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

• 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?

emergence models...flocking?vantsgenetic drift

chaos models...SCL diffusion graphicsSCL life

complexity models...simple birth rateswolf-sheep predationdisease spread

system/model states

states...

• equilibrium

• cyclic

• random / chaotic

• complex / emergent

behaviours...

• converging

• choatic

• tipping points -micro/macro

• annealing

see also...

• Schelling racial segregation [ NL > Social Science > segregation ]

• Granovetter (joining a riot: thresholds, integration & aggregation)

• Standing Ovations

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%

Granovetter

"joining a riot"

thresholds, integration & aggregation

eg: fashion thresholds (5 people)

• 0 1 2 3 3

• 1 1 2 1 2

...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 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)

Wolfram classification

110 111 108 106 102 126 78 46 228

000 0 1 0 0 0 0 0 0 0 1001 1 1 0 1 1 1 1 1 1 2010 1 1 1 0 1 1 1 1 1 4011 1 1 1 1 0 1 1 1 1 8100 0 0 0 0 0 1 0 0 0 16101 1 1 1 1 1 1 0 1 1 32110 1 1 1 1 1 1 1 0 1 64111 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 cells2- stable state / simple periodic pattern3- chaotic (?) non-periodic4- complex patterns / structure (emergence?)

do “systems at the edge of chaos have the capacity for emergent computation”?

Life, John Conway

2D grid of square cellsstates Σ = {1, 0}, |Σ| = 2a 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

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state machinesNL state machines...statesguardstransition-rulesstate functions

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statefunction

exit function

entry function

condition

state definition

transition details

statefunction

entry function

onestate

definition

multipletransition

rulesexit function exit function

condition condition

state machinesNL state machines...statesguardstransition-rulesstate functions

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statefunction

exit function

entry function

condition

state definition

transition details

statefunction

entry function

onestate

definition

multipletransition

rulesexit function exit function

condition condition

agency

reactive situated (& environmental?) deliberative intentional communicative

agents & state machines?

referencescomplexity

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