The Yin and Yang of Chaos and Order

James Stanard
February 15, 2000.

Abstract. For centuries, scientists have recognized that from relatively simple systems, chaos emerged. Systems could only be tracked for a short time before accumulated error blew up to enormous proportions. It seemed that at last Nature had finally won with its impossible indeterminism. Now, Science is showing that a balance exists between Chaos and Order at which highly interesting patterns emerge. In fact, it seems that systems gravitate toweard this balance, thus creating emergent behavior in many systems ranging from Ecology to Economy. This is about these very Systems.

References

Gleick, James, Chaos: Making a New Science
Kauffman, Stuart, At Home in the Universe
Stuart, Ian et. all, The Collapse of Chaos: Discovering Simplicity in a Complex World
Waldrop, M. Mitchell, Complexity: The Emerging Science at the Edge of Order and Chaos

Lecture Notes

Chaos
- The quality of nonlinear dynamic systems to magnify small perturbations.
- Chaos as a driving force for adaptive systems.
- Nonlinear Systems = Pseudo-random Behavior
- "The Butterfly Effect"
Edge of Chaos Effect
- Phase Transitions
- Critical Complexity (Criticality)
- The sandhill analogy-->reference later
- Autocatalytic Sets
Evolution in Systems
- Requirements
  - Mutation
  - Selection
- Pertinence to Adaptation
Sandhills
- The drive for balance.
- Power Laws
Other Systems
- Economy (money)
- Religion (ideas) -- Memes
- Ecology (energy)
Research
- Conway's Game of Life
- Artificial Life
- Genetic Programming - Evolutionary Algorithms
Endpoints
- Can machines evolve?
- Can machines think?
- Can machines be considered alive?
Undergraduate Research
Questions