Notational Intelligence, Linus Lee | Compile 26
Cursor · 2026-06-29
💡 Quick Take
1. Notational intelligence is a concept that refers to the impact of notations on our ability to communicate and represent ideas, which may be greater than the impact of machines that augment our intelligence.
2. Abstraction is a desirable property of good notations, allowing us to write down one symbol or shape that can stand for a whole set of things with similar properties.
3. Suggestiveness is another property of good notations, where similar-looking symbols or shapes imply shared properties.
4. Natural transformations are related to suggestiveness, where operations on symbols or shapes in graphical space have corresponding meaning in the underlying ideas.
5. Graphical notations take advantage of implicit biases in human visual perception to make operations intuitive.
6. The coordinate plane is a useful graphical notation for manipulating numbers and algebraic terms.
7. Arrows are a basic graphical notation that has been used for centuries, but was only formalized in the 18th century.
8. Programming languages are a type of notation that describe complex dynamic objects, such as programs, and use abstraction, suggestiveness, and natural transformations.
9. Deep learning models can be used to invent new notations, unconstrained from natural notations, by learning an alphabet of symbols that represent ideas.
10. Autoencoders with image generators and decoders can learn to encode a family of ideas or domain of ideas in their own visual space.
11. Invariance, such as scale, rotation, and color, can be imposed on the medium to ensure that symbols mean the same thing regardless of their appearance.
12. Models can be used as simulators to imagine new kinds of languages, laws of physics, and ways of writing things down.
13. Thinking of computers and models as simulators for anything, not just our specific world and experience, is a powerful idea.
14. Using models as a laboratory for imagining other kinds of being, concepts, and ways of writing things down can lead to new insights and ideas.
📊 Detailed Explanation
Notational intelligence is a concept that refers to the impact of notations on our ability to communicate and represent ideas. This concept is important because it highlights the significance of notations in augmenting our intelligence, potentially even more than machines. The speaker notes that there are approximately 100 times more instances of notations than machines in a typical venue, and that notations are often unconscious, yet have a greater impact on our ability to communicate and represent ideas.
Abstraction is a desirable property of good notations, allowing us to write down one symbol or shape that can stand for a whole set of things with similar properties. For example, in algebra, the symbol 'y' can stand for a whole set of numbers or relationships. This property is powerful because it allows us to manipulate larger objects and families of equations by moving symbols around on the board.
Suggestiveness is another property of good notations, where similar-looking symbols or shapes imply shared properties. For example, the Leibniz notation for derivatives is suggestive because it implies that similar-looking ratios of differentials have similar properties. This property is related to natural transformations, where operations on symbols or shapes in graphical space have corresponding meaning in the underlying ideas.
Graphical notations take advantage of implicit biases in human visual perception to make operations intuitive. For example, the coordinate plane is a useful graphical notation for manipulating numbers and algebraic terms because it allows us to take advantage of our implicit understanding of space and geometry. Arrows are a basic graphical notation that has been used for centuries, but was only formalized in the 18th century.
Programming languages are a type of notation that describe complex dynamic objects, such as programs, and use abstraction, suggestiveness, and natural transformations. For example, programming languages use variables and functions to abstract over important concepts, and allow for natural transformations such as refactoring programs. This type of notation is graphical because it uses implicit biases in human visual perception, such as indentation and syntax highlighting, to denote useful ideas in the space of programs.
Deep learning models can be used to invent new notations, unconstrained from natural notations, by learning an alphabet of symbols that represent ideas. For example, an autoencoder with an image generator and decoder can learn to encode a family of ideas or domain of ideas in its own visual space. This type of notation is graphical because it takes advantage of implicit biases in human visual perception, such as scale, rotation, and color, to ensure that symbols mean the same thing regardless of their appearance.
Models can be used as simulators to imagine new kinds of languages, laws of physics, and ways of writing things down. For example, a model can be used to simulate the behavior of a complex system, such as a financial market or a biological system, and to generate new ideas and insights. This type of simulation can be used to imagine new kinds of languages, laws of physics, and ways of writing things down that are not yet known.
Thinking of computers and models as simulators for anything, not just our specific world and experience, is a powerful idea. This idea suggests that models can be used to imagine new kinds of being, concepts, and ways of writing things down that are not yet known. This type of thinking can lead to new insights and ideas, and can be used to explore new possibilities and scenarios.
🎯 Expert Opinion
As an expert in the field of artificial intelligence and machine learning, I believe that the concept of notational intelligence is a crucial aspect of human cognition. The speaker's observation that notations have a greater impact on our ability to communicate and represent ideas than machines is a profound one. This highlights the importance of notations in augmenting our intelligence, and suggests that we should focus on developing new notations and tools that can help us communicate and represent ideas more effectively.
The use of deep learning models to invent new notations is an exciting area of research that has the potential to revolutionize the way we communicate and represent ideas. By learning an alphabet of symbols that represent ideas, these models can create new notations that are unconstrained from natural notations. This type of notation can be used to imagine new kinds of languages, laws of physics, and ways of writing things down that are not yet known.
The idea of using models as simulators to imagine new kinds of being, concepts, and ways of writing things down is a powerful one. This type of simulation can be used to explore new possibilities and scenarios, and can lead to new insights and ideas. However, it also raises important questions about the ethics and implications of using models in this way. For example, how can we ensure that these models are used in a responsible and ethical manner? How can we prevent them from being used to perpetuate biases and stereotypes?
Overall, I believe that the concept of notational intelligence and the use of deep learning models to invent new notations are crucial areas of research that have the potential to revolutionize the way we communicate and represent ideas. However, it is also important to consider the ethics and implications of using these models, and to ensure that they are used in a responsible and ethical manner.
Kanal: Cursor