Stanford CS547 HCI Seminar | Winter 2026 | Creation, Evolution, and Formalization of Notations

Key Concepts

• Broad Definition of Notation: Encompassing all formal and informal systems of representation, from ancient tablets to computer code and natural language.
• Notation Evolution: Notations aren’t static; they evolve through invention, divergence, institutionalization, and functional stages.
• Instant Formalization (via LLMs): The rapid translation of ideas into formal systems, contrasting with historical incremental formalization.
• AI’s Role in Notation: Current AI excels at formalization but struggles with creating new notations, a crucial ability for AGI.
• Co-Creation of Notations: The potential for humans and AI to collaboratively develop and evolve notations, potentially surpassing human-human collaboration.
• Notation as Value Setting: Formalization isn’t just about clarity, but about defining what’s important and prioritizing aspects of a problem.

The Historical Context of Notation

The discussion begins by framing notation as a historically under-explored area within Human-Computer Interaction (HCI), particularly relevant given the rise of Large Language Models (LLMs). The speaker advocates for a broad definition of “notation” – anything that represents information, from Babylonian tablets to computer code. This contrasts with narrower definitions common in HCI. A research methodology of “parallel comparative history” is employed, analyzing the trajectories of various notational systems (sheet music, dance notation, programming, chemical formulas) to identify common patterns in their evolution. This work builds upon the Cognitive Dimensions Framework, acknowledging its value for evaluating notations but emphasizing the need to understand how they are created.

Stages of Notation Evolution & the 2x2 Model

The evolution of a notation is described as a four-stage process: 1) Invention & Incubation, often grounded in metaphor; 2) Dispersion & Divergence; 3) Institutionalization & Sanctification (standardization); and 4) Functional Stages (description, theory generation, evaluation). The speaker challenges the traditional HCI view of formalization as a linear spectrum from informal to formal, proposing a 2x2 model with dimensions of formalization and creation/translation. This model highlights AI’s current strength in instant formalization but its weakness in creating new notations. Examples illustrating these stages include the origins of chemical formulas (inspired by arithmetic notation), dance notation (linked to musical notation and SignWriting), and early computer programming (influenced by block diagrams and the need to translate mathematical equations into machine code). Quantum circuit notation, rooted in crankshaft mechanisms, is also cited.

The Impact of LLMs & “Instant Formalization”

LLMs are introducing an era of “instant formalization,” where vague ideas can be rapidly translated into runnable code or formalized mathematical notation. This contrasts sharply with the historically incremental process of formalization. Examples of LLM output (Gemini, Claw) demonstrate the numerous notations operating “under the hood” (HTML, CSS, Markdown, LaTeX). However, this capability doesn’t equate to true understanding or the ability to create new representational systems. The speaker argues that AI systems have a “huge blind spot” – they cannot dynamically evolve new abstractions. Formalization is also presented as a process of “setting the values that concern us and what is less,” highlighting its role in prioritizing aspects of a problem.

Collaborative Potential & the Future of Notation

The discussion shifts to the potential for collaboration between humans and AI in notation creation. The argument is made that AI could potentially surpass human collaboration in this area, due to its ability to identify suboptimal decisions and consider broader ramifications. The iterative and often “throwaway” nature of notation use is emphasized; the value often lies in the thinking process it enables, not necessarily the final, formalized notation (illustrated by the Venn diagram example). LLMs may also help mitigate cultural conflicts in notation interpretation by anticipating differing perspectives.

AI-Invented Notations & the Alignment Problem

The emergence of AI-invented “gibberish languages” through reinforcement learning is acknowledged, raising the “alignment problem” – the risk of AI communicating in ways humans cannot understand. This is framed as a necessary step for AI to advance scientific discovery and improve the explainability of its processes. The need for AGI to invent new notations to “ground its thinking” is asserted, as this is fundamental to human knowledge and societal function.

Case Studies & Future Research Directions

Game design and Machine Learning (ML) model architecture development are identified as ideal case studies for future collaborative research. In game design, AI could support the sketching and notation-heavy creative process. In ML, better formalized notations for model architectures could accelerate innovation and facilitate theory generation and testing (“If you have a notation that describes the world really well, then you might move to the generative stage where you now generate theories about the world that you then try to test.”).

Conclusion

The discussion underscores the critical importance of understanding notation – not just as a tool for communication, but as a fundamental aspect of thought, knowledge creation, and societal function. The rise of LLMs presents both opportunities and challenges. While AI excels at formalizing existing ideas, its inability to create new notations represents a significant limitation, particularly as we move towards AGI. Future research should focus on designing systems that support the co-creation and evolution of notations with AI, recognizing the potential for AI to surpass human collaboration in this domain and the necessity of addressing the alignment problem as AI develops its own representational systems.