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Lecture 9

Lecture 9. Complex adaptive systems. 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

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Lecture 9

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  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

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