Equation 41 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale
Symbol m^2
What this part means
the square of m; the number of steps.
Its job in the formula
is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.
Full expression→Symbol m^2→Article meaning
Where the article explains it
Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic.
The passage around this formula
…history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic. The summarization step itself is not free — reading through a full segment once to compress it costs roughly what one…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.