Equation 2 · Part 6 · Apprenticeship as Information Transfer

Symbol i_k

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

i_k

What this part means

what is genuinely added at that step.

Its job in the formula

$i_k$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol i_kArticle meaning

Where the article explains it

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.

The passage around this formula

…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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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