Illustration of a Julia Set by Scott Hotton. Dynamical Systems Theory (a branch of mathematics used to describe the behavior of complex systems by employing differential and difference equations) is another limited framework for modeling complex systems. More accurate than linear and non-linear models, but none-the-less reductionist. (Well, talk about restating the obvious when it comes to anything mathematical, as the concept itself is a reduced language for expressing natural phenomena — I don’t subscribe to the early Greek concept where mathematics does not represent but is a universal and perfect thing unto itself). While human-generated system solutions (say, engineering problems such as placing satellites into orbit) are solved through classic computational modeling with linear systems, natural systems like the brain need something more.
Chaotic systems are especially sensitive to initial conditions. initial conditions are necessary for any reductive system analysis because in the abstraction process of reduction, the system is extracted and disconnected from the continuum of life. Good for mathematical (computational) modeling. But when defining a real-world problem, how feasible is it to define initial conditions at all? Is there a way to not define initial conditions?