Tuesday, April 19, 2011

Majority Text: True Power of the Probability Argument (pt III)

...Finishing off Hort
Before moving into a proper discussion of the Majority Reading Probability Model, we would like to finish off our discussion of some of Hort's assertions in the previous post. 
Hort insisted that 'majority readings' were only valid when it came to singular readings (with only 1 or 2 witnesses in support), because only these could in his view be almost certainly identified as errors by the actual scribe of the surviving manuscript.  But the line isn't anywhere near so clear and easy as this.

(1)  Many accidental omissions avoid detection because the text still makes sense, and the lost content isn't critical to the text.  Dittography errors (accidental repetitions) by contrast are easy to spot, and quickly and easily repaired.   As a result, omissions were copied repeatedly, since the most common error-correction was done against the very same master-copy with the errors.  

(2)  Many accidental errors were copied because of lax error-correction, especially in early times, before standardized practices were developed.  This helps explain why so many errors are very early. 

(3)  Many errors would be mistaken for the correct text, and would invade other copying streams through cross-correction and mixture.   As a result, often diverse copies can attest to rare minority readings. 

(4)  Some omissions of key material would make that material appear to be a deliberate addition for doctrinal purposes, and cause correctors to prefer the omission.

(5)  Some areas of the text were prone to accidental error from stretches of similar words, giving independent copyists many opportunities to make the exact same errors:

Click to Enlarge
(6) Many minority readings would have originated as singular readings in previous copies, and there is no reason to treat scribes whose work is now known only through copies differently than scribes we can directly access.  A large number of minority readings will have the same features and probable causes as singular readings, and to refuse to apply our knowledge of scribal habits to non-singular readings is not sensible.  

Accepting only singular readings is a good skeptical methodology when assessing both an individual scribe and gathering data on general scribal tendencies.   But once knowledge of scribal tendencies can be generalized, it needs to be applied to all parts of the copying stream, including ancestors and lost exemplars behind surviving documents.   

Because of all these well-known factors, extreme minority readings cannot be ignored simply because they are not 'singular'.  Variety and quantity of independent attestation to a reading still counts as an important factor in evaluating variants. 

Factors that Further Enhance the Probability Argument 
for Majority Readings

Before we critique the Probability argument, it is important to look at other well-known and understood factors that uniformly increase the reliability of the majority reading.

In the original model, we showed minimal manuscript reproduction.  Each manuscript was only copied twice.   In the Hodge's original illustrations, they actually used a reproduction rate of 3 copies per master.  "each MS was copied three times, as in other generations..." (App. C, p. 162, footnote - online version).

Both of these rates however are extremely low and unrealistic.   In practice, it is almost certain that master-copies would usually be copied far more than just 2 or 3 times.  A good master-copy might be used dozens, or even scores of times over many years, until worn out or destroyed:

The result of actual practice will be a much bushier tree than the commonly  seen binary branches of simplified models.

 Nonetheless, sparse trees with low reproduction rates can represent a "worst case" scenario to test the robustness of the model.  Consider the following model tree, with a few enhancements (4 copy generations, 30 copies):

Click to Enlarge

Here we've chosen a start-rate of about 3 copies per master (2 generations), followed by a slow-down (3rd generation), slightly less than 3 per master, and finally  2 copies per master (4th generation).   We have also allowed that some copies will be dead-ends, and not copied at all.  This is a much more realistic picture of the probable beginnings of a copying run.  

Error Packets:

Multiple errors are added to a large book when copied; however, we can treat these as a single "Error Packet" which will now be transported in bulk from copy to copy, once obvious errors are caught.   This packet will infect all future copies down the line.  Above, the Yellow Packet (2nd generation error) has passed to 8 copies (8/31 = 26%).  The Red Packet, (3rd generation) has only spread to 3 copies (3/31 = 10%).   These low percentages show good reliabilty in the percentage indicators, providing basic conditions have held (moderately close copying rates in each generation).   A 4th generation error would drop to a 3% minority reading.

Varying Copy-Rates:

Even significantly retarding the copying rate in following generations has not affected the basic result.  The early 'dead-end' copies in fact could be connected almost anywhere.  A strict rate of 2 copies per master would have put them under the middle two (uncopied) 3rd generation copies.    The white uninfected copies could be arranged in almost any independent manner, with the same result.  This shows the robustness of the model even with varying copy-rates.  A steadier copy-rate would have actually lowered the Yellow Packet score further to about 22% (a 4% loss in votes). 

In fact it is difficult to force the MS support of an Error Packet high enough to mislead.  Most random fluctuations in the copying stream do not enhance MS counts for Error Packets, but lower them further.  Since there are almost infinite combinations of such 'negative' events possible, and relatively few 'beneficial' variations that would cause a significantly high 'false positive', the odds are greatly against an Error Packet achieving a majority vote in a random, undirected process.
  Most often, even significant and very 'lucky' anomalies in the copying process will not affect the count enough to turn an Error Packet into a 'Majority Reading'.   Thus not only will all negative and 'neutral' variations leave Error Packets with low scores, so will positive variations that don't score high enough.  Most equally probable random variations then will leave Error Packets as minority readings.
 This is important, for it means that only a directed process, (e.g., a deliberately manipulated copying stream) could result in Error Packets becoming Majority readings.

(to be continued...)


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