the critical state
power law3
Power Law
  • Structure due to fact that constituents are not independent, as in the normal distribution, but interconnected
  • No built-in bias toward a typical value
  • Melt copper so that it becomes a liquid
    • A steady state of randomly moving particles
    • No history because one moment is like another
  • Place the melted copper in a bath of ice water
    • It is now far-from equilibrium
    • History develops in the movement toward solidity
        • Directionality – moving toward solidity
        • Irreversibility –the solid does not spontaneously melt
    • Complexity develops
      • Snow flake like appearance
      • Uniqueness of each structure, no one typical form
    • Internal structure develops
      • Scale-invariance or self-similarity
  • Interaction among components dominates the system
    • Self-reinforcing processes
    • Pattern building
ising model
Ising Model
  • http://physics.syr.edu/courses/ijmp_c/Ising.html
  • Average number of others that an individual influences (n)
    • n<1 , then avalanche dies off quickly
    • n=1 , then critical point and avalanche cascades through the system
    • n> 1, then super-critical state and the possibility of growing exponentially is highly probable
  • http://arxiv.org/PS_cache/physics/pdf/0412/0412026v1.pdf
    • P. 6
  • Slow Acceleration with power law growth due to growing interdependencies on larger and larger scales
  • Power law relaxation due to cascades
  • http://arxiv.org/PS_cache/physics/pdf/0412/0412026v1.pdf
    • P. 6
  • Outliers (extreme events) occur more often than predicted by chance
    • Extreme earthquakes
    • Extreme extinctions
    • Stock market crashes
log periodic power law
Log-Periodic Power Law
  • Discrete scale invariance
    • looks the same if multiplied by a fixed number. (Benoit Mandelbrot, Fractals)
  • Positive feedback creates an accelerating cycle
  • Super-exponential growth occurs
  • At critical time, a singularity is reached.
linear limitations
Linear Limitations
  • Linear models appear to work when viewed (and experienced) for a brief period of time, particularly in the early stages of an exponential trend when not much is happening.
  • At the bend in the curve, exponential growth explodes, and the linear models break down.