Complexity. A guided tour

by M. Mitchell

If you like the notes, go ahead and buy the book!

Main idea

How to define and measure complexity in the world?

Dynamics, chaos and predictions

• Aristotele - one of the first motion theories: movement on earth and in the sky differs + objects naturally are in resting state (both wrong)
• Galileo - one of pioneers of empirical science, he promoted Copernicus theory, applied rules to all objects
• Kepler - he detected and described elliptical movements of planets
• Newton - motion laws apply to all objects (classical mechanics)
• Laplace - he thought that we could predict using Newton’s laws
• Heisenberg - “uncertainty principle” for quantum mechanics
• Poincare - dynamic systems theory - 3 body problem, dependence on initial conditions
• Feigenbaum - logistics maps and period doubling route to chaos (bifurcation)

Random behavior can emerge from deterministic systems.

Information

• Thermodynamics laws - (1) energy is conserved and (2) entropy always increases on it’s own
• Boltzman - statistical mechanics (properties emerges on higher levels: heat)
• …

Computation

• Hilbert’s problems with mathematics
  • Godel’s theorem - math is either complete or consistent
  • Turing’s machines - math is undecidable (t. machine uncomputability)

(not finished)