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Equation 14 · Part 5 · The Bandwidth of Culture: Transmission Fidelity to 2100

=

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

What this part means

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

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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