Endogenous vs. Exogenous Causality Dr. Green. Extreme Events Mass Biological Extinctions occurred 65...
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Transcript of Endogenous vs. Exogenous Causality Dr. Green. Extreme Events Mass Biological Extinctions occurred 65...
Endogenous vs. ExogenousCausality
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– Exogenous—virus– Endogenous—regulatory failure
• Discoveries– Exogenous—unpredicted and discontinuous– Endogenous—result of previous build up of
knowledge
Thing Ontology
• Things are lumpy• To be cut off from other things it has to have
an identity constituted by some internal traits
Normal Distributrion
Normal Distribution
• Values cluster around a central or “typical” value
• This assumes that many small, independent effects are additively contributing to each observation.
Normal Distribution
• A sequence is independent and identically distributed if – each has the same probability distribution as the
others – all are mutually independent.
Exogenous
• Serious of random shocks• Each random shock– Abrupt peak– Power law relaxation as a fast rate
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 Walk
Random Walk
• http://www.rpi.edu/dept/materials/MEG/Java_Modules_files/RandomWalk/RandomWalkApplet.html
Process Ontology
• Processes can vary from minutely small to tremendously large
• There need be no typical size
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 Law
Power Law
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 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
Copper
• Melt copper so that it becomes a liquid– A steady state of randomly moving particles– No history because one moment is like another
Copper
• 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
History
• Interaction among components dominates the system– Self-reinforcing processes– Pattern building
Ising Model
• http://physics.syr.edu/courses/ijmp_c/Ising.html
Networks
• 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
Supercritical
Singularity
Exogenous
• http://arxiv.org/PS_cache/physics/pdf/0412/0412026v1.pdf– P. 6
Endogenous
• 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
Endogenous
• Outliers (extreme events) occur more often than predicted by chance– Extreme earthquakes– Extreme extinctions– Stock market crashes
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.
Discrete-Scale Invariance
Log-Periodic Power Law
Log-Periodic Power Law
Log-Periodic Power Law
Log-Periodic Power Law
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.
Linear Limitations