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Complexity and Hierarchy

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

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Complexity and Hierarchy

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  1. Complexity and Hierarchy

  2. 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 iin circuits • Allows for scientific exploration of emergence • Gödel, Escher, Bach

  3. 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.

  4. 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

  5. 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 usedto predict when behavior switches from orderly to chaotic

  6. 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 turbulance • Feedback mechanisms can be used to restrict movement to within noise levels

  7. 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

  8. 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

  9. Evolution of Complex Systems • Parable of watchmakers • The existence of stable intermediate subsystems • Not 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

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

  11. Description of Complexity • Comprehension of systems • Nearly-decomposable systems are easier to discover/comprehend • Non-decomposable systems may escape our detection/observation • 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

  12. 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

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