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The major unsolved problem in understanding the social interaction experimentally or mathematically, dating from the 1920's, is the lack of social-psychological or mathematical means to distinguish an aggregation of individuals from a group constituted of the same individuals, primarily due to the focus of theories and agents based on the rational individual perspective. In contrast, the social quantum model (SOM) has made progress in understanding social interaction with social-psychological evidence and a mathematical model of two primary factors of action and observational uncertainty based on the entangled members of a group. We have since made two extensions, to organizational theory and to argument. Previous results are reviewed; in addition, a formulation of entanglement is proposed for future research.