by M. Mitchell
If you like the notes, go ahead and buy the book!
How to define and measure complexity in the world?
- 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.
- Thermodynamics laws - (1) energy is conserved and (2) entropy always increases on it's own
- Boltzman - statistical mechanics (properties emerges on higher levels: heat)
- ...
- 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)