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Equation 3 · Part 5 · How AI Models Learned to Use Tools: A Protocol History

multiplication

Cbespoke=M×NC_{\text{bespoke}} = M \times N
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

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 Cbespoke=M×NC_{\text{bespoke}} = M \times N. separate integrations, because nothing built for one pair transfers to any other. A protocol that both sides implement exactly once instead collapses this to

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.