The Working Space Hypothesis: On Representation Dimensionality and the Geometry of Learning, Optimization, and Reasoning

This paper proposes the Working Space Hypothesis: that many apparent limitations in learning, optimization, and reasoning arise not from the intrinsic difficulty of the problem, but from the dimensional and structural constraints of the representation space in which the problem is formulated. We revisit historical examples in mathematics — including complex numbers, analytic continuation, and contour integration — where extending the working space made previously intractable problems solvable. We introduce the Divergence Diagnostic Principle: that intrinsic analytical divergence is a structural signal of insufficient dimensionality rather than a genuine infinity. We propose the Delayed Projection Principle: reasoning systems should maintain high-dimensional latent representations as long as possible before projecting to low-dimensional outputs. This is a position paper intended to outline a research program connecting high-dimensional geometry, representation learning, and predictive latent-space architectures such as Joint Embedding Predictive Architectures (JEPA). Second edition, enriched.