Wednesday, November 17, 2010

Documentary: Secret Life of Chaos

Interesting documentary on the chaotic systems, particularly the process of self-organization and emergence. Some really nice visuals illustrating the processes as well.


  1. CHAOS: "a system that is completely described by mathematical equations is more than capable of being unpredictable without any outside interference whatsoever."

    CHAOS: "very simple rules and equations, with nothing random in them, completely determined, we know everything about them, can have outcomes that are entirely unpredictable."

    Using or Orary with cogs as a a model, "differences in the starting positions of the cogs, differences too small to notice, can get bigger and bigger with each turn of the [cogs].

  2. Turing's work on morphogenesis used mathematical formulas usually found in astronomy or physics. Turing's equations describe how a biological system could self-orgnaize"

    "Turing discovered that by starting very simple processes governed by very simple equations, suddenly complexity emerges, the pattern suddenly came out as a natural consequence."

  3. "the prevailing idea in science up to mid-century was that if one observed irregular behaviour in a phenomenon, it was caused by some external factor. Chaos theory says that an unpredicted change in a system can be entirely internally generated by the system itself."

  4. CHOASE: "self-organization consists in a system's capacity to spontaneously generate change within itself with no external perturbation."

  5. "Turing, Belusoff, May and Lorenz discovered different facets of the same phenomenon: that there was a fundamental link between nature's power to self-organize and the chaotic consequences of the butterfly effect. . . they discovered that the natural world could be deeply, profoundly unpredictable; but the very same factors that make it unpredictable also allow it to create pattern and structure. aka order out of chaos"

    "First, though chemistry and weather systems behave in complex ways, these behaviours are governed by very simple mathematical rules. Secondly, these rules have a unique property known as "coupling" or "feedback."

  6. Simplicity and complexity. "The natural tendency is to think that complexity arises out of complexity. But the mathematics shows that simple mathematical rules generate complexity. Complexity arises out of simplicity. The same object that looks complex is also very simple. We have to rethink the relationship between simplicity and complexity."

  7. '"the same simple mathematical rules that govern a system, rules that produce chaos, also produce order, patterns and structure."

    "Pattern formation is woven very deeply into the fabric of the universe."

    Mandelbrott: self-similarity in structure and pattern; fractal geometry; the same pattern is repeated at smaller and smaller levels.

  8. "evolution is an algorithm that selects characteristics that generate the most effective adaptations. Evolution is a chaotic, self-generating system that is based on a simple rule: the organism must replicate. A few unpredicted, unforeseen mutations generate the difference that is adaptive and conducive to replication.

    Evolution also produces ever more complex, and therefore adaptive, organisms. Less complex systems, organisms spontaneously generate new patterns and structures, which add to the complexity of the organism. So evolution tends toward complexity.

    The feedback comes from the environment that favours the mutations that are best suited to it.

    "Emergence" describes how these changes and patterns arise without volition, without conscious thought, and manifest in populations.

    -Populations evolve, not individuals Individuals generate mutations, which are then replicated in future generations of populations.

    -Emergence is an evolutionary phenomenon that occurs through successive cycles of feedback and regeneration. It doesn't happen in one cycle alone, and certainly not in the first cycle.