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

What does this equation mean?

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}.

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.

Start withA_t
Divide byc_v
This relates toV_t
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

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.

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VtV_t

Symbol V_t

VtV_t occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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AtA_t

Symbol A_t

the nothing pushes usefully on.

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cvc_v

Symbol c_v

the historically pushed on.

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ϕt\phi_t

Symbol phi_t

the fraction.

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GtG_t

Symbol G_t

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.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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fraction

fraction

Divide the expression above the line by the one below it.

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subscript

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.

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cv Gtc_v \, G_t

Denominator: c_v G_t

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

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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

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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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 cvc_v falls proportionally or AtA_t expands proportionally. Institutions are the mechanism by which societies have historically pushed on cvc_v . Nothing pushes usefully on AtA_t .

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