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Equation 1 · Part 6 · The Bandwidth of Culture: Transmission Fidelity to 2100

=

Ct+1=ρtCt+It−LtC_{t+1} = \rho_t C_t + I_t - L_t
=

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

A useful way to hold fidelity, bandwidth, and the machine-mediated layer in one place is a simple stock-and-flow account of a corpus’s cultural complexity — the accumulated stock of techniques, texts, and transmissible content a population (human, or now human-plus-model) actually carries forward. In its classical form, without any machine term, this recurrence says that next period’s complexity is this period’s complexity that survived transmission, plus whatever genuinely new content was added, minus whatever was lost to forgetting or to a shrinking population of transmitters: Ct+1=ρtCt+It−LtC_{t+1} = \rho_t C_t + I_t - L_t. Here CtC_t is the stock of cultural complexity in circulation at time t ; ρt\rho_t ∈\in [0,1] is…

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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.

Open the illustrated equality: what the equals sign claims guide →

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