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## PowerPoint Slideshow about ' Endogenous vs. Exogenous Causality' - shoshana-reynolds

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### 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 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

- 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

- 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

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.

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.

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