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

Paper Title

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

Publication Info

• Topic area: Historical and theoretical analysis of notation development and implications for human-computer interaction (HCI).
• Keywords: Notation evolution, formalization, human-computer interaction, abstraction, cognitive dimensions, semiotics, user-defined languages, design implications.

Background and Problem

• Problem / challenge: Current AI systems rely on pre-existing formalisms and struggle to support the creation, evolution, and formalization of novel notations. The process by which humans develop new notations remains underexplored, particularly in terms of its cognitive, social, and material dimensions.
• Significance: Understanding how notations evolve can inform the design of systems that better support user-defined abstractions, enabling more flexible and dynamic human-computer interactions.
• Motivation and related work: Prior research has focused on usability heuristics for existing notations, historical studies of individual notations, and incremental formalization. However, general mechanisms and patterns of notation creation and evolution are less understood. This paper builds on semiotics, cognitive science, and HCI to address this gap.

Solution

• Proposed approach: A comparative historical analysis of notation development across disciplines, identifying patterns and stages of evolution, and deriving implications for system design.
• Novelty:
  1. Identification of 33 patterns of notation creation, evolution, and formalization across three social stages (invention/incubation, dispersion/divergence, institutionalization/sanctification) and three functional stages (descriptive, generative, evaluative).
  2. Introduction of cognitive and social mechanisms such as linking metaphors, grounding metaphors, and dimensions of meaningful variation.
  3. Development of a "square of formality" framework to conceptualize formalization as both translation to existing systems and creation of new ones.
  4. Preliminary design implications for systems that support user-defined notations and incremental formalization.
• Procedure and key techniques:
  • Conducted a parallel comparative historical analysis of notations from diverse domains (e.g., music, chemistry, programming).
  • Iteratively identified patterns through inductive iteration and interpretivist methodology.
  • Categorized patterns into cognitive, social, formalization, and constraint-related factors.
  • Proposed a theoretical framework for notation evolution and implications for HCI design.

Results

• Concrete findings:
  • Notations evolve through iterative processes involving cognitive alignment, social adoption, and material constraints.
  • Linking and grounding metaphors play critical roles in early stages of notation development.
  • Dimensions of meaningful variation are mapped to perceptual channels, which are extended or saturated over time.
  • Formalization involves social processes of standardization, institutionalization, and governance.
• Advantage over baselines: Provides a comprehensive, multi-disciplinary framework for understanding notation evolution, addressing gaps in prior work that focused on individual notations or usability heuristics.
• Experiments / evaluation:
  • Historical case studies of notations such as Feynman diagrams, SignWriting, molecular formulas, and programming languages.
  • Analysis of patterns across stages of development, supported by primary and secondary sources.
• Limitations and future work:
  • Focused on macro-scale patterns; lacks detailed moment-by-moment depictions of formalization processes.
  • Limited coverage of informal, real-time interactions in notation creation.
  • Future work could explore experimental semiotics and dynamic, user-defined abstractions in HCI.

Summary

This paper presents a historical analysis of how notations are created, evolved, and formalized, identifying 33 patterns across social and functional stages. Key contributions include the roles of linking and grounding metaphors, dimensions of meaningful variation, and the "square of formality" framework. The findings have implications for designing systems that support user-defined abstractions, enabling dynamic and flexible interactions. Future work could explore micro-level processes of formalization and the integration of these insights into AI and HCI systems.