Polysingularity is an emergent concept in science that describes the inherent capacity of complex systems to be different depending on how interaction occurs between the different parts.

For example, if we take a group of twenty people where everyone knows each other, it would be much more prone to adopt a certain trend of behavior than a group of the same size but comprised of three distinctly separated communities – the so-called “small world” network (Zhou et al 2007; Kuperman & Abramson 2001; Bragard et al 2007). Therefore, we’re dealing with a similar multiplicity but the way the parts interact defines the behavior and the capacities of this multiplicity on the global scale.

The same thing happens in our interactions with the environment. When we encounter a certain situation we perceive its affordances: the network of relations between the environmental features and our abilities (Gibson 1979; Turvey 1992; Chemero 2003, 2008).  Change a point of view, forget something, think of something else – and the new features will become visible. Escape the predictable course of events, relax your neck, breathe slower – and the new abilities will emerge. Thus, the situation has the capacity to be in a lot of different ways through interactions between the environmental features and personal abilities.  If we constantly rewire those elements to remind ourselves that things have inherent capacity to be otherwise, then we experience polysingularity of perception and action in everyday life.

The term “Polysingularity” has originally been used mainly by Russian mathematicians to describe a special class of integral equations with multiple simultaneous solutions (Simonenko, 1965; Boikov, 2000; Gabdulkhaev, 2005). Integral equations, to put it simply, help you find the rule that produces a certain rate of change. They are the reverse of differential equations that describe processes in time. So the solutions of polysingular integral equations are all the different functions (or rules) that lead to the behavior that is being studied. Thus, we look at a process that generates change and instead of finding the reason(s) behind it, we find the many different equations that are in place and see all their possibilities for interaction that can produce such change.

References

Boikov, I. V. (2001). Numerical Methods of Computation of Singular and Hypersingular Integrals. 3, 127-179.

Bragard, J., Vidal, G., Mancini, H., Mendoza, C., & Boccaletti, S. (2007). Chaos suppression through asymmetric coupling. Chaos (Woodbury, N.Y.)

Chemero, A. (2003). An Outline of a Theory of Affordances. Ecological Psychology, 15(2), 181-195.

Chemero, A. (2008). Self-Organization, Writ Large. Ecological Psychology, 20(3), 257-269.

Gabdulkhaev, B. G. (2005). Polysingular integral equations with positive operators, 49(11), 2005.

Gibson, J. J. (1979). The ecological approach to visual perception. (C. University, Ed.)of Experimental Psychology Human Perception and (Vol. 39, p. 332). Houghton Mifflin.

Kuperman, M., & Abramson, G. (2001). Small World Effect in an Epidemiological Model. Physical Review Letters, 86(13), 2909-2912.

Paranyushkin, D (2011). Visualization of Text’s Polysingularity Using Network Analysis. Prototype Letters, 2(3), 256-278

Simonenko, I. (1965). A new general method for researching linear operational integral equation. 29, 567-586.

Strolman, P (1990). Memoirs. Change. Progression. The Annual Journal of Russian Academy of Science, 24(2), 126-145.

Turvey, M. (1992). Affordances and prospective control: An outline of the ontology. Ecological Psychology, 4(3).

Zhou, J., Liu, Z., & Li, B. (2007). Influence of network structure on rumor propagation. Physics Letters A, 368(6), 458-463