The Challenge of Semantic Symmetry in Visualization

We present a fundamental problem which arises within an emerging theory of visualization, and provide examples that illustrate the challenge of what we call semantic symmetry. This theory of visualization distinguishes data domains (e.g., Numbers and symbols) from picture domains (e.g., Shapes, shading, colour), and provides a framework for specifying a variety of mappings between data and picture domains. Visualization is about enabling inferences about data within the human visual system, so crucially depends on the management of mappings from the data to the picture domain. But there are many possible choices for these mappings, and only in the last decade has there emerged any serious assessment of how one might measure the quality of a visualization. The situation is further complicated by what is now called visual analytics, where data to picture mappings allow manipulation of that picture to further understand or reveal the underlying data relationships. This kind of picture manipulation is exactly the departure point for our presentation of the problem of semantic symmetry. Semantic symmetry considers the problem of how to couple data and picture so that changes in one are accurately reflected in the other. We illustrate the foundational nature of the problems arising from the desire for semantic symmetry, and explain the kinds of constraints and framework that are necessary in order to be able to support a more complete theory of visualization.