Equation 13 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol pi_s
p is part of the quantity the equation computes from the expression on the right.
Symbol c_L
is one of the signed contributions combined to compute the quantity on the left.
Symbol s
s is part of the quantity the equation computes from the expression on the right.
Symbol c_A
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Denominator: c_L(s)
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
where is the baseline economic share of task s and = represents the proportional cost reduction achieved on that task [ 2 ] .
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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