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Explore the impact of geometric world models on behavior in this 23-minute conference talk from the Models of Consciousness Conferences. Delve into the Projective Consciousness Model (PCM) and its framework for understanding the relationships between consciousness, cognition, and behaviors. Learn how 3D projective geometry models subjective perspectives and how the 3D projective group structures internal representations for active inference and optimal control. Discover mathematical proofs demonstrating how changing the group structure (Euclidean versus Projective) influences the quantification and maximization of "epistemic value" and subsequent exploratory behaviors. Examine the potential for extending these concepts to general groups and the stability of group-structured representations. Gain insights into designing experiments with human participants to test the model's predictions, aiming to build a comprehensive theory of consciousness and derive principles for controlling social robots.