Sunday, May 8, 2011

Majority Text (VIII): Cross-Pollenation - Correction and Mixture

It has been claimed in the past that the problem of "mixture", (the correction of manuscripts and copying of readings across genealogical lines) negates or destroys any genealogical arguments and claims.

This is simply not true, and shows a poor understanding of the real effects of such activity.   Consider first of all, the simple act of double-checking, proof-reading a copy, against its own master-copy.  This action will very rarely introduce further errors, but most often and quite frequently will simply correct copying mistakes from the 'first pass'.    The effect of error-checking and correction is quite predictable:  The rate of accumulation of errors is drastically reduced.

Error-correction has the main effect of severely retarding any corruption over copying generations, and greatly extending the staying-power of the original readings;  error-checking always increases the percentage score of any and every majority reading (i.e., correct reading).

What happens, however with true "mixture", where readings cross into parallel transmission lines?  The answer is similar, but has an added complexity:

Transmission Model with MIXTURE (click to enlarge)
"Mixture" occurs when a manuscript is corrected from some other copy not involved in or descended from its own transmission branch.   This happens just as in ordinary correction, but now, readings not found in the master-copy can enter into the manuscript and continue in the copying stream.

In the above diagram, blue lines indicate "successful" corrections, that is, cases where the corrector was himself correct in making the change.  Red lines show places where an incorrect reading was copied into a manuscript that originally had the correct one.   We have allowed that good corrections will occur slightly more often than bad ones, which is a reasonable expectation.

On the top-right, a copy containing the Green Packet gets corrected from a very old copy, and has its "Green" readings restored (it now becomes white).  This is one of the most likely scenarios, since early copyists will naturally assume older manuscripts are more accurate (just like modern critics do!).  As a result, the "Green Packet" loses many votes that would have accumulated from this copy.  The errors become even smaller minority readings.   Now we allow a Yellow Packet  to be 'corrected' by a faulty Green Packet, which now carries both Yellow and Green errors.  This will not compensate for the loss of an earlier Green Packet, because it comes later.   It fathers instead a peculiar minority 'text-type' or family with mixed readings.

Now on the left side, an early mistake is made: a Yellow Packet copy is 'corrected' by an Orange Packet copy, resulting in a boost of Orange Packet readings.   The Yellow Packet readings are unaffected.  Even if this corrupted copy is recopied twice more (not shown), The Orange Packet manuscripts will only amount to 10 copies out of 26 (38% up 5% from 33%), staying minority readings.

Correcting a Red Packet copy using an Orange Packet copy does nothing for Orange readings however!  In this case, the Red Packet readings decrease, but the Orange readings were already in this copy, so there are no gains.  Its only the Red readings that get corrected.   Since this is more likely than not (similar copies will be in similar geographic regions), minority readings will lose out more than half the time.  In this case, "Mixture" has only purified the transmission stream, and this is actually the most common scenario, even when correcting from diverse copies.

Again, when an Orange Packet copy is corrected by a Yellow Packet, the only net result is purification of the copying stream.   The errors in the Yellow Packet are already present in the Orange copy and no correction is made there.  Only Orange readings are removed.   It is perfectly reasonable and effective to correct a copy from another copy with errors.   The average result will not be any increase in errors, but usually only an exchange, with as many Error Packets getting corrected as there are Error Packets getting perpetuated.

The error-count within an Error-Packet is not relevant here (i.e., the 'size' of the Error Packet).   Of course Error Packets can be of different sizes and degrees of seriousness.    But they can only be transmitted manuscript to manuscript in groups, and each act of copying a manuscript must be treated as a single discrete event.  We cannot switch back and forth between Error-Packets and errors within a packet indiscriminately, as this would violate proper analysis of the error transmission process.

Again as in the non-Mixture model, varying copying rates only moderately affect minority readings, mostly in a random fashion and not with the consistency needed to cause minority readings to become majority readings.

(to be continued...)


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