Complexity and Hierarchy

Concept of Complexity

• “whole is more than the sum of its parts”– Holism

• new properties not found in subsystems• “mechanistic explanations of emergence rejected”

• Weaker view of emergence– Parts in complex system have mutual

relations not existing for isolated parts• Consider terms with i in circuits

– Allows for scientific exploration of emergence

• Gödel, Escher, Bach– Aunt Hilda

Studying Complexity

• Interactions between components often slower than interactions within components– Approximations of internal behavior can often be

described independent of interactions among subsystems.

– Approximations of interactions among subsystems can often be described independent of internal behavior of subsystems.

Catastrophe Theory

• Classification of nonlinear systems according to their behavior– Stable states include static equilibria and periodic

cycles– Small perturbation can send to another stable

state or unstable state• Example: budworm population• Not applicable to many contexts so not

discussed much today

Chaos Theory and Chaotic Systems

• Deterministic dynamic systems whose paths change radically based on minor changes in input– Their detailed behavior is unpredictable due to the influence

of small changes/error• Most engineers learn – Linear differential equations– Design of systems where

these are good models• Chaos theory can be used

to predict when behavior switches from orderly to chaotic

Complexity and Design

• Chaos should not be assumed to be present or lacking

• Details may not be predictable but manageable as aggregate phenomena– Example of designing for

turbulence • Feedback mechanisms can

be used to restrict movement to within noise levels

Complexity and Evolution

• Genetic Algorithms– Features/combinations providing fitness multiply more

rapidly– Build system to model evolution with specified

mutation rate and crossover• Self-replicating systems– Need proper representation (feature selection and

abstraction)– Can be used for education/simulation (Core wars)– Example of computer viruses

Back to Hierarchic Systems

• Many types of hierarchic systems besides organizations– Biological: nucleus, cell, tissue, organ, organism– Physical: subatomic particals, atoms, molecules, …

suns, solar systems, galaxys– Social: families, villages, states, countries– Symbolic: letters, words, sentences, paragraphs

Evolution of Complex Systems• Parable of watchmakers– The existence of stable intermediate

subsystems– Intelligence is not (necessarily) hierarchy

by assembly from components but hierarchic structure through specialization

• Problem solving as natural selection– Trial and error where partial result plays

role of a stable subassembly– Evaluation of trials plays role of selectivity– Past successful paths used as starting points

• Complex systems will evolve much more rapidly if there are stable intermediate forms

Nearly-Decomposable Systems• Interactions between subsystems are weak but not

negligible– Short run behavior is independent of other components– Long run behavior depends

on aggregate behavior of other components

• Example of heating a building with rooms and cubicles

• Representation – sparse matrix with large numbers in submatrices along diagonal

Comprehension of Systems

• Nearly-decomposable systems are easier to discover/comprehend

• Non-decomposable systems may escape our detection/ observation

Description of Complexity

• State description vs. process description– Theory that “ontogeny recapitulates phylogeny”• States of embryo mimic

evolutionary transitions because genetic code is a process model

• Largely discredited biological hypothesis

• Recapitulation still considered plausible in other fields

• Perceived complexity is influenced by representation

Conclusions

• Perceived complexity does not imply internal complexity

• Many complex systems can be described as nearly-decomposable systems

• Selection of representation of problems/systems is crucial

• Design of complex systemsrelies on similar properties

• Need to teach all of these skills