  Understanding intelligence is a central pursuit in neuroscience, cognitive
science, and artificial intelligence. Intelligence encompasses learning,
problem-solving, creativity, and even consciousness. Recent advancements in
geometric analysis have revealed new insights into high-dimensional information
representation and organisation, exposing intrinsic data structures and dynamic
processes within neural and artificial systems. However, a comprehensive
framework that unifies the static and dynamic aspects of intelligence is still
lacking. This manuscript proposes a mathematical framework based on Riemannian
geometry to describe the structure and dynamics of intelligence and
consciousness. Intelligence elements are conceptualised as tokens embedded in a
high-dimensional space. The learned token embeddings capture the
interconnections of tokens across various scenarios and tasks, forming
manifolds in the intelligence space. Thought flow is depicted as the sequential
activation of tokens along geodesics within these manifolds. During the
navigation of geodesics, consciousness, as a self-referential process,
perceives the thought flow, evaluates it against predictions, and provides
feedback through prediction errors, adjusting the geodesic: non-zero prediction
errors, such as learning, lead to the restructuring of the curved manifolds,
thus changing the geodesic of thought flow. This dynamic interaction integrates
new information, evolves the geometry and facilitates learning. The geometry of
intelligence guides consciousness, and consciousness structures the geometry of
intelligence. By integrating geometric concepts, this proposed theory offers a
unified, mathematically framework for describing the structure and dynamics of
intelligence and consciousness. Applicable to biological and artificial
intelligence, this framework may pave the way for future research and empirical
validation.
