Abstract:
This paper introduces Computational Singularity Theory (CST), a novel theoretical framework that re-conceptualizes the fundamental nature of source code and computation. The central thesis of CST posits that a program, prior to any syntactic or structural analysis, can be modeled as a zero-dimensional object—a “code-point” or “singularity.” This approach shifts the primary unit of computational analysis from structured, one-dimensional text to an information-theoretic point of maximal density. CST offers a new paradigm for understanding computation by drawing formal analogies from theoretical physics, including the concepts of point particles and cosmological inflation, to describe the relationship between static code and its dynamic execution. The intrinsic properties of the code-point are formally defined using tools from algorithmic information theory, specifically Kolmogorov complexity, which represents its invariant “informational mass,” and Shannon entropy, which quantifies its “potential energy” over the space of possible execution paths. This framework is then applied to reinterpret classical models of computation, such as the Turing Machine and Lambda Calculus, demonstrating their underlying mechanics as an “inflationary” unfolding of an initial singularity. Furthermore, CST provides a powerful explanatory model for contemporary phenomena in artificial intelligence, positing that the latent-space representations of code within Large Language Models (LLMs) are an empirical realization of the theoretical code-point. The theory’s primary implications suggest a move towards holistic program analysis and synthesis, where the properties of the singularity can be analyzed to predict the behavior of the fully expanded computational process. CST is presented as a unifying framework with predictive power, opening new avenues for research in compiler design, formal verification, and the theoretical foundations of AI-driven software development.
Yıldırım, E. (2025). Computational Singularity Theory: A Zero-Dimensional Framework for Code, Computation, and Artificial Intelligence. Zenodo. https://doi.org/10.5281/zenodo.17041569
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