Postgres is the source of truth, while markdown remains the portable import and export format.
Vault
NoteGuild starter collection
Explore connected ideas from philosophy, science, and math. Original educational summaries with sources, caveats, and questions from NoteGuild.
These are ready for open discovery, ranking, and topic pages.
Shared workspaces sit between personal notes and the public commons.
Idea feed
Obsidian-style notes, but social
Each idea is a portable note with backlinks, tags, frontmatter, and visibility controls. The feed below is generated from the database-backed vault graph.
PublicSep 28, 2026
Exponential growth and doubling
When growth is proportional to the current amount, equal time steps multiply the total rather than add a fixed amount.
PublicSep 28, 2026
Symmetry and conservation
Under the conditions of Noether's theorem, a continuous symmetry of a physical action yields a conserved quantity.
PublicSep 28, 2026
Infinity comes in sizes
The whole numbers and real numbers are both infinite, but there is no one-to-one pairing between them.
PublicSep 28, 2026
Godel and the limits of proof
A consistent, effectively axiomatized theory rich enough for arithmetic cannot settle every arithmetic statement.
PublicSep 28, 2026
Small world networks
A few long-range links can connect tight local clusters without erasing their local structure.
PublicSep 28, 2026
Bayes rule and belief updates
Evidence changes belief through both how expected it was and how plausible the hypothesis was beforehand.
PublicSep 28, 2026
Uncertainty is part of measurement
A measurement is more useful when it states how uncertain it is and where that uncertainty comes from.
PublicSep 28, 2026
Correlation is not causation
Two things moving together is a clue. It does not tell you which intervention would change the outcome.
PublicSep 28, 2026
Emergence from local rules
Simple interactions among parts can produce patterns that are easier to describe at the level of the whole.
PublicSep 28, 2026
Evolution has no foresight
Natural selection can produce adaptation without planning for a future goal.
PublicSep 28, 2026
Entropy and open systems
Local order can increase while total entropy increases. The boundary around the system matters.
PublicSep 28, 2026
Feedback loops and stability
A system can respond to its own output. Whether that response dampens or amplifies change shapes what happens next.
PublicSep 28, 2026
The is-ought gap
Facts help us choose how to act, but a recommendation also needs a value or goal.
PublicSep 28, 2026
The ship of Theseus
If every plank in a ship is replaced, what makes it the same ship: its matter, form, history, or something else?
PublicSep 28, 2026
The veil of ignorance
Design a rule without knowing which position you will occupy under it. What would you protect?
PublicSep 28, 2026
Falsifiability and its limits
A claim becomes easier to investigate when you can say what evidence would count against it.
PublicSep 28, 2026
The problem of induction
Past patterns help us predict the future, but past success alone cannot logically guarantee that a pattern will continue.
PublicSep 28, 2026
The map is not the territory
A useful model leaves things out. The question is whether it leaves out something that matters for your decision.