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The conceptualization of material spaces within materials science has traditionally relied on Euclidean distance metrics, yet this approach overlooks the inherent complexities of material properties and structures. This manuscript explores the interpretive dimensions of non-Euclidean geometries in representing material relationships, emphasizing how manifold learning and Riemannian frameworks reveal intricate interaction dynamics among atomic configurations and physical attributes. By synthesizing recent literature on geometric neural operators and hyperbolic embeddings, the analysis underscores the trade-offs between simplified Euclidean assumptions and the richer, curvature-aware interpretations that align with multiscale material behaviors. Conceptual interpretations highlight how distance metrics influence systems-level insights in materials informatics, where flat spaces fail to capture hierarchical or topological nuances. The proposed framework integrates these elements through a steering logic that navigates the epistemic challenges of metric selection, fostering a deeper understanding of material continuity and discontinuity without empirical assertions. Ethical reasoning is woven into considerations of the implications for knowledge representation in computational materials discovery. This critique advocates an integrative view that enhances conceptual coherence in the field by bridging abstract geometric principles with material phenomenology.