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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 nearlydecomposable systems
• Selection of representation of problems/systems is
crucial
• Design of complex systems
relies on similar properties
• Need to teach all of these skills