The Periodic Nature of Emergent Systems

More tasks for StillFlame:

Prove that some of the following can be derived from metamathematics:

• There are degrees of emergence
  • which may or may not correspond to the periods? of The Pattern
• Within each level of emergence defined by the above there are:
  • less significant increments of emergence which do not represent qualitatively different kinds of emergence but more the degree to which a particular kind of emergence is realized
  • similarities between how each level behaves when it is first achieved
  • similarities between how each level behaves just before another level is achieved
  • ways to categorize these similarities into groups which are repeated at each level
    • which may or may not correspond to the groups? of The Pattern
• a tendency for more complete levels of emergence to become more complex than less complete levels

Or

Prove the same from the necessity of non-linear systems as put forward by Gottman et al. in <i>The Mathematics of Marriage</i>, where they argue that since linear systems can never have a stable set point non-linear systems will come to predominate. Steven Strogatz in <i>Nonlinear Dynamics and Chaos</i> may be another useful source. I'm not sure I see much value in the approach taken in his <i>Sync: The Emerging Science of Order</i>, however. Let's not leave out <i>Mathematical Biology</i> by J.D. Murray (also known as "et al" above).

See also Math and The Goedel Connection.

— Scotus - 26 May 2002