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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 - PowerPoint PPT Presentation
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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