Equation 4 · Standardising the Record: How Writing Became Evidence
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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 i
i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Symbol n
n appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Symbol f_i
the probability that generation i of a copy reproduces a given passage faithfully.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →Starting index or lower bound: i=1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Ending index or upper bound: n
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
It is tempting to model manuscript transmission as pure decay. If is the probability that generation i of a copy reproduces a given passage faithfully, then fidelity after n generations of independent copying is . which for any constant per-generation fidelity below one falls exponentially in n . The model is illustrative and its value lies in the assumption it exposes rather than in any number it produces. It assumes errors accumulate independently and are never removed. The correction apparatus is exactly the violation of that assumption: a corrector comparing a copy against another exemplar can subtract error as well as add it, which is why long manuscript…
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It is tempting to model manuscript transmission as pure decay. If is the probability that generation i of a copy reproduces a given passage faithfully, then fidelity after n generations of independent copying is . which for any constant per-generation fidelity below one falls exponentially in n . The model is illustrative and its value lies in the assumption it exposes rather than in any number it produces. It assumes errors accumulate independently and are never removed. The correction apparatus is exactly the violation of that assumption: a corrector comparing a copy against another exemplar can subtract error as well as add it, which is why long manuscript traditions do not simply dissolve. Where the assumption does hold — where a single exemplar is copied without collation — the exponential intuition is closer to right. The historical variable that matters is therefore not copying rate but access to independent witnesses.
Sources cited in the article section
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