complex systems complexity chaos the butterfly effect emergence

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

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

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).

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

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

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

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

Schelling segregation model [SCL: segregation 2. nlogo] note. . . • low desired similarity leads to high segregation • non-convergence above 75% (without annealing) • annealing from 75%-80% • non-convergence above 80%

Granovetter "joining a riot" thresholds, integration & aggregation eg: fashion thresholds (5 people) • 01233 • 11212. . . etc

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?

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

cellular automata simple atoms/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 1 D 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)

Wolfram classification 110 111 108 106 102 126 78 46 228 000 001 010 011 100 101 110 111 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 Class 4 2 2 3 3 3 1 2 1 1 2 4 8 16 32 64 128 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”?

Life, John Conway 2 D 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

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]

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

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

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

NL state machines… NL state machines. . . defstate-name entry-fn state-fn defstate "working" (task sign-in) (task work-stuff) transition from to condition exit-fn transition "working" "walking“ (task [daytime = 1600]) (task sign-out) transition "walking" "at-home" (task [clock= 30]) null-task transition "playing" "eating“ (task [trigger prob%]) null-task

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

references complexity A set of slides from Awareness (a group looking at self-awareness in autonomic systems) http: //www. aware-project. eu/documents/04 -Complex. Systems. 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/Elementary. Cellular. Automaton. html