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Strange Attractors and Ideality

| On 15, Feb 2008

Michael S. Slocum

Dissipative dynamical systems contain some sort of friction. The chief feature of a dissipative system is loss of energy. A pendulum swinging in air will have dissipation. Energy is lost continuously through the various kinds of friction experienced by the pendulum. We call a system where energy is maintained, a conservative dynamical system. This would describe a system with no friction. Heavenly bodies sustain so little friction we describe their motion as being conservative; no energy is lost. Mathematics tells us that the long-term behavior of dissipative systems may be described by a simple pattern of motion whose final state is a point or a limit circle. The final state of a dissipative system that is highly complex and demonstrates chaos is described as a strange attractor. Let us describe a strange attractor that we may utilize to describe the phenomenon:

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                                        The Feigenbaum Scenario (TFS)

Let us focus on The Feigenbaum Scenario to illustrate a few innovation analogies. Notice how the TFS is described by a series of bifurcations. The bifurcations increase geometrically until the model describes the domain of deterministic chaos. However the first several bifurcations determine the final region that comprises the Deterministic Chaos. It is therefore critical that the domain of Conscious Choice be exploited. This is where the concept of Ideality comes in. Ideality is the ultimate outcome of the problem solving process (at least from a tactical innovation scenario where you are solving a problem in an existing system).  Therefore, Ideality is a philosophical construct that dictates the direction problem solving should take to yield the perfect resolution. Ideality can also be described as a series of decision points that must be satisfied in order to describe the target resolution. These decision points are analogous to the bifurcations in the Conscious Choice Domain of the TFS. The innovation process can be controlled to the extent allowable as the problem statement and ideal goal are specified. At a certain point the bifurcations are too numerous and determinism is no longer possible. Therefore, systematic innovation is possible to a certain extent but determinism breaks down at a certain point. The fuzzy front end of problem solving can be brought into focus but the mental operations of the human brain still allow for chaotic thought generation.