Grant Holland, Apr 25, 2014
Slide: Some Ideas and Viewpoints I Want to Highlight
A New Dynamical Systems Theory
It is reasonable to contrive a new dynamical systems theory whose idea of state is system organization, and trajectory is change of system organization.
And such a theory has important applications.
It is possible to account for chance variation in the dynamics of this theory without its time evolution becoming wildly unstable. This can be done through the introduction of stochastic processes and information theory.
Some highly complex applications require an accounting for chance variation.
This theory intends to be complementary to existing theories.
We shall see that the nature of the complex applications I am trying to model have pulled me somewhat outside of mainstream treatments of established mathematical forms.
For example, only very large, but finite, systems of elements (e.g. > 109) are targeted by this theory, e.g. the biomolecular.
I want to show in this theory that the dynamics of certain highly complex adaptive systems can be sufficiently articulated using probability theory and its sub-disciplines – alone.
Such exemplar systems include the evolution of life – which is the principle inspiring application of this theory.