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Equation 7 · How AI Models Learned to Use Tools: A Protocol History

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M×NM \times N

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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MM

Symbol M

the when.

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NN

Symbol N

both large and still growing, the gap between M ×\times N and M + N dominates every other consideration.

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multiplication

multiplication

Multiply the quantities on either side.

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What the article says around this equation

The assumption a shared protocol is betting on is that the fixed cost of building and maintaining the standard itself is smaller than the integrations it removes, and that those removed integrations were genuinely redundant rather than differently necessary. When M and N are both large and still growing, the gap between M ×\times 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.

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