# Singularity (systems theory)

(Redirected from Singularity (system theory))

## Characteristics

The attributes of singularities include the following in various degrees, according to context:

1. Instability: because singularities tend to produce effects out of proportion to the size of initial causes.
2. System relatedness: the effects of a singularity are characteristic of the system.
3. Uniqueness: The nature of a singularity does not arise from the scale of the cause, so much as of its qualitative nature.
4. Irreversibility: Events at a singularity commonly are irreversible; one cannot un-crack a glass with the same force that cracked it.
5. Subjectivity: In phenomenology rather than physical science, awareness is dependent on human perception.
6. 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).
7. Complexity: Occurrence of singularities often arises from the complexity of the system in its relation to its environment.
8. Interaction: Singularities often arise when unexpected interactions occur between two systems.[1]

## In dynamical 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.[2]

## In social systems

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.[3] 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.[4]

## In universal history

Biological evolutionary history shows that not only mutations that give rise to microevolution can amount to singularities, but that macroevolutionary events that affect the entire course of the history of the biosphere also amount to singularities.[5][6] Recently, Ward and Kirschvink have argued that the history of life has been more influenced by disasters that generated singularities, than by continuous evolution.[7] Disastrous singularities that create niches for biological innovations that give rise to productive singularities.[8]

## Singularities and complexity

Complexity may amount to a breeding ground for singularities, and this has emerged in the downfall of many, perhaps all, ancient cultures and modern countries. Individual causes such as intruders, internal conflicts or natural disasters commonly do not suffice to destroy a culture. More often an increasing complexity of interdependent factors has rendered a community vulnerable to the loss of a few infrastructural necessities that lead to successive collapse in a domino effect.[9]

The financial crisis of 2007-2008 illustrated such effects. Accordingly, the complexity of financial systems is a major challenge for financial markets and institutions to deal with.[10] Notionally one solution would be to reduce complexity and increase the potential for adaptation and robustness. In a complex world with increasing singularities, some people assert that it is therefore necessary to abandon optimization potential to gain adaptability to external shocks and disasters. However, no one has yet demonstrated how to implement such a solution.[11]

## References

1. ^ Holzkämpfer, Hendrik (1996). Management von Singularitäten und Chaos : außergewöhnliche Ereignisse und Strukturen in industriellen Unternehmen (in German). Wiesbaden: DUV, Dt. Univ.-Verl. p. 91. ISBN 978-3-8244-0296-0. OCLC 613466903.
2. ^ Tu, Pierre N. V. (1994). Dynamical systems : an introduction with applications in economics and biology. Berlin New York: Springer-Verlag. p. 195. ISBN 978-3-540-57661-7. OCLC 30544550.
3. ^ Weizsäcker, C. C. von: Ordnung und Chaos in der Wirtschaft, in: W. Gerock/ H. Haken u.a. (Hrsg.): Ordnung und Chaos in der unbelebten und belebten Natur. Stuttgart 1989. S. 46.
4. ^ Bühl, W.L.: Sozialer Wandel im Ungleichgewicht: Zyklen, Fluktuationen, Katastrophen, Stuttgart 1990, S. 207.
5. ^ Hagemann, R.: Mutationen als produktive Singularitäten, in: J.-H. Scharf (Hrsg.): Singularitäten, Nova Acta Leopoldina, Abhandlungen der Deutschen Akademie der Naturforscher Leopoldina, Vorträge anläßlich der Jahresversammlung vom 30. März bis 2. April 1985 zu Halle (Saale), Leipzig 1989, S. 155-169.
6. ^ Vogel, C.: Die Hominisation, ein singulärer Sprung aus dem Kontinuum der Evolution?, in: J.-H. Scharf (Hrsg.): Singularitäten, Nova Acta Leopoldina, Abhandlungen der Deutschen Akademie der Naturforscher Leopoldina, Vorträge anläßlich der Jahresversammlung vom 30. März bis 2. April 1985 zu Halle (Saale). Leipzig 1989, S. 141–154.
7. ^ Ward, P., Kirschvink, J .: A New History of Life, Munich 2016, S.30.
8. ^ Holzkämpfer, H .: Management of Singularities and Chaos, Wiesbaden 1996, pp. 133ff and 139ff.
9. ^ Tainter, J.A.: The Collapse of Complex Societies, Cambridge, New York u.a. 1988, S. 42ff.
10. ^ Landau, J.-P.: Complexity and the financial crisis, Introductory remarks at the Conference on The Macroeconomy and Financial Systems in Normal Times and in Times of Stress, jointly organized by Banque de france and the Bundesbank, 8. June, 2009.
11. ^ Conrad, M.: Adaptability: The Significance of Variability from Molecule to Ecosystem, New York, London 1983.