When I started looking for solutions to systems in which variables have multiple relations, I found that there had been several thinkers who looked at these types of problems using diverse mathematical perspectives. Most of these perspectives were based on statistics and stochastic analysis. Some tried to fit complex models to differential equations. Others, looked at fractals. All the approaches were interesting, but none seemed right.
For a while, I was one of the first members of the Society for Chaos Theory in Psychology and Life Sciences, but soon I felt disappointed at the approach taken by the mainstream academicians and theorists in the field. First, I felt that most of the literature in dynamic systems was focused on creating mathematical terms that were useless outside of mathematics. For instance, attractors are pieces of space that when an object enters, a substantial force is needed to make the object leave. Bifurcations are defined as patterns of instability. Fractals are just seen as geometrical forms. Second, the dynamic systems theorists have attempted to use statistics and stochastic analysis as a tool for analysis of dynamic systems. However, statistics are not really tools to determine causality, or even sequentiality. Statistics tell us if different samples share the same variance, giving a high probability that they belong to the same sample or population.
Dynamic systems describe complex processes. Therefore, the mathematical elements I use as tools for dynamic system analysis are: systems, sets, functions, loops, groups of loops, and fractals. Since I believe dynamic systems is the form of mathematics best describes thinking processes, I have created my own concepts that relate directly to human development and to the thinking process. I define frameworks, functions, and operators as they apply to human development, developmental psychology, organic systems, and the way mental processes are structured.