Endogenous vs. Exogenous Causality

1. Endogenous vs. ExogenousCausality Dr. Green

2. 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

3. Extreme Events • Immune Deficiencies • Exogenous—virus • Endogenous—regulatory failure • Discoveries • Exogenous—unpredicted and discontinuous • Endogenous—result of previous build up of knowledge

4. Thing Ontology • Things are lumpy • To be cut off from other things it has to have an identity constituted by some internal traits

5. Normal Distributrion

6. Normal Distribution • Values cluster around a central or “typical” value • This assumes that many small, independent effects are additively contributing to each observation.

7. Normal Distribution • A sequence is independent and identically distributed if • each has the same probability distribution as the others • all are mutually independent.

8. Exogenous • Serious of random shocks • Each random shock • Abrupt peak • Power law relaxation as a fast rate

9. 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

10. Random Walk

11. Random Walk • http://www.rpi.edu/dept/materials/MEG/Java_Modules_files/RandomWalk/RandomWalkApplet.html

12. Process Ontology • Processes can vary from minutely small to tremendously large • There need be no typical size

13. 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

14. Power Law

15. Power Law

16. 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

17. 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

18. Copper • Melt copper so that it becomes a liquid • A steady state of randomly moving particles • No history because one moment is like another

19. 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

20. History • Interaction among components dominates the system • Self-reinforcing processes • Pattern building

21. Ising Model • http://physics.syr.edu/courses/ijmp_c/Ising.html

22. 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

23. Supercritical

24. Singularity

25. Exogenous • http://arxiv.org/PS_cache/physics/pdf/0412/0412026v1.pdf • P. 6

26. 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

27. Endogenous • Outliers (extreme events) occur more often than predicted by chance • Extreme earthquakes • Extreme extinctions • Stock market crashes

28. 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.

29. Discrete-Scale Invariance

30. Log-Periodic Power Law

31. Log-Periodic Power Law

32. Log-Periodic Power Law

33. Log-Periodic Power Law

34. 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.

35. Linear Limitations