shuding's essay 'Metaphors': protocols turn n×n integrations into n+n, and programs are proofs
shuding · x · 2026-09-23
Vercel engineer shuding published a blog post, Metaphors, reframing metaphor as a structure-preserving function that lets you reason in a familiar domain and carry the answers back to an unfamiliar one.
- Protocols turn × into +: n editors × n languages means n² integrations; the Language Server Protocol collapses it to n+n. The same pattern explains USB, HTTP, TCP/IP, and MCP between models and tools — protocols win because their payoff grows with n, even when any single custom integration is better.
- The shared structure is increasingly the program: pendulums, cells, and markets can all be written as code and thus talk to each other. Under the Curry–Howard correspondence a type is a proposition and a program is its proof — in Lean, mathematicians write theorems as programs refereed by the type checker.
- Dimensional analysis is type checking for the world program: adding meters to seconds is wrong the way a type error is wrong, not the way a miscalculation is.
The piece opens with Poincaré's line that mathematics is the art of giving the same name to different things.
More from AGI Musings
- People Building AI Are the Ones Most Afraid of It — cneuralnetwork · 2026-09-23
- Frontier models are flooding CVE queues — 90-day disclosure windows must shrink to 30 — chrisrohlf · 2026-09-23
- Education critic Benjamin Riley explains why he's not betting on Alpha School's future — benjaminjriley · 2026-09-23
- A data company's ARR jumped from $10M to $300M in 3 months as new frontier models shipped — menhguin · 2026-09-23
- An Idealistic Constitution for Human-AI Coexistence — lommelinn · 2026-09-23
- Where's the line? Author argues >80% AI-flagged writing should be disclosed as AI-written — soumitrashukla9 · 2026-09-23