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 – 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

_Modules_files/RandomWalk/RandomWalkAp plet.html _Modules_files/RandomWalk/RandomWalkAp plet.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

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 ml ml

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 v1.pdf v1.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 v1.pdf v1.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

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