Equation 21 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale
Symbol τ
What this part means
τ 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
τ 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 τ→Article meaning
The passage around this formula
The middle term is the one that matters. It grows as n(n-1)/2 — quadratically in step count — while the other two terms grow only linearly. For a short loop, the quadratic term is negligible next to the fixed tax and the output cost. For a long one, it dominates completely, and no amount of shrinking or changes that; the loop’s own length has become the largest line item, all by itself.
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.
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Sources cited in the article section
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