The hypothesis that human intelligence represents a phase transition in animal intelligence is explored, as is the hypothesis that General Collective Intelligence (GCI), which has been defined as a system that organizes groups into a single collective cognition with the potential for vastly greater general problem-solving ability than that of any individual in the group, represents a phase transition in human intelligence. At these phase transitions, cognition can be demonstrated to gain the capacity for exponentially greater general problem-solving ability. If valid, then when generalized as an Nth order pattern, these N phase transitions represent successively more powerful super-intelligences, where each of these super-intelligences can potentially be implemented as an Artificial General Intelligence (AGI), or as a General Collective Intelligence (GCI).