Notational intelligence | thesephist.com

🌈 Abstract

The article explores the importance of notation in augmenting human intelligence and creativity. It discusses:

• The diversity of notations across various domains like mathematics, music, dance, and programming
• How good notation can shape our thinking and enable us to work with more complex abstractions
• Defining intelligence as the ability to generalize and compress information
• The potential for developing more dynamic and interactive notations using software
• Guidelines for designing effective new notations
• Future directions in improving notation to enhance human intellect

🙋 Q&A

[01] A brief tour of notational diversity

1. What are the key properties of good notation identified in the article? The article highlights the following desirable properties of good notation:

• Unambiguity - Every valid expression has a unique interpretation
• Expressiveness - Every idea in the domain can be described using the notation
• Suggestiveness - Similar concepts have similar-shaped expressions
• Natural transformation - Natural ways of working with ideas correspond to natural manipulations of symbols

2. How does the article contrast the strengths of written language and mathematical notation? Written language provides expressive flexibility, while mathematical notation derives its strength from rigidity and precision. Written language allows us to record and preserve ideas over time, while mathematical notation enables us to work with abstract concepts like unknowns and infinities using the same cognitive processes as working with physical objects.

3. What examples of specialized notations does the article discuss beyond language and mathematics? The article mentions notations used in dance, juggling, music, screenwriting, theater, electrical circuits, and professional copy editing. It suggests that humans invent notation whenever we need to work with common abstractions.

[02] Interpreting intelligence

1. How does the article define intelligence in terms of adaptation and generalization? The article defines intelligence as the ability to rapidly adapt and respond to new environments and challenges, which requires broad generalization power - the ability to find abstract patterns and apply them to novel problems. This is contrasted with narrow specialization or rote memorization.

2. How does the article relate intelligence to data compression? The article suggests that intelligence can be understood as the ability to effectively compress information, discarding irrelevant details while retaining the meaningful abstractions needed to generalize to new situations. This is akin to how data compression algorithms work.

[03] Notational intelligence

1. What is the key insight about the role of notation in augmenting human intelligence? The article argues that inventing better notation is a powerful way to increase our effective intelligence, as good notation allows us to more easily work with complex abstractions and discover new ideas that were previously unthinkable.

2. What are some examples of how software could enable more dynamic and interactive notations? The article speculates about possibilities like direct manipulation of symbolic representations, integrating rich media like audio and 3D models into notations, and quantitative representations of abstract concepts.

3. What guidelines does the article propose for designing effective new notations? Some guidelines include:

• Focus on expressing properties of concepts that current notation handles poorly
• Roll up complex ideas into more concise symbols
• Suggest dualities and relationships between ideas that current notation doesn't capture
• Explore non-linguistic, 2D/3D interactive forms of notation

[04] Future directions

1. What are the two main paths for improving notation that the article highlights?

1. Making existing notations more interactive and dynamic using software
2. Inventing new notations to quantitatively represent more abstract ideas

2. How does the article suggest we should measure the value of new notational innovations? The article argues that notation should be judged by its ability to enable previously unthinkable or inexpressible thoughts and ideas, rather than just improving productivity on existing tasks. The goal should be to augment human intellect, not just human productivity.