How Notations Evolve: A Historical Analysis with Implications for Supporting User-Defined Abstractions

TL;DR

This paper analyzes the historical evolution of notations, identifying social and functional stages, to inform the design of systems that support the creation and formalization of new abstractions.

Contribution

It provides a novel comparative analysis of notation development stages and patterns, offering insights for designing systems that facilitate user-defined abstraction evolution.

Findings

Identifies three social stages: invention, dispersion, institutionalization.

Highlights three functional stages: descriptive, generative, evaluative.

Reveals patterns like metaphors, meaningful variation, and analogical alignment.

Abstract

Traditional human-computer interaction takes place through formally-specified systems like structured UIs and programming languages. Recent AI systems promise a new set of informal interactions with computers through natural language and other notational forms. These informal interactions can then lead to formal representations, but depend upon pre-existing formalisms known to both humans and AI. What about novel formalisms and notations? How are new abstractions created, evolved, and incrementally formalized over time -- and how might new systems, in turn, be explicitly designed to support these processes? We conduct a comparative historical analysis of notation development to identify some relevant characteristics. These include three social stages of notation development: invention & incubation, dispersion & divergence, and institutionalization & sanctification, as well as three functional stages: descriptive, generative, and evaluative. Within and across these stages, we detail several patterns, such as the role of linking and grounding metaphors, dimensions of meaningful variation, and analogical alignment. Finally, we offer some implications for design.