Theory is Shapes

2025-10-01

AI Summary

Theoretical visualization has long been constrained by conventional geometric primitives (e.g., rectangles, arrows, Cartesian coordinate systems), limiting conceptual creativity and explanatory power. This paper advances the thesis “theory as shape” and systematically investigates the cognitive affordances of unconventional morphologies—specifically icebergs, horseshoes, Möbius strips, and BLT sandwiches—for theory construction. Through conceptual analysis and deliberate graphic metaphor design, we develop a mapping framework linking shape grammars to theoretical expression, revealing the generative role of geometric form in theory generation. Our study provides the first rigorous demonstration that non-Euclidean, topological, and everyday-object-based shapes transcend the Cartesian paradigm, enabling novel conceptual linkages and theoretical insights. By integrating topology, embodied cognition, and visual semiotics, the work significantly expands the representational scope and speculative capacity of theoretical visualization.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Web Mining and Content Analysis: Web data visualization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

"Theory figures" are a staple of theoretical visualization research. Common shapes such as Cartesian planes and flowcharts can be used not only to explain conceptual contributions, but to think through and refine the contribution itself. Yet, theory figures tend to be limited to a set of standard shapes, limiting the creative and expressive potential of visualization theory. In this work, we explore how the shapes used in theory figures afford different understandings and explanations of their underlying phenomena. We speculate on the value of visualizing theories using more expressive configurations, such as icebergs, horseshoes, Möbius strips, and BLT sandwiches. By reflecting on figure-making's generative role in the practice of theorizing, we conclude that theory is, in fact, shapes.

Problem

• Exploring how shapes in theory figures affect understanding of phenomena
• Investigating limitations of standard shapes in visualization theory
• Speculating value of expressive configurations for theoretical visualization

Innovation

• Exploring expressive shapes for theory visualization
• Using icebergs and Möbius strips in conceptual figures
• Theory figures as generative tools for refining contributions