Theory is Shapes

TL;DR

The paper argues that theory figures shape how visualization theories are constructed and understood, challenging the dominance of conventional shapes like Cartesian planes, matrices, networks, and set diagrams. It analyzes the affordances of these shapes and demonstrates how they guide interpretation, then proposes four expressive shapes—Horseshoe, Iceberg, Möbius strip, and BLT—to expand theorizing. Through a provocational, speculative lens, it shows how these shapes can reveal new narratives and depth, while acknowledging potential downsides such as increased complexity and abstraction risks. The work calls for broader experimentation with diagrammatic forms to enrich visualization theory, offering a framework for memoing and reflection in theorycrafting.

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.

Figures (8)

• Figure 1: Cartesian planes afford continuous positioning as well as discrete segmentation of their elements. In (a), Sedlmair et al. SedlmairMeyerMunznerDesignStudyMethodology2012 provide guidance on when it is suitable to conduct a design study, based on task clarity and information location. The xkcd comic in (b) organizes fruits along axes of tastiness and ease of eating xkcdFuckGrapefruit.
• Figure 2: Matrices organize knowledge into a neat grid, allowing rapid comparison and scanning. In (a), Adar and Lee use a matrix to modify an existing educational taxonomy AdarLeeCommunicativeVisualizationsLearning2021. The meme in (b) organizes different ways of storing bread based on character alignments from the game Dungeons & Dragons AlignmentCharts2009.
• Figure 3: Networks are suitable for representing processes, connections, or hierarchies. In (a), Lee et al. LeeetalNOVIS2016 depict the sensemaking process as a directed graph containing cycles and branches. In (b), Lee et al. show the hierarchy of actions in visualization recommendation systems.
• Figure 4: Set diagrams can show intersection, membership, and dependency. Munzner's model in (a) depicts visualization design layers as a series of nested subsets MunznerNestedModelVisualization2009. Meanwhile in (b), Crisan and McNutt use an Euler diagram to show the relationships between good, bad, and user-desired inputs for linting CrisanMcNuttLintingPeopleExploring2025.
• Figure 5: Elhamdadi et al.'sElhamdadietalVistrustMultidimensionalFramework2024 framework of trust in visualizations contains both matrix and flowchart elements.