Deterministic non-linear Systems and Complexity

• Order rules complexity - Newton and Descartes work out the basics, Laplace reigns supreme, and, when considering the nitty-gritty, few things work the way they are supposed to.
  • linear differential equations - Newton's laws of motion and of celestial mechanics
  • Laplace's Universal formula and Reductionist thinking:
  • the search for the Perpetuum mobile - the crushing forces of entropy
  • Randomness vs. disorder: Boltzmann (thermodynamics) and Darwin (evolution) save the day
  • Classical mechanics and electrodynamics power the industrial revolution
• Disorder rears its ugly head
  • Ultraviolet Catastrophe and the Hydrogen Disaster - how does it feel to be off by 40 orders of magnitude? Boltzmann looses his head ...
  • Rutherford and Bohr: Non-linear dynamics and Quantum mechanics
  • Linear approximations to non-linear problems
  • Schroedinger's Cat speaks of waves - and he comes up with an equation to describe them
  • Born's Probability Function makes Einstein very unhappy " I can't believe that god plays dice"
• Chaos breaks through
  • Newton's three body problem cannot be solved - it can only be approximated
  • Poincaré bites Newton: closed systems are not immune to disaster
  • Poincaré considers the gravitational pull of a grasshopper in Australia and shows that, with bad luck, solar systems come unstuck
  • Feedback, iterative magic and the significance of initial states: Spinal Tap and the art of baking bread
• Phase diagrams and Attractors
  • single point
  • limit cycle
  • torus
  • strange attractor
• Randomness, Chaos, Entropy: Confusing a Lack of Predictability with Randomness - the Source Fallacy

Further Reading:

Hayes, B. (2001) Randomness as a resource. American Scientist 89: 300-304.