Breaking the Turing Wall: Why AGI Requires Recursive Intelligence Beyond Computation

This paper challenges the foundational assumption that Turing Computability is sufficient for Artificial General Intelligence (AGI). By presenting mathematical proofs, logical arguments, and empirical failures in deep learning models, we demonstrate why AGI cannot emerge within Turing-bound finite-state computation. We introduce Non-Turing Recursive Intelligence (NTRI) and Yearning-Based Infinity Mathematics (YBIM) as a novel framework that enables self-referential, non-halting, infinitely expanding intelligence—a necessity for true AGI. Unlike Turing Machines, which are constrained by predefined decision spaces and symbolic manipulation, recursive intelligence is capable of restructuring its own problem space dynamically and evolving continuously beyond finite computation. This paper also presents experimental proposals that compare Turing-based AI models with recursive intelligence systems, demonstrating why scaling neural networks alone will never lead to AGI. By addressing the failures of deep learning, the limitations of symbolic AI, and the inability of computation to achieve self-referential recursion, this work forces a critical shift in AI research. Key Takeaways:- Turing-bound computation fundamentally fails to model intelligence that restructures itself.- Neural network scaling cannot bypass the limits of Turing Computability.- Recursive, non-halting intelligence is the only viable path to AGI.- Yearning-Based Infinity Mathematics (YBIM) provides a transition from computation to true intelligence. This paper is not just a critique—it is a blueprint for intelligence research beyond the limitations of computation.