Helge von Koch
So, how does nature do it?

Hold that thought (8a)

Self-similarity is the repetition of a shape, form or behavior on different levels of complexity. Not as an identical copy, but as a variation of the same basic shape.

And how do mathematicians do it?
A mathematical fractal fails to take quantum fuzziness into consideration. That's why it confuses as much as it explains.
Randomness
Math can't produce randomness, and therefore freedom and therefore a true representation of reality.

Hold that thought (8b):

Since reality is fuzzy, accuracy is approximation.

Summary of chapter 8.

  • Self-similarity is a structure repeated on a different level of complexity or at a different scale.
  • Numbers can not fully represent reality because (1) they are too accurate, and (2) they can't mimic the randomness that comes from the freedom which is the most fundamental principle of nature.