Metaphysically speaking, I cannot (and will not) argue with your assertions. Perhaps the transitional state between order and chaos (i.e., the point of bifurcation) necessarily constitutes a stage for heightened creativity. However, scientifically speaking, I do believe that chaos theory and fractal geometry can be effectively employed to examine the effects of unstable processes on product quality. In fact, I have done some fundamental research in this area. Some of this work has been published:
1) Harry, M. J. (2003) Resolving the Mysteries of Six Sigma: Statistical Constructs and Engineering Rationale. First Edition. Palladyne Publishing. Phoenix, Arizona. Note: this particular publication will be available by October 2003.
2) Harry, M.J. and Prins, J. (1991). The Vision of Six Sigma: Mathematical Constructs Related to Process Centering. Motorola University Press, Motorola Inc., Schaumburg Illinois.
As discussed in the last section of the 2003 book, the study of complex designs can be significantly enhanced using dynamic Monte Carlo simulation. In particular, it was concluded that the use of chaos theory and fractal geometry has the potential to shed light on the structure of engineering problems and manufacturing behavior. It is also generally believed that the suggested approach has the potential to constitute a new paradigm in engineering simulation methodology.
As demonstrated in the book, the approach consists of projecting the intersect of k sets of Cartesian coordinates (resulting from a fractal rule set) into the time domain. The resulting pattern emulates the behavior of a dynamic process mean. Interestingly, it was noted that such behavior may be described by an autoregressive model. Once the projections are made, the means are used as a basis for dynamic Monte Carlo simulation. After application of the transfer function, the resulting autocorrelated response vector is formed into a histogram for subsequent study.
The net effect of such dynamic simulation results in an expanded variance when compared to that of the classical Monte Carlo method. From this perspective, the suggested methodology provides a better basis for the a priori study of producibility during the product design cycle.
If you have published some mathematically based research in this area (not metaphysical speculation), I would certainly like to know about it. I believe the future of engineering simulation will one day be fully predicated on the application of chaos theory and fractal geometry to realize many of its aims. In my opinion, the field of chaos theory will become to physics as semiconductors became to the field of electrical engineering. Once fully understood, it will constitute a “tsunami of reasoning,” therein leading to many new discoveries.
