csc2720h:% systems%thinking%for%% global%problems%sme/systemsthinking/2016/slides/07...complex...
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© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license.
Prof Steve Easterbrook Dept of Computer Science
h8p://www.cs.toronto.edu/~sme/SystemsThinking
CSC2720H: Systems Thinking for Global Problems
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 2
Week 7
Week 7 ➜ Chaos Theory
Ä Game: The Chaos Game Ä Case Study: Chaos in Weather Forecasting
➜ Complexity Science
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 3
Calculating the weather…
Zonal (East-West) Wind:
Meridional (North-South) Wind:
Temperature:
Precipitable Water:
Air pressure:
1904: Vilhelm Bjerknes identified the “primitive equations”
These capture the flow of mass and energy in the atmosphere;
Sets out a manifesto for practical forecasting
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 4
Towards Numerical Forecasts 1910s: Lewis Fry Richardson performs the first numerical weather
forecast, imagines a giant computer to do this regularly;
First plan for massively parallel computation
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 5
First Computer Model of Weather 1950s: John Von Neumann develops a killer app for the first programmable electronic computer ENIAC: weather forecasting
Imagines uses in weather control, geo-engineering, etc.
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 6 Image Source: Lynch, P. (2008). The ENIAC Forecasts: A Recreation. Bulletin of the American Meteorological Society
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 7 Bauer, P., Thorpe, A., & Brunet, G. (2015). The quiet revolution of numerical weather prediction. Nature, 525(7567), 47–55.
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 8 Source: http://www.vets.ucar.edu/vg/T341/index.shtml
Global Precipitation in CCSM CAM3
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 9
The discovery of Chaos 1950s: Edward Lorenz discovers non-linear effects in weather
forecasting, develops Chaos Theory;
Basis for understanding what is predictable and what isn’t
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 10
Chaos Theory - Key concepts ➜ Non-linear Dynamical Systems
Ä Inputs are not proportional to outputs Ä Determinism: Can you work out future states?
➜ Sensitivity to Initial Conditions Ä The “butterfly effect” Ä E.g. The Lorenz Attractor
➜ Denseness ➜ Attractors (Simple and Strange) ➜ Criticality and Tipping Points ➜ Self-similarity and Fractals
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 11
Example of the butterfly effect
Source: https://www.youtube.com/watch?v=FYE4JKAXSfY
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 12
Forecasting Weather and Climate
Analysis
Initial condition uncertainty
Climatology
Forecast uncertainty
Deterministic forecast
Time
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 13
Deterministic Complexity Pattern of population
for x' = rx(1-x)
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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Iteration
Po
pu
latio
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 14
Bifurcation Diagram for x’ = rx(1-x)
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 15
Example: population growth
Source: Sterman, J. D. (2012). Sustaining Sustainability
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 16
Finding Equilibria
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 17
Eckmann Recurrence Plots
White Noise:HarmonicOscillation
Chaotic dataw. linear trend
Auto-regressiveprocess
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 18
Example: The ice ages
➜ Milankovitch cycles: Ä 26,000yr cycle in the earth’s precession (axis rotation) Ä 41,000yr cycle in the earth’s obliquity (axis tilt) Ä 100,000yr cycle in the earth’s orbital inclination & eccentricity
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 19
Aggregate Complexity ➜ Learning and Memory
Ä …through persistence of internal structure Ä A system “learns” by reconfiguring internal structure
➜ Emergence
➜ Change & Evolution Ä Self-organization Ä Dissipation (push towards a disorganized state) Ä Self-organized criticality (re-structuring on the edge of chaos)
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 20
Complex Systems ➜ Complex Adaptive Systems (e.g. Levin)
Ä Sustained diversity & individuality of components Ä Localized interactions among those components Ä Autonomous process that selects subsets for replication or
enhancement
➜ Adaptive Non-Linear Networks (e.g. Brian Arthur) Ä Dispersed Interaction Ä No Global Controller (no privileged agent) Ä Cross-Cutting Hierarchical Organization (much tangling across levels) Ä Continual Adaptation (the system learns and adapts) Ä Perpetual Novelty (new niches created & filled) Ä Out-of-equilibrium dynamics (system can never reach an optimum)
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University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 21
Study via Simple models?
The Abelian Sandpile ModelConway’s Game of Lifehttp://www.bitstorm.org/gameoflife/ https://www.youtube.com/watch?v=-d7_OGn22d4
University of Toronto Department of Computer Science
© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 22
Self-Organized Criticality
Simple model of how avalanches work:Bak, Tang, and Wiesenfeld’s Sandpile model
https://www.youtube.com/watch?v=h737qbQRPME&feature=youtu.be&t=4m