Abstract:
The disparate paradigms of symbolic and subsymbolic artificial intelligence, alongside the foundational models of computation, lack a unifying, first-principles framework for knowledge representation. This paper introduces the Dimensionality Postulate, a novel theoretical framework that posits any computable phenomenon or information state can be exhaustively and uniquely described as a point within a structured, ten-dimensional information manifold. We formally define these ten fundamental dimensions, categorizing them as Spatiotemporal (Sequentiality, Contiguity, Temporality), Semantic (Abstraction, Relationality, Invariance), Causal (Causality, Potentiality), and Epistemic (Uncertainty, Observational Frame). Within this framework, the fundamental unit of information is not the bit, but a rank-2 Information Tensor of type (1,1), whose components capture the multilinear interactions between these dimensions. Consequently, computation is redefined not as a symbolic manipulation on a one-dimensional tape, but as a geometric transformation of these tensors—a trajectory across the Information Manifold. This geometric perspective offers a powerful new lens through which to view foundational concepts. It reinterprets Shannon’s information entropy as a reified dimension, recasts computational complexity classes like P and NP in terms of manifold topology, and provides a common mathematical language that bridges the gap between discrete, logical AI and continuous, connectionist models. The primary implication of the Dimensionality Postulate is the potential to unify the theories of computability, information, and complexity under a single geometric framework, drawing a direct and powerful analogy to the role of higher-dimensional spaces in the unification of forces in theoretical physics.
Yıldırım, E. (2025). The Dimensionality Postulate: A Ten-Dimensional Framework for Universal Knowledge Representation and Computation. Zenodo. https://doi.org/10.5281/zenodo.17046585
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