Logic, Information, Holography: A Recursive Unification of Complexity Across Computational, Physical, and Geometric Substrates
- 1Independent Researcher
Abstract
This paper proposes a three-layer recursive framework that unifies three complexity measurespreviously confined to separate disciplines: logical depth from algorithmic information theory,information density and thermodynamic dissipation bounds from physical information theory, andentanglement-geometric encoding from holographic gravity. We argue that these are not parallelindependent metrics but concrete manifestations of the same irreducible generative cost on threedifferent substrates: computational, physical, and geometric. The paper reviews Bennett'sdefinition and philosophical motivation for logical depth, the information-physical bounds set byLandauer's principle and the Bekenstein bound, and the spacetime-geometric emergence revealedby the Ryu-Takayanagi formula and the first law of entanglement entropy. It then proposes amapping chain from logical depth to information density to holographic encoding, introduces theconcept of metric involution to describe the resulting evolutionary direction of complex systems,and discusses observational criteria by which the framework could be tested against the traditional,energy-throughput-based paradigm of system complexity.
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BibTeX
@misc{chen2026logic,
title = {{Logic, Information, Holography: A Recursive Unification of Complexity Across Computational, Physical, and Geometric Substrates}},
author = {Yunjing Chen},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.22685374},
url = {https://doi.org/10.5281/zenodo.22685374},
note = {CC BY},
}
RIS
TY - UNPB
TI - Logic, Information, Holography: A Recursive Unification of Complexity Across Computational, Physical, and Geometric Substrates
AU - Yunjing Chen
PY - 2026
DA - 2026/09/10
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22685374
UR - https://doi.org/10.5281/zenodo.22685374
AB - This paper proposes a three-layer recursive framework that unifies three complexity measurespreviously confined to separate disciplines: logical depth from algorithmic information theory,information density and thermodynamic dissipation bounds from physical information theory, andentanglement-geometric encoding from holographic gravity. We argue that these are not parallelindependent metrics but concrete manifestations of the same irreducible generative cost on threedifferent substrates: computational, physical, and geometric. The paper reviews Bennett'sdefinition and philosophical motivation for logical depth, the information-physical bounds set byLandauer's principle and the Bekenstein bound, and the spacetime-geometric emergence revealedby the Ryu-Takayanagi formula and the first law of entanglement entropy. It then proposes amapping chain from logical depth to information density to holographic encoding, introduces theconcept of metric involution to describe the resulting evolutionary direction of complex systems,and discusses observational criteria by which the framework could be tested against the traditional,energy-throughput-based paradigm of system complexity.
ER -