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Equation 14 · Part 7 · The Bandwidth of Culture: Transmission Fidelity to 2100

subtraction

ρt=ρh+(ρm−ρh) st,ρm<ρh\rho_t = \rho_h + (\rho_m - \rho_h)\, s_t, \qquad \rho_m < \rho_h
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

MtM_t is the net machine-mediated contribution: positive where model-assisted re-emission genuinely helps a human originator reach or refine an audience they could not otherwise reach, negative where it substitutes synthetic recombination for content that would otherwise have required, and thereby preserved, a human transmission chain. The mechanism Shumailov and colleagues describe operates by pulling ρt\rho_t itself down as the share of machine-mediated content in what gets re-ingested rises: ρt=ρh+(ρm−ρh) st,ρm<ρh\rho_t = \rho_h + (\rho_m - \rho_h)\, s_t, \qquad \rho_m < \rho_h. where ρh\rho_h is ordinary human-to-human transmission fidelity, ρm\rho_m is the fidelity of a machine-mediated re-emission — empirically lower per the tail-collapse result above — and…

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Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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