Recent AI models can instantly formalize rough ideas into formal representations like code and mathematics. However, these models function by reproducing and amplifying notational systems that are already well-established, like Python and sheet music notation. What about new notations? Humans working together frequently develop ad-hoc notations to ground their communication, treating notations more like malleable resources that they may formalize over time, rather than systems of rigid rules. How might we design future systems that honor and support the dynamic processes of notation co-creation, evolution, and formalization? To address that question, we first need to understand those processes more clearly than we do at present. In this talk, I present historical research that identifies some common patterns and stages for the development of notations across computational, scientific, and artistic fields, from computer notations such as JavaScript and Markdown, to physics notations such as Feynman-Dyson diagrams, to dance notations such as Labanotation, to sign language writing notations such as SignWriting. Through examples, I highlight the role of cultural context, linking and grounding metaphors, and cognitive processes of analogical alignment. Finally, I present some implications and thoughts toward building a more pluralistic future for human-AI communication.