Abstract:
This paper introduces the Volumetric Lambda Calculus (VλC), a novel model of computation that departs from the linear, one-dimensional paradigm of the Turing machine and the discrete memory-processor architecture of von Neumann. We posit that computation can be more fundamentally understood as the evolution of a three-dimensional information field, or state-space. The fundamental unit of information is the “voxel-state,” and computational operations are defined as geometric transformations on this volume. The VλC’s dynamics are governed by the holographic principle, where the state of the N-dimensional volume is fully encoded on, and driven by, its (N-1)-dimensional boundary. This architecture inherently resolves the von Neumann bottleneck, provides a natural substrate for spatial computing and multi-physics simulations, and exhibits intrinsic fault tolerance through a mechanism analogous to quantum error correction. By grounding computation in geometric and topological principles, the VλC offers a potential path toward unifying formal computation theory with fundamental physics
Yıldırım, E. (2025). The Volumetric Lambda Calculus: A Holographic Formalism for State-Space Computation. Zenodo. https://doi.org/10.5281/zenodo.17044323
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