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Published equation contexts

Fn=∏i=1nfiF_n = \prod_{i=1}^{n} f_i

Why this formula appears here

It is tempting to model manuscript transmission as pure decay. If fif_i is the probability that generation i of a copy reproduces a given passage faithfully, then fidelity after n generations of independent copying is Fn=∏i=1nfiF_n = \prod_{i=1}^{n} f_i. 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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ii

Symbol i

i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

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nn

Symbol n

n appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

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i=1i=1

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.

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nn

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.

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Published contexts (1)

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Fn=∏i=1nfi,F_n = \prod_{i=1}^{n} f_i,

Equation 4 · Writing & Information

Standardising the Record: How Writing Became Evidence

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

It is tempting to model manuscript transmission as pure decay. If fif_i is the probability that generation i of a copy reproduces a given passage faithfully, then fidelity after n generations of independent copying is Fn=∏i=1nfiF_n = \prod_{i=1}^{n} f_i. 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…

Meanings in this article

  • FnF_n: fidelity after n generations of independent copying.
  • fif_i: the probability that generation i of a copy reproduces a given passage faithfully.
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