complex systems

1. complex systems • complexity • chaos • the butterfly effect • emergence • determinism vs. non-determinism & observational non-determinism

2. Complex Systems… • …investigates interactions & relationships between components and how these give rise to aggregated system behaviours which may appear more than the sum of individual behaviours • …some people suggest that this is a (new?) approach making it possible to understand systems that have not previously been possible to describe

3. Chaos theory • …concerned with behaviour of systems that are highly sensitive to changes in their initial conditions. • ie: where (apparently minor) differences in initial conditions give rise to large differences in later structures (so longer-term system state is unpredictable). • NB: Butterfly Effect (Edward Lorenz).

4. Emergence Emergent systems exhibit... • some "radical novelty" or • produce "interesting" macroscopic behaviours …which are not predictably defined by the behaviours of their parts.

5. determinism • determinism • non-determinism • observational non-determinism (dice, code-books, random numbers)

6. questions • can simple systems give rise to complexity & emergent properties? • can non-deterministic systems give rise to complexity & emergent properties? • are minds an emergent property of high levels of cognition in a 'complex' social structure? complexity models... simple birth rates wolf-sheep predation disease spread emergence models... flocking? vants genetic drift chaos models... SCL diffusion graphics SCL life

7. system/model states • behaviours... • converging • choatic • tipping points -micro/macro • annealing • states... • equilibrium • cyclic • random / chaotic • complex / emergent • see also... • Schelling racial segregation [ NL > Social Science > segregation ] • Granovetter (joining a riot: thresholds, integration & aggregation) • Standing Ovations

8. Schelling • segregation model [SCL: segregation2.nlogo] • note... • low desired similarity leads to high segregation • non-convergence above 75% (without annealing) • annealing from 75%-80% • non-convergence above 80%

9. Granovetter • "joining a riot" • thresholds, integration & aggregation • eg: fashion thresholds (5 people) • 0 1 2 3 3 • 1 1 2 1 2 • ...etc

10. Standing Ovations • what do we model? • Quality of performance • Threshold of reaction (each individual) • Error / Discrimination of quality (each individual) • so if ( Q-E > T ) then react [Granovetter] • what else?

11. Standing Ovations • what else? • groups • celebraties • (influencial) leaders • vision cones

12. cellular automata • simple atoms/cells • cells have finite set of states • change in parallel at discrete time steps • according to update fns / transition rules • using only local interactions example: Netlogo “CA 1D Elementary” • “perfect knowledge of individual decision rules does not always allow us to predict macroscopic structure. We get macro-surprises despite complete micro-knowledge” (Epstein 1999)

13. Wolfram classification 110 111 108 106 102 126 78 46 228 000 0 1 0 0 0 0 0 0 0 1 001 1 1 0 1 1 1 1 1 1 2 010 1 1 1 0 1 1 1 1 1 4 011 1 1 1 1 0 1 1 1 1 8 100 0 0 0 0 0 1 0 0 0 16 101 1 1 1 1 1 1 0 1 1 32 110 1 1 1 1 1 1 1 0 1 64 111 0 0 0 0 0 0 0 0 1 128 Class 4 2 2 3 3 3 1 2 1 1- ends with homogeneous state in all cells 2- stable state / simple periodic pattern 3- chaotic (?) non-periodic 4- complex patterns / structure (emergence?) do “systems at the edge of chaos have the capacity for emergent computation”?

14. Life, John Conway • 2D grid of square cells • states Σ = {1, 0}, |Σ| = 2 • a cell's neighbourhood is its eight neighbouring cells transition rules... • birth:if dead, become alive if exactly three neighbours are alive • survival:if alive, stay alive if exactly 2 or 3 neighbours are alive • death:if alive, die if <2 or >3 neighbours are alive

15. CAs some theory • can be multi-dimensional • abstract mathematical entities • computational systems • can emulate Turing m/c – so can compute anything Turing m/c's can also may be used to... • simulate/study complexity • models of physics & biology[http://plato.stanford.edu/entries/cellular-automata]

16. CAs review so far... • CAs mostly 2 state (but can be more) • some models used NL agents in different states but... • can formally represent computations as systems which switch between states

17. state machines • can formally represent computations as systems which switch between states • standard FSMs are weaker than Turing m/c's • but can be augmented

18. state machines NL state machines... • states • guards • transition-rules • state functions

19. state machines NL state machines... • states • guards • transition-rules • state functions

20. agency • reactive • situated (& environmental?) • deliberative • intentional • communicative • agents & state machines?

21. references • complexity • A set of slides from Awareness (a group looking at self-awareness in autonomic systems) http://www.aware-project.eu/documents/04-ComplexSystems.pdf • cellular automata • Berto, Francesco and Tagliabue, Jacopo, "Cellular Automata", The Stanford Encyclopedia of Philosophy (Summer 2012 Edition), Edward N. Zalta (ed.)... • http://plato.stanford.edu/entries/cellular-automata/ • A chapter from "The Nature of Code" by Daniel Shiffman (an online text that has some good sections) http://natureofcode.com/book/chapter-7-cellular-automata/ • also... • http://mathworld.wolfram.com/ElementaryCellularAutomaton.html