Equation 1 · The Bandwidth of Culture: Transmission Fidelity to 2100
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol C_t+1
+1 is the next indexed value. The formula starts from and applies the additions and subtractions shown on the right.
Symbol rho_t
rh is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
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: . Here is the stock of cultural complexity in circulation at time t ; [0,1] is…
Read the full surrounding passage
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: . Here is the stock of cultural complexity in circulation at time t ; [0,1] is the transmission-fidelity coefficient — the share of that survives one round of copying, the same quantity Henrich’s Tasmania case shows collapsing when the effective transmitting population shrinks; is genuinely new human innovation entering the pool; and is loss from forgetting, obsolescence, or population decline. This is the formal skeleton underneath everything in the two sections above: print and the internet acted mainly by raising and the volume can reach an audience with; the telegraph and broadcast acted mainly by collapsing the delay between an addition to and its arrival everywhere else in the network.
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