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Equation 6 · Part 9 · When Generation Becomes Free, Attention Becomes the Scarce Good

Denominator: c_v G_t

Vt  =  Atcv,ϕt  =  VtGt  =  Atcv Gt.V_t \;=\; \frac{A_t}{c_v}, \qquad \phi_t \;=\; \frac{V_t}{G_t} \;=\; \frac{A_t}{c_v \, G_t}.
cv Gtc_v \, G_t

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

cvc_v GtG_t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

An accounting identity makes the consequence visible. Let GtG_t be the number of claims placed before some audience in period t , let AtA_t be that audience’s total attention budget, and let cvc_v be the average attention cost of verifying one claim. The number of claims that can be verified, and the fraction ϕt\phi_t of what arrives that is actually checked, are then Vt  =  Atcv,ϕt  =  VtGt  =  Atcv GtV_t \;=\; \frac{A_t}{c_v}, \qquad \phi_t \;=\; \frac{V_t}{G_t} \;=\; \frac{A_t}{c_v \, G_t}. This is bookkeeping, not a finding. Its only content is what it forbids. Simon’s point was that AtA_t is bounded by hours and by human processing capacity, and that this bound is not responsive to technology in the way that GtG_t is. If GtG_t rises by an order of magnitude, ϕt\phi_t falls by an order of magnitude unless…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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