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