Equation 3 · Apprenticeship as Information Transfer
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the starting repertoire. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
subscript
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What the article says around this equation
Here is the starting repertoire, is the fraction of it that survives step k , and 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 average fidelity does more for long-run complexity than raising the innovation rate — which is precisely the claim that the experimental literature has tried to test, and precisely the assumption that the demographic…
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Here is the starting repertoire, is the fraction of it that survives step k , and 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 average fidelity does more for long-run complexity than raising the innovation rate — which is precisely the claim that the experimental literature has tried to test, and precisely the assumption that the demographic models discussed later depend on.
Sources cited in the article section
- [1] What is cumulative cultural evolution? ↗
- [2] Ratcheting up the ratchet: on the evolution of cumulative culture ↗
These citations give research context. Read each source to check which claims it supports.