Singularity (system theory)

The term singularity for an explanation of unstable systems was first, and in a most general meaning used in 1873 by James Clerk Maxwell. Maxwell does not differentiate between dynamical systems and social systems. Therefore, a singularity refers to a context in which a small change can cause a large effect. The existence of singularities is primarily an argument against determinism and absolute causality for Maxwell. Indeed, following the same initial conditions will always achieve the same results, but such a statement is of little value in a world in which the same initial conditions are never repeated.
Characteristics.
In summary, singularities are determined by the following characteristics which can vary in strength:
In dynamical systems.
A further development of Maxwell's thoughts in relation to dynamic systems was carried out first by the French mathematician Henri Poincaré. Poincaré distinguished four different simple singularities (points singuliers) of differential equations. These are the node (les noeuds), the saddle (les cols), the focus (les foyers) and the center (les centers).
In recent times, the chaos theory found special attention. However, deterministic chaos is just a special case of a singularity in which a small cause produces a large observable effect due to a 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 it was demonstrated by Poincaré.
Singularities are a common staple of chaos theory, catastrophe theory, and bifurcation theory.
In social systems.
In social systems, deterministic chaos is unlikely, because the elements of the system have some individuals who engage with awareness, will, and foresight purposefully as part of the dynamic behavior of the system. However, this does not exclude that approaches deterministic chaos in social systems are available. Rather, there is also an increase in the social development of nonlinear dynamics and instabilities .
Chaos in the colloquial sense of complete disorder or confusion, however, is to be found. It is often the basis for singularities, where cause-and-effect relationships are not clear. There are already numerous examples of singularities in social systems with Maxwell and Poincaré. Maxwell states that a word can start a war and all the great discoveries of man based on singular states. Poincaré gives the example of a roofer who drops a brick and randomly kills a passing man.
In natural history.
The development of systems provides the science currently so before that by a singular Big Bang uniformly dispersed plasma spread after the creation of the universe in space, which is cooled with increasing expansion, so that formed atoms and finally for very small (singular) fluctuations in the uniform density inhomogeneities created self-reinforcing. They subsequently led to the formation of galaxies, stars and other systems in the universe, from which humans emerged at the end. Even if the singularity of the Big Bang can be avoided in the mathematical models, singularities remain an essential element of history.
The evolutionary history shows that not only successful mutations can be perceived as positive singularities, but the humanization and the human becoming, the singular most important event in the evolution and represents a jump from the continuum of past evolutionary development of the planet Earth.
Recently, Ward and Kirschvink show that the history of life has been more influenced by disasters than by continuous evolution. Disasters are here first destructive singularities that create space for new developments in the sense of innovations as productive singularities.
Singularities and complexity.
Closely related is the notion of singularity with the concept of complexity. J.C. Maxwell has already pointed out that a system has all the more singular points, the more complex it is. Complexity is also the basis of perceived chaos and singularities. 
Suppose a seemingly insignificant event that produces a great effect, even in a simple context, how difficult would it be to detect the reason in a complex situation with tremendously many elements and relationships.
Complexity that is kind of a breeding ground for singularities, shows the downfall of ancient cultures. Causes such as intruders, internal conflicts or natural disasters are not sufficient alone to justify the destruction of a culture. Rather requirement is an increasing complexity and associated declining marginal returns.
The financial crisis of 2007-2008 shows how difficult decisions are in a very complex environment. Thus, the complexity of financial systems and financial products is a major challenge of the financial markets and institutions to look at. One solution is to reduce complexity and increase the potential for adaptation and robustness. In a complex world with increasing singularities, it is therefore necessary to abandon optimization potential to gain adaptability to external shocks and disasters.