Singularity (systems theory)

The attributes of singularities include the following in various degrees, according to context: Instability: because singularities tend to produce effects out of proportion to the size of initial causes. System relatedness: the effects of a singularity are characteristic of the system. Uniqueness: The nature of a singularity does not arise from the scale of the cause, so much as of its qualitative nature. Irreversibility: Events at a singularity commonly are irreversible; one cannot un-crack a glass with the same force that cracked it. Subjectivity: In phenomenology rather than physical science, awareness is dependent on human perception. Randomness: Some classes of singularities are seen as random because the causes or their effects are unknown or nonexistent (e.g., in QM or coin-flipping). Complexity: Occurrence of singularities often arises from the complexity of the system in its relation to its environment. Interaction: Singularities often arise when unexpected interactions occur between two systems. In recent times, chaos theory has attracted a great deal of work, but deterministic chaos is just a special case of a singularity in which a small cause produces a large observable effect as a result of nonlinear dynamic behavior. In contrast the singularities raised by Maxwell, such as a loose rock at a singular point on a slope, show a linear dynamic behavior as Poincaré demonstrated. Singularities are a common staple of chaos theory, catastrophe theory, and bifurcation theory. In social systems, deterministic chaos is infrequent, because the elements of the system include individuals whose values, awareness, will, foresight, and fallibility, affect the dynamic behavior of the system. However, this does not completely exclude any notional possibility of deterministic chaos in social systems. In fact some authorities argue an increase in the development of nonlinear dynamics and instabilities of social systems.