1. Endogenous vs. Exogenous Causality 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. http://www.rpi.edu/dept/materials/MEG/Java _Modules_files/RandomWalk/RandomWalkAp plet.html http://www.rpi.edu/dept/materials/MEG/Java _Modules_files/RandomWalk/RandomWalkAp plet.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

16. 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.ht ml http://physics.syr.edu/courses/ijmp_c/Ising.ht ml

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/0412/0 412026v1.pdf http://arxiv.org/PS_cache/physics/pdf/0412/0 412026v1.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/0412/0 412026v1.pdf http://arxiv.org/PS_cache/physics/pdf/0412/0 412026v1.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

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