Lecture 9

1. Lecture 9 Complex adaptive systems

2. In the beginning... • Newtonian sciences • Initial conditions, laws and predictability • If the initial conditions of the system are completely specified it will be possible to compute its further states precisely • God-created, optimal universe • Universe is optimal and infinitely precise because it was created by God • Determinism and reductionism • We can completely understand the functionality of the whole if we break it into parts and understand the functionality of its parts

3. Paradigm is shifting... • Quantum mechanics • Non-determinism • It is only possible to measure speed or location of elementary particle with precision of Plank’s constant • Our own interference, our apparatus disturb the path of the particle • Probabilistic universe • Gödel & Turing • Limitations of logic • It is not possible to construct mathematical system based on logic, such that it is both sound and complete • Unpredictability in computing • Halting problem

4. The Flow • Dynamical systems • We find ourselves among ever-changing systems • There is an intractable number of branches • Feedback • Systems change and develop by receiving feedback from the environment and responding to environment. Thus systems are inextricable parts of the environment • Self-reference • The systems around us are heavily recursive, self-bootstrapping • Co-evolution • There is no stand alone evolution, everything is co-evolving. • Everything is dependent and influences everything else.

5. Cybernetics • Norbert Wiener • Trying to understand how control & communication worked • Greek kybernetes (steersman) (Web of life pp.. 97) • We are but whirlpools in a river of ever-flowing water • Self-regulation • We are not stuff that abides, but patterns that perpetuate themselves Situation Assessment Action Impact on environment

6. Ilya Prigogine • Second law of thermodynamics • In closed system, the amount of entropy in a given system does not decrease • Entropy means disorder • Living organisms and equilibrium • Living beings are in order, away from equilibrium • Open thermodynamical systems • Nonlinear equations • Self-Organization Equilibrium (ice) Order (edge of chaos) Chaos (gas)

7. Gaia theory • James Lovelock and Lynn Margulis • Search of life on Mars • Earth is open system, away from equilibrium • Life on Earth regulates atmosphere • 25% increase of heat from sun • Gaia - the living system • Adaptation to available resources • Crucial dependents and interdependence of living and non-living systems • Symbiosis

8. Cellular automation • John von Neumann’s cellular automation • grid of cells, each cell can be in some state • discrete space and time, synchronous updates • updates are based on local interaction rule • equivalent to Turing Machine in computational power! • John Conway’s Game of Life • if ( # of neighbors < 2 or > 3 ) die • if ( # of neighbors == 2 and you are alive live ) • if ( # of neighbors == 3 new cell is born )

9. Classification of CA • Stephen Wolfram Single attractor (dies out) Periodic attractors (oscillations) Complex structures (increasing) Strange attractors (chaos)

10. Artificial Life • Chris Langton • Interpreting the classification I &II IV III Equilibrium Complexity Chaos Solid Phase Transition Fluid

11. Fractals • Bernoit Mandelbrot • geometry of ‘irregular’ natural phenomena • language to speak of clouds • Julia sets • Z -> Z^2 + C, for different Z • Why are we fascinated with fractals? • We are looking for patterns in nature • Abstractions created by human brain

12. How did it all come about? • Stuart Kauffman • Skeptics • Probability and complexity • Autocatalytic sets & closures • Self-bootstrapping properties Catalyst/Adapter A C B A BA AB B

13. Santa Fe Institute • Formed in 1985 • Think tank to deal with complexity • Scientists from all areas including physics, chemistry, biology, computer science, economics, ecology, sociology, history, etc. • http://www.santafe.edu

14. John Holland • Complex adaptive systems • BACH group in University of Michigan • Burks, Axelrod, Cohen, Hamilton • Genetic algorithms • Quotation from ‘Complexity’

15. Seven basic elements of CAS • Aggregation • Economy and markets • Body and nervous, immune, endocrine system • World economy and country economies • Emergence as a result of interactions • whole > sum of the parts • higher level of organization • meta agents

16. Seven basic elements of CAS • Tagging (mechanism) • Identification of alike agents • Grouping • Attribute • contracts between firms • form of adaptation - delegation • Divisions in a firm Equities, Fixed Income, etc. • collaboration, formation of aggregate and diversification via tagging

17. Seven basic elements of CAS • Nonlinearity (property) • aggregation & tagging • threshold of emergence (H >sum(P)) • predator/prey interaction • One of the standard example of nonlinear dynamical model is predator/prey interaction. Observe that increases in either population increase the likelihood of a contact. Let Predator(t), and Prey(t) be number of predators and prey at some time t, and let c be the constant that reflects efficiency of a predator. We can calculate the number of interactions per unit of time as c*Predator(t)*Prey(t). That is, with c = 0.5, Predator(t) = 2 and Prey(t) = 10, we would have 10 encounters. Now, let us double each population so that Predator(t) = 4 and Prey(t) = 20, then we will have 40 encounters. • nonlinearity is a result of a product instead of a sum

18. Seven basic elements of CAS • Flow (property) • nonlinearity induces flow • multiplier effect • feedback and cycles = Dead = Alive

19. Seven basic elements of CAS • Diversity (property) • arise from exploration of multitude of possibilities (local adaptations) • firms enter and leave market • mimicry

20. Seven basic elements of CAS • Internal models (mechanism) • ‘anticipation’ • survival of the fittest • subconscious mode

21. Seven basic elements of CAS • Building blocks (mechanism) • decomposition • quark, nucleon, atom, molecule, organelle, cell • generation of internal models

22. What is complexity? • Complexity is ‘digested’ information • It is order out of chaos • It is inevitable, it is intricate part of nature

23. Information theory • Definition of entropy • measure of uncertainty in the random variable • how many bits are necessary to describe an event (coin flip) • We learned to see patterns around us • Patterns represent information which can be compressed as oppose to random information • Why do math professor stare at the ceiling when they speak?

24. Modeling issues • Emergence of behavior • Global properties based on local interactions • No optimum, the only measure of fitness is survival • Free interactions • Least amount of rules

25. References • Complexity • by Mitchell Waldrop • Hidden order: How adaptation builds complexity • by John Holland • At home in the universe • by Stuart Kauffman • The web of life • by Fritjof Capra