This preprint proposes thought density as an upstream generative variable of adaptive learning capacity. It argues that transfer, metacognition, strategy adjustment, error correction, and learning speed should not be treated only as external manifestations of ability, but may arise from differences in the density of internal cognitive operations under similar inputs, feedback, and learning directions.
The paper introduces the Circle-and-Tangent Model as an intuitive framework for describing adaptive learning. In this model, the circle represents an ideal performance model closer to underlying regularities, while tangents represent external constraints, calibration paths, learning methods, feedback structures, or communicable cognitive formulas. Learning is described as a process in which thought extends, is constrained, and gradually approaches the circle through accumulated tangents, cognitive arc length, and thought density.
The paper further connects GPT to the Circle-and-Tangent Model. GPT is interpreted as indirect support for the model: its general effectiveness can be understood as the compression and use of public external tangents, while its limitations in personal-experience-based judgments can be explained by the absence of individual implicit tangents. When users provide more personal background, constraints, examples, and feedback, GPT can more closely approximate the intended answer because those implicit tangents are being externalized as usable constraints.
Finally, the paper argues that talent should not be treated as an indivisible black box. Learning ability may be understood as the social manifestation of the interaction between thought density and formulaic constraints. Formulaic constraints can be acquired through education, training, feedback, and environment, while thought density may be a more hidden, harder-to-measure upstream variable. The paper therefore frames thought density as a possible hidden multiplier of learning efficiency rather than an absolutely fixed or completely unchangeable trait.
Note: This preprint is an independent theoretical proposal rather than a literature review. The core framework was developed independently by the author. AI-assisted literature searches were used only after the framework had been formed, for comparison, critical challenge, and boundary checking; therefore, no reference list is included.