Human perception is rarely uniform. Familiar objects appear crisp and meaningful, while unfamiliar ones blur into undifferentiated shapes. This suggests that knowledge does more than add information—it reshapes the space in which information is represented. In this paper, I introduce a minimal geometric framework formalizing this idea. Knowledge is modeled as a scalar coordinate K that acts as a hidden dimension: not an additional axis of sensory data, but a parameter that deforms the intrinsic metric along task-relevant directions. I motivate this concept using a historical analogy: Einstein's extension of classical three-dimensional space by adding time as a fourth dimension did not create new spatial directions, but reinterpreted motion through a geometric coordination rule. Similarly, I propose that the knowledge variable K governs the geometry of the existing manifold. By modeling this as an anisotropic deformation of a Riemannian metric, I derive mathematical guarantees showing that increasing Kmonotonically improves discrimination thresholds and reduces Bayes-optimal error. This framework connects the philosophy of awareness with the rigor of information geometry.