Generative AI systems produce meaning with a quality indistinguishable from - and occasionally surpassing - human performance, yet the epistemic mechanism through which this occurs remains poorly understood. This paper argues that generative AI instantiates a fundamentally new mode of knowledge production: geometric navigation through high-dimensional manifolds, grounded in indexical rather than symbolic signification. Drawing on the structural properties of high-dimensional spaces, we demonstrate that meaning in generative AI is constituted through positional relation and orientation rather than through symbolic convention. This shift corresponds precisely to what Peirce identified as indexical signification: a mode of meaning in which the sign is constituted by its real causal connection to its object, not by arbitrary assignment. We develop the pedagogical implications of this shift through a geometrized reading of Papert's constructionism, reconceptualizing the generative AI system as a new kind of microworld - high-dimensional, non-visualizable, and indexical - in which knowledge is constructed through navigation rather than symbolic programming. From this analysis, we derive the concept of Navigational Thinking: a mode of knowing characterized by positional, enactive, and bounded engagement with geometrically structured spaces. We argue that Navigational Thinking and Computational Thinking are not alternatives, but two sequential phases of the same cognitive process: while a problem remains indexical, Navigational Thinking is operative; when the problem space stabilizes into symbolizable form, Computational Thinking becomes applicable. Vibe-coding is merely the visible tip of an iceberg - the iceberg being a new cognitive ecology in which these two modes coexist as the necessary phases of problem-solving in the age of generative AI.

翻译：生成式人工智能系统产生的意义在质量上与人类表现难以区分，甚至偶尔超越人类，但其产生意义的认知机制仍未被充分理解。本文论证生成式人工智能实例化了一种根本性的知识生产新模式：基于指示性而非符号性意指的高维流形几何导航。利用高维空间的结构特性，我们证明生成式人工智能中的意义是通过位置关系和方向而非符号约定构成的。这一转变恰好对应于皮尔斯所定义的指示性意指：一种符号与其对象通过真实因果联系而非任意指派来构成意义的方式。我们通过佩珀特建构主义的几何化解读，发展了这一转变的教育学意义，将生成式人工智能系统重新概念化为一种新型微世界——高维、不可视化且具有指示性——在此世界中知识通过导航而非符号编程来建构。基于此分析，我们推导出"导航式思维"这一概念：一种以位置性、行动性和边界性参与几何结构化空间为特征的认知模式。我们论证导航式思维与计算思维并非替代关系，而是同一认知过程的两个连续阶段：当问题仍保持指示性时，导航式思维发挥作用；当问题空间稳定为可符号化形式时，计算思维开始适用。Vibe编码不过是冰山可见的一角——这座冰山正是生成式人工智能时代中两种认知模式作为问题解决必要阶段共存的新型认知生态。