Equation 6 · When Generation Becomes Free, Attention Becomes the Scarce Good
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.
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Symbol V_t
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol G_t
the number of claims placed before some audience in period t , let be that audience’s total attention budget, and let be the average attention cost of verifying one claim.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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_v G_t
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
An accounting identity makes the consequence visible. Let be the number of claims placed before some audience in period t , let be that audience’s total attention budget, and let be the average attention cost of verifying one claim. The number of claims that can be verified, and the fraction of what arrives that is actually checked, are then . This is bookkeeping, not a finding. Its only content is what it forbids. Simon’s point was that is bounded by hours and by human processing capacity, and that this bound is not responsive to technology in the way that is. If rises by an order of magnitude, falls by an order of magnitude unless…
Read the full surrounding passage
An accounting identity makes the consequence visible. Let be the number of claims placed before some audience in period t , let be that audience’s total attention budget, and let be the average attention cost of verifying one claim. The number of claims that can be verified, and the fraction of what arrives that is actually checked, are then . This is bookkeeping, not a finding. Its only content is what it forbids. Simon’s point was that is bounded by hours and by human processing capacity, and that this bound is not responsive to technology in the way that is. If rises by an order of magnitude, falls by an order of magnitude unless falls proportionally or expands proportionally. Institutions are the mechanism by which societies have historically pushed on . Nothing pushes usefully on .
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