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 i in circuits
Allows for scientific exploration of emergence
Gödel, Escher, Bach
Aunt Hilda

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 used to 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 turbulence
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. 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

9. 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

10. 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

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

12. 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

13. 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 systems relies on similar properties
Need to teach all of these skills