Navigational Thinking as an Emerging Paradigm of Computer Science in the Age of Generative AI

TL;DR

This paper introduces Navigational Thinking as a new paradigm in computer science, explaining how generative AI's meaning arises from high-dimensional geometric navigation rather than symbolic representation, impacting how we understand knowledge construction.

Contribution

It proposes a novel conceptual framework of Navigational Thinking grounded in high-dimensional geometry, linking it to generative AI and pedagogical implications, expanding traditional computational paradigms.

Findings

Generative AI models instantiate knowledge through geometric navigation.

Meaning in generative AI is based on indexical relations, not symbolic conventions.

Navigational Thinking complements Computational Thinking as sequential cognitive phases.

Abstract

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.