Equation 2 · Part 1 · How AI Models Learned to Use Tools: A Protocol History
Symbol N
What this part means
both large and still growing, the gap between M N and M + N dominates every other consideration.
Its job in the formula
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol N→Article meaning
Where the article explains it
When M and N are both large and still growing, the gap between M N and M + N dominates every other consideration; when either is small — a single application talking to a handful of tools it controls — a bespoke integration can still be cheaper than adopting a shared protocol at all, and treating standardization as free in that case would be cargo-culting rather than economizing.
The passage around this formula
That parallel is precise enough to formalize, and doing so exposes the actual economic assumption both protocols are making rather than merely asserting it. Let M be the number of distinct hosts — editors, for LSP; agent frameworks and model-serving applications, for MCP — and N be the number of distinct targets — languages, for LSP; tools and data sources, for MCP. Wiring every host to every target independently, the way plugins and early framework wrappers did, requires
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Sources cited in the article section
- [10] Introducing the Model Context Protocol ↗
- [11] Specification ↗
- [12] JSON-RPC 2.0 Specification ↗
- [13] Language Server Protocol ↗
These citations provide research context; check each source for the exact claim it supports.