Equation 32 · Part 1 · The Token Tax of Giving a Model More Tools
Symbol n
What this part means
n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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
The passage around this formula
…gives a short, honest account of where a tool protocol’s overhead actually lives. A single request pays a fixed tool-use tax the moment any tool is attached, plus roughly tokens for every one of the n tools visible in that request, repeated on every turn because the underlying inference API carries no memory between calls. Lazy discovery — Anthropic’s Tool Search Tool, or a disciplined use of MCP’s own paginated listing — replaces the n in that formula with a much smaller m , the tools…
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value guide →
See this notation across published equations →
The article lists its research sources here.