The Illusion of Accelerating Intelligence: Closed Optimization, Open-Ended Reality, and the Two-Thirds Limit
Examining the gap between closed AI optimization and open-ended reality through object detection evidence and a mathematical model of information limits.
Author: Hugo Latapie, Taijitu AI Inc.
Preprint | Version 13 | Published November 6, 2026
Abstract
AI appears to be accelerating because its benchmark scores are accelerating. Yet the systems being measured are trained and selected through closed procedures, while useful intelligence is ultimately judged against an open-ended world. Object detection provides an unusually direct empirical test of this mismatch. The high-end conventional COCO record reviewed here reached approximately 66 average precision in 2023 and has changed little through 2026 despite sustained research, large models, new architectures, new supervision, synthetic data, prompting, and architecture search. This is not a comparison between obsolete vision technology and modern language AI: object detection now uses the same fundamental machinery—transformers, learned representations, gradient optimization, sequence prediction, and in some systems the same multimodal parameters. Pix2Seq explicitly formulates detection as language modeling; Florence-2 and PaliGemma perform both perceptual and linguistic tasks.
We develop a mathematical model of the closed/open mismatch. Let an open causal state space have effective dimension d while the information admitted by a closed optimizer lies on a codimension-one boundary. At resolution ε, the number of distinguishable open states scales as (R/ε)^d while the boundary scales as (R/ε)^(d−1). The corresponding metric-entropy ratio approaches (d−1)/d. Under a state-identification model, Fano's inequality converts this information ratio into the same asymptotic upper bound on exact identification. For a three-dimensional causal volume and its two-dimensional boundary, the result is 2/3.
The theorem is mathematical: it establishes what follows from the stated information geometry. Its application to AI is scientific: observation determines whether contemporary closed-ended systems serving open-ended objectives exhibit that geometry. The empirical record is strikingly consistent with the resulting two-thirds hypothesis. Closed language benchmarks can exceed two-thirds easily because the objective itself is closed. More reality-coupled end-to-end tasks remain much harder. Recursive self-improvement does not escape the information boundary merely by searching it more aggressively. Under the stated information constraint, additional optimization alone cannot remove the modeled limitation.
License
Creative Commons Attribution 4.0 International (CC BY 4.0).
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