Chapter 2: Dimensions and Attractors

II. Dimensions and Attractors

  1. Logical Typing
    1. Bertrand Russell
    2. Biological Epistemology: the meta-thinking of Gregory Bateson
  2. Distinct levels of reality
    1. subatomic: quantum-mechanical
    2. visual: clasical mechanics
    3. macroscopic: relativistic
    4. mental: edge-of-chaos dynamic (different levels are characterized by distinct qualities, described in different qualitative terms, and hence the descriptions of which are not always reducible to each others' terms.)
  3. Types of dimensional shapes:
    1. Euclid (Linearity)
    2. Gauss, Riemann, Lobyachevski (Curved linearity)
    3. Mandlebrot, Cantor, Poincare (Strong nonlinearity)
  4. Types of attractor shapes:
    1. point attractor (single point)
    2. limit cycle attractor (stable loop)
    3. chaotic or strange attractor (never-repeating, never-complete toral shape [as an example])
      1. mapped by fractals
      2. sensitive dependance on initial conditions
      3. unpredictability