Historical thinkers like Leonardo da Vinci maintained a set of standing questions they were interested in, and when encountering new observations or mental models, they would apply these existing questions as lenses to see if the new tools yielded insights into their standing questions.

We do not yet have a map of the skills required for knowledge structuring and mapping work, and we definitely do not have a map of the most effective exercises and training methods to develop and transfer those skills.

By explicitly identifying the characteristics or properties that define what makes something 'best' in a category, you can extract this into a reusable framework that can be applied to compare different entities across multiple contexts.

The world is a messy, nebulous place of all sorts of things, and understanding it requires applying different conceptual lenses (different questions, mental models, techniques) that cause you to notice different patterns depending on perspective.

Human knowledge and concepts are organized in the mind as a network of interconnected, overlapping pieces rather than as linear sequences or hierarchies.

The next stage of note-taking sophistication beyond sparse pointers is writing prose that lays out coherent reasoning where the author has mentally separated chunks of knowledge, carved out natural conceptual joints, and articulated the connections between pieces.

Roam is designed as an authoring platform for context-sensitive information graphics that represent conceptual space, similar to how Google Maps authors a platform for geographic information graphics that allow users to explore spatial relationships.

Roam has technical properties around user extensibility that no other application possesses, allowing users with modest technical knowledge to create entirely different interaction experiences with structured data.

When knowledge is transmitted through linear media like video, text, or speech, the network structure of knowledge must be linearized into a sequential stream, which causes information loss and creates inefficiencies in knowledge transfer.

When a person takes notes only for themselves, they write single-word reminders or partial phrases because they already have the full context in their head; these notes are pointers into their own memory rather than self-contained information.

When someone expert in one narrow domain needs to provide feedback on a multi-dimensional problem, they must read far more context than necessary—reading sections irrelevant to their expertise—because the knowledge is linearized in a document format that forces sequential reading.

One of the first aims in building Roam is to extract prose-based knowledge into data structures that allow more efficient allocation of attention for both knowledge transfer and parallelizing complex problems.

Einstein needed a mathematical language (non-Euclidean geometry) to describe gravity that didn't previously exist in common use; a friend helped him identify which specific mathematical concepts from an unfamiliar branch of mathematics were necessary, allowing him to learn minimally and create general relativity.

Mathematical writing historically underwent an innovation when proofs began to be written with explicit enumerated logical claims and instructions, allowing readers to track dependencies between claims and verify reasoning structure.

Philosophy departments have attempted to use argument mapping as a visualization technique to represent logical structure with pros and cons, but this approach is limited because it's a lossy data structure that loses important contextual information.

The James Baldwin quote 'the purpose of art is to identify the questions behind the answers' encodes the idea that beneath any definitive statement lies an implicit question, and understanding the questions is as important as understanding the answers.

By restructuring knowledge as question-answer pairs rather than declarative statements, you enable easier comparison between different answers to the same question and can break down complex questions into sub-questions.

All web and mobile applications are fundamentally context-sensitive information graphics—different representations of underlying data that are dynamically generated based on user inputs and constraints.

The second stage of Roam knowledge work is applying different templates or lenses to a document—for example, asking what statements within it constitute agreement, what questions the author is answering, how terms are being defined, what claims are being made as true.

When analyzing an essay to extract what the author claims to be true, you must often compress information across multiple paragraphs into new words that the author didn't explicitly use, representing the author's distributed claims in condensed form.