Linear change is the least likely scenario in the contemporary world, where discontinuous jumps are predominant, with multiple causes working together, starting from the bottom up and generating tipping points, catastrophes, and bifurcations. Markets are often governed by uncoordinated bottom-up actions that have the capability to generate abrupt change. In mathematics, a point at which a given mathematical function is not defined or has strange properties is called a singularity. This chapter explores the singularity issue in a social context (e.g., from the perspective of black swan events, dynamical rare events, cusp catastrophe theory, the butterfly effect, bifurcations, phase transition, and the dynamics of attractors theory and the emergence of new phenomena). Black swan events are defined as unpredictable, generating extreme impact and after the fact, making people tend to fabricate an explanation that makes it appear more predictable than it really was (generating hindsight that make it seem plausible and predictable. A cusp catastrophe represents a sudden destabilization of the equilibrium, causing a “jump” from one state to another. The butterfly effect is a metaphor reflecting the idea that small things can have a nonlinear impact on a complex system. The complexity theory mentions the unexpected appearance of new emergent entities.