Saturday, April 23, 2011

Majority Text: The True Power of IMPOSSIBILITY (pt VI)

In the last post, we looked at the exploding growth of unlikelyhood of a sequence of individually unlikely events.   Specifically, in a copying series, we considered Error-Packets added generation by generation.

We discovered that even though the Error-Packets were 'independent' in some sense, the best-case scenario would be like a series of independent coin-tosses.  The chances of an unlucky circumstance falsely favoring a minority reading more than a few times in a row was progressively more and more unlikely.

Mutually Exclusive Events are Impossible, not Improbable!

But now we are going to look more closely at the situation, and discover something far more fatal to the theory of a build-up of minority readings: 
Accumulated groups of readings cannot occupy majority positions.

Consider the following diagram, much more realistic, but also potentially dangerously favoring minority readings:

The first Error-Packet A introduced in first-generation copy # 10 here, is multiplied, because it is chosen as a master-copy.   For our purposes, we may allow that most other first-generation copies (#0 - 255) are simply destroyed by the Romans.  Now the Error-Packet is found in an undisputed majority (80% or more) of manuscripts. 

But now by definition and premise, copy # 10 must also be multiplied greatly, and its copies must stay in the copy-stream and be copied themselves, perpetually and in high numbers.  This is exactly what will allow Error Packet A to continue holding its majority-reading position.   If those too are destroyed, they were copied for nothing, and  Error Packet A effectively drops off the face of the earth, while copies without it carry on.

But now consider Error-Packet B, in second-generation copy # 1:  We want it also to become a Majority Reading.  But this is impossible, without destroying most other copies made from copy #10.   That is, if we again use the same trick, and multiply copies of manuscript #1 to beef up its readings down the line, and destroy the competing lines from copy #10, we have actually contradicted ourselves.  Because the whole purpose of multiplying copies of copy #10 was to provide a high manuscript count, by keeping them in the copying stream and having them continually multiply in excess of all others. 
In order to boost Error-Packet B, we have to abandon boosting other copies of Error-Packet A.   We want to boost both Error-Packets, so we can only boost copies of second generation copy #1, which contains both Error-Packets.
But this means all the extra copies of earlier generations in this line must be suppressed: either not copied, or else destroyed.  The net effect of this strategy will indeed guarantee that each error will be a majority reading, and all copies will support all Error-Packets equally.  But now the fans of copies from each previous generation are erased, and we are only allowed one copy in each generation! 
Errors Accumulate in a sequential series, not a branching stream
 In order to keep each new error in a majority position, we have to prevent all fanning of generations.  Only the key stream can be perpetuated, and only the final copy can be multiplied.   Early branching is simply not allowed in significant numbers.

Even here however, most errors can be identified and removed, without comparing manuscripts to independent lines, by the manuscript count!  Early errors will be majority readings, but most errors, and especially later errors, will be minority readings.

It is trivially true that any copy down the line will have accumulated errors from multiple generations.  And it is also trivially true that only copies along this line will have all the errors we are accumulating.  But it is also true that even now, even with a completely pruned genealogical tree, we still can't get evenly distributed errors as majority readings.   The later errors will simply not be present in the earlier copies.  The only genealogical tree which allows the majority of errors to become majority readings is as follows:

 This scenario is the only 'catastrophe' that can possibly generate a large number of errors as false majority readings, and only those errors in the copying line can become majority readings.   Two simultaneous events must occur:

(1)  Most previous copies must be destroyed, to remove good readings.

(2)  Copies must be mass-produced only at the final stage of transmission.

This is what the modern critical model is really proposing. 


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