$$C_n = C_0 \prod_{k=1}^{n} f_k + \sum_{k=1}^{n} i_k \prod_{j=k+1}^{n} f_j$$

Equation 2 · Cumulative Culture

Apprenticeship as Information Transfer

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A useful way to make the retention condition inspectable is to write the accumulated complexity after n transmission steps as a product of per-step fidelities plus whatever is added along the way: $C_n = C_0 \prod_{k=1}^{n} f_k + \sum_{k=1}^{n} i_k \prod_{j=k+1}^{n} f_j$. Here $C_0$ is the starting repertoire, $f_k$ is the fraction of it that survives step k , and $i_k$ is what is genuinely added at that step. This expression is illustrative rather than a result from any of the studies cited here, and it should not be mistaken for one. Its only job is to expose an assumption: because fidelities multiply, a small shortfall per step compounds, and later innovations are discounted by every fidelity term that follows them. Under this framing, raising…

Meanings in this article

• $C_0$: the starting repertoire.
• $f_k$: the fraction of it that survives step k.
• $i_k$: what is genuinely added at that step.

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