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.

翻译：传统的人机交互通过结构化用户界面和编程语言等形式化系统进行。近年来的人工智能系统有望通过自然语言及其他符号形式实现一系列新型非正式人机交互。这些非正式交互可进一步转化为形式化表征，但其实现依赖于人类与人工智能共同掌握的既有形式体系。那么新型形式体系与符号又当如何？新的抽象概念如何被创造、演化并随时间逐步形式化——反过来，新系统又该如何通过显式设计来支持这些过程？我们通过符号发展的比较历史分析，识别出若干相关特征。这包括符号发展的三个社会阶段：发明与孵化、传播与分化、制度化与神圣化，以及三个功能阶段：描述性、生成性与评估性。在这些阶段内部及阶段之间，我们详细阐述了若干模式，例如联结与基础隐喻的作用、意义变异的维度以及类比对齐机制。最后，我们提出若干设计启示。