Engineering 101: Part VI - Error Distribution and Bell Curves

Scientists, especially in biological and statistical work with 'populations' continually find and make use of the 'Bell Curve'.

The Bell Curve is a typical pattern of population distribution, so typical in fact, that equations are used to plot it, and parameters are tweaked to align its contours with given data, fill out and predict unknowns, and predict expectations for future research.

By 'population', we mean any group of independent objects, like people, animals, items, measurements,  or even more abstract things like 'instances', 'examples', 'cases', elements, or anything that can be separated and distinguished as individuals, forming a group.  Bell curves are as frequent with abstractions as they are with physical objects.  The scales, parameters, coordinates can also be just about anything, and Bell-like curves will appear.

Almost any such group will exhibit some kind of  'Bell Curve' shape when plotted on a graph.  This strange coincidence is actually based on well-understood probability factors.  Simply put, there are more opportunities and chances for an individual to be somewhere in the middle of the scale than at the extremes.  Its easy to be average or mediocre.

Above, we will find that there are few really great copyists (near-perfect), and equally few really bad ones (they would be replaced).  We might find very few copyists making 30 or more errors per page, and equally few making 1 or less per page, while most copyists might score in the 5 or 10 errors per page range.

If we are simply observing raw error rates, these will be rather constant, with minor variations in certain times and places, depending upon training or copying methods.  This is important, for errors can be plotted over time.   If we imagine the copying stream as an ever-expanding fan, we may notice that the average density of errors will be rather constant, while the number of errors in each time-zone goes up, not only the total error-count:

We can modify this view to make it even more realistic, by allowing that early copyists produced more errors (i.e., a lower skill base), but this will be more than offset by the actual exponential (fibbonaci-like) growth of the manuscript count:

From this we can see that it will remain true that most raw errors will happen later in time, and not be early errors.   Why does this seem to contradict the recent acknowledgement by textual critics that in fact "most errors are early"?

The reason is that most errors are actually ignored, and critics only focus on a small subset of the actual errors found in the manuscripts.  For instance, most 'singular errors' (occuring in only once) are not even noticed or recorded.   Only readings that have an added 'life-line' (by being copied), or have support (they may have spread by coincidence or mixture) are generally discussed.  But this is not proper sampling, and gives a misleading picture of the history and spread of errors.


Now we enter into the most remarkable and subtle part of the analysis.  This will require the reader's careful attention and insight.

Those who advocate for the 'early readings' (Alexandrian) as a group as against the 'later' Majority readings (Byzantine) would say "Aha!  Most errors are late, and so the probability is therefore that most Byzantine readings are late, vindicating the antiquity of the Alexandrian text-type."

That conclusion however is a demonstrably false analysis: 

(1) The majority of errors are not majority readings.  These are two completely different groups of variants.    The majority of errors are in fact minority readings, and must be, by the nature of the case.  Most will have occurred very late in the copying stream, and cannot have had any opportunity whatsoever to become majority readings.  The true distribution of raw errors will indeed resemble the lopsided 'bell curve' below:

click to enlarge

 But the errors represented by this bell-curve will almost all be minority readings.

Perhaps even more importantly, the early errors represented here, may indeed be themselves majority readings, but they will not be the majority of majority readings.  They will be a small subset of the total number of majority readings. Most majority readings will not be errors, but rather will represent the correct text.

Furthermore, the small subset of early majority readings represented above, which may indeed be errors, will be clustered, each associated with some severe anomaly that caused them to become majority readings.  The competing clusters of variants (correct readings), especially those coming earlier in this one singular source (the archtype of the Byzantine transmission stream) will necessarily have been purged from all other copying streams.

The basic Byzantine text-type can be seen to have been in existence since the 5th century.  If that is so, then its unique "Majority" readings (whether errors or not) must have originated much earlier than this, to become dominant from this time onward, both in the Greek and Latin copying streams.

Click to Enlarge

The Majority readings of the Byzantine text, and the majority of errors (which again are found mostly in the Byzantine texts) are two completely different sets of variants (entities).

Contrary to uncritical expectations, the nature of the error-producing process and the spread of errors over time, prevent the bulk of errors from becoming majority readings, whether they are copied or not by future copyists.


- The Engineer

Engineering 101: The Receiver/Reader Impact

Much has been written about the potential for distortion of the signal by the reader/interpreter, in literary criticism circles.

But another very well-known technical phenomenon regarding the impact of the receiver of a transmission has found little awareness or discussion.    Lets look at the following transmission graph:

Transmission Signal vs. Background Noise Floor

The signal transmission begins, and the signal is clear and unambiguous (error-free, for all practical purposes).   But during periods of non-transmission, we can see the background random noise-floor rises up to a typical level.   What happens to the noise-floor during transmission?  How can it just disappear?

In fact, the background noise doesn't just disappear.  However, it is removed from the signal by processes which are only activated when the receiver of the signal is alerted and begins differentiating between noise and signal, effectively removing noise that would otherwise interfere or negatively impact the reception.

This is a very real effect, and is hard-wired into human perception.  It is linked to attention-span and attention-focus, and activates powerful information filters already designed into our input receptors.   If it were not for this advanced and largely uncontrolled, automatic function, we would be overwhelmed with non-essential and distracting information from all our senses.   But human beings are designed to automatically filter out distractions (background noise), detect and selectively concentrate on the signal of interest, in part chosen by the listener.

While mechanical and electronic filters are usually very primitive and crude, simply shutting down or stopping the flow of frequency ranges or patterns known to be "noise-full"  or "noise-like" (i.e., carrying noise), the human brain and itsprocesses are quite sophisticated and can be trained via pattern-matching and reasoning processes to intelligently and very effectively mask out unwanted noise from the signal.

As a result, humans are able to perform nearly 'super-human' feats of concentration, memory, and filtering that ordinary electronic devices are incapable of.  The analogy can be likened to imagining the difference between a person with good eyesight and lighting, versus a blind person, in attempting to do the dishes, or drive a car.  Even in such a simple and usually easy task, the trained eye is a powerful and essential tool, changing what is nearly impossible   (for the blind person) into a virtually error-free operation.


The key component here is not the "background noise level" facing the transmitter of the message, but the amazingly gifted ability of the receiver, who can have quite fantastic powers to filter out noise and errors in the process of transmission.   These powers are based on extremely intelligent and sophisticated processes possessed by the receiver, and enable very crude and primitive transmissions to be very successful with a high accuracy, frequency and duration.


- Joe Layman

Engineering 101: The Nature of a Transmission Signal

At the very basic level, each individual manuscript, and the entire transmission stream as a whole, can be viewed as a transmission-signal. This can be broadly represented by an instructive graph:

Click to Enlarge - use backbutton to return here

Although the information content may be pre-decided, or fixed in advance, like a snap-shot or finished writing, the transmission process in most cases will still be sequential, and involve a process extending over time, like the act of copying or a radio broadcast.   The nature of this transmission process is such that the information must be broken down into packets and transmitted piece by piece, both in ancient times and even in the modern digital age.

This process actually works in favor of inerrancy in the overview.   For instance, a Gospel will normally be broken down into 'pericopes' or paragraphs, each of which is complete and functional in terms of carrying its information content.   If a Gospel breaks down into say 40 paragraphs or Units, 39 of them can still be transmitted successfully, even if one suffers loss or damage.    With parallel or redundant copies or transmissions, the entire 40 units can still be transmitted without error, even if every individual copy (or set of units) suffers some hits.

Making a significant number of good copies of a document, even by hand, ensures the essential integrity of the information and the accuracy of the text as a whole, provided all or a reasonably good sample of the copies is preserved and used to establish the text.

It is perhaps surprising but not totally unexpected, that a message can be fully preserved, even with such a simple mechanism as reasonably careful copying.  The idea is very simple in fact.  With reasonably good copying, it is unlikely that two copies will have the very same errors.  Even if two copyists occasionally make the same mistake, this mistake will remain a very small minority reading.

Some good statistical discussion of this issue can be found in Pickering's Online book, in an appendix here:

Appendix C: The Implications of Statistical Probability

The best technique to ensure error-free transmission is in fact the simplest:

(1) Multiply Good Copies: Make as many good copies as possible of each document,
(2) Minimize Copy Generations: Always start as close to the original as possible.
(3) Preserve Adequate Samples: Keep a good number of MSS available,  or at least recoverable, at the end of the transmission process.
(4) Avoid Emendations: Resist the temptation to 'correct' or edit the text, but duplicate as accurately as possible what is found in your master-copy.

That is, all that is required is to make say 3 or more copies of each copy,  and preserve a good representative sample of the same collection of copies.   The technique is surprisingly robust, even without special methods or techniques to improve accuracy.   Any well-executed application of this basic method will create what may be reasonably labelled a "bullet-proof" transmission.

What is perhaps remarkable, but goes unnoticed, is that what is true for hand-copying manuscripts is also true for printed edited texts!   This is because the same rules govern any transmission process.  Any critical text which breaks these basic rules will inevitably introduce errors into the transmission process.  Examples of such cases are these:

(1) Failing to rely on adequate samples of available manuscripts.

(2) Making conjectural emendations without statistical foundation in the surviving copies.

We will examine the special cases in which a transmission may go awry later, and also simple and reasonable techniques for countering information loss and correcting the transmission process.

Joe Layman

Happy New Year, and Congrats!

Congratulations to all the posters, contributors and commentators here at the KJVOnly2 blog.

We have managed to bust 1,000 views by interested people, which must be a first. That makes us about twice as popular as Nazaroo's own blog, and possibly more than his and Mr. Scrivener's combined (snicker).

But I think the popularity has to do with the subject matter and the high quality of the articles being posted.

Keep up the good work!

Looking forward to a productive new year.

Sincerely,
Joe Layman

Manuscript Production

I enjoyed Mr. Scrivener's monologue on geneaological charting. It inspired me to create this diagram which attempts to show probable production in rough numbers, the various 'text-types' (more like textual streams, allowing for some mixture).

(Click on image to enlarge it)

As noted, displaying information in a new form can lead to insight, sometimes a profound one.

The first thing one tends to ask on viewing this chart, is "why?". Why did we have a heterogeneous collection of 'text-types', and how did it miraculously come to be under control and dominance of a single type? The answer that there was a "Lucian Recension" is simply inadequate.

Some conscious policy must have been instituted, and it must have been so reasonable and transparent, that it caused no real protests or fuss among the many hundreds of scriptoriums ( manuscript-making centers) spread across the two Empires (East and also West).

We include the West here, although the predominate language and copying centers worked in Latin for the most part of the 4th to 14th centuries, because the Latin text has a strikingly similar pattern: Some mixed texts, followed by an 'official recension' (Jerome's Vulgate, c. 400 A.D.), and rather rapid increase in numbers (finally up to 20,000 copies of later Latin MSS), with inevitable dominance (with some reversions/corrections back to the Old Latin & Greek texts).

The early history of Jerome's Vulgate is somewhat instructive, in that it faced strong opposition in some places over some changes of text (notably his abandoning of the LXX Greek O.T. readings for those of the 4th century Massoretic Hebrew text). Jerome's handling of the NT was not so extreme, although it was plainly well-researched, since to make his Latin translation, he went to Constantinople, the center of the Eastern Greek copying stream, to get good manuscripts. He claims he himself bypassed all three of the then popular Greek recensions, namely Origen's Hesychius' and Lucian's texts, each popular in their own local center of production.

Yet the Greek standardization was not an 'official' text, or imposed from the top-down. There is no record of any official policy among the Greeks, or in the Eastern Empire regarding an official text. What we do know is that in some cases, Constantine and Eusebius proposed special policies of translation into other languages, such as the Gothic, holding back for instance the Books of the Kings, because Constantine felt that the Goths were too warlike already, and this would only encourage them.

The kind of policy which would have a strong impact on the textual stream, and yet go completely unchronicled in the history of the church, must have been a simple policy that could and would be implemented by every scribe without even questioning the logic of it. The policy had to be self-evident and not only draw no resistance, but draw no comment.

It had to be a simple 'copying policy', one that was something trivially mechanical in nature and so self-evident once seen that no scribe would want to do anything else.

To meet these plausibility requirements, the policy had to include the 'oldest and best manuscripts' available at the time, in all areas. It had to include a mechanical procedure that would guarantee a new homogenization of the text to an unprecedented degree.

I suggest some combination of the obvious. Somebody proposed that all scriptoriums from now on, adopt an 'offical master-copy' (or small subset of copies, however created or chosen), and use them and them only for the next 500 years. This would naturally require no great news flashes or raise any eyebrows of protest, because of its innate reasonableness.

This suggestion, or rather adopted practice, quickly transferred from scriptorium to scriptorium, because the idea traveled alongside good copies. It would spread across Europe, at least to the major centers of production, and result in a new order of homogenized text.

While total conformity would not be possible, because of local variations in quality, the end result would indeed be a large quantity of later MSS presenting a tight, uniform text (relative to previous circumstances).

In order to meet the historical criteria of a grassroots, non-discussed trend, it would naturally involve the best available manuscripts, and this suggests that contrary to popular characterizations of the Byzantine text, it was indeed a fairly good, naturally created text based on ancient manuscripts.

Joe Layman

Engineering 101: Differences in Transmission Quality

Referring back to my first post (Dec 6), Lets look closer at the two main transmission lines, or text-types:

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The Byzantine Transmission

The Byzantine is represented in full only by the vast majority of later copies, of various origins, ranging from the 4th century to the 14th century, and also with partial support from early writers and versions, but with little or partial support from the earliest surviving manuscripts.

The very existance of this tight, coherent Byzantine text-type points to a clean, relatively error-free transmission process.

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The Alexandrian Transmission

The Alexandrian is represented by a handful of 3rd and 4th century manuscripts, and partially supported by readings from early NT writers and versions.

It is this loose and wild Alexandrian cluster of manuscripts and readings that suggests a 'dirty transmission'.

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From a transmission process point of view, the Westcott/Hort position goes against common sense, and the agreed-upon state of the manuscript evidence. Based on the transmission evidence, the Byzantine is the purer signal transmission, and the Alexandrian clusters and other groups are the relatively error-prone and 'dirty' signals.

To overcome this basic scientific observation, some kind of 'special pleading' is necessary.

Hort's followers propose a 'catastrophic event', namely an early recension, to explain how the clean transmission-line could have the most distorted signal. Its essentially a "pre-emptive strike" upon the message (circa 300 A.D.), before the 'clean signal' transmission begins. They make a complimentary claim that the 'true readings' can be easily recovered from the 'dirty signal', in spite of the widespread errors in the Alexandrian manuscripts, because of a few "oldest and best" copies (Aleph/B).

The Defenders of the Traditional Text reject the idea of any wholesale and successful recension, pointing to very real attempts like those of Jerome (the Latin Vulgate, c. 400 A.D.), which were based on good early exemplars (older than Aleph/B), or even earlier ones like Lucian, Hesychius, and Origen, which were simply unsuccessful in dominating the many independent copying streams. They would accept the transmission-line evidence at face-value, granting the Byzantine text greater likelihood of reaching back earlier to the original, and assuming the agreements between Aleph/B are simply "agreements in error" pointing to a common (corrupt) early 2nd century ancestor.

Only a careful examination of the key significant differences between the two texts (Traditional and Aleph/B) can determine which view, if either, is the more accurate model of what really must have happened.

This is precisely where Nazaroo's 70 homoeoteleuton examples (or even the 50 best of them) come to bear on the problem. These constitute at least a third of the significant differences (some 200 omissions) between them. They suggest that certainly in these cases, the Aleph/B text is severely corrupted. The plain conclusion is that in the other cases also, the corruption of the Alexandrian text must be strongly suspected.

- The Engineer

Engineering 101: The Basic Mechanism of Transmission

One of the startling things about the textual evidence is the vast difference in quality and quantity in the textual support for essentially two competing text-types, Alexandrian and Byzantine.

The Alexandrian is represented by a handful of 3rd and 4th century manuscripts, and partially supported by readings from early NT writers and versions.

The Byzantine is represented in full only by the vast majority of later copies, of various origins, ranging from the 4th century to the 14th century, and also with partial support from early writers and versions, but with little or partial support from the earliest surviving manuscripts.

How did this peculiar situation come to pass?


A Data Transmission Problem:

All textual critics seem to agree on the basic processes involved in the historical transmission of the text (hand-copying):

1) bifurcation (isolation and splitting into local texts)
2) divergence (independent insertions, substitutions and omissions)
3) mixture (corrections, cross-pollination between competing text-types)
4) evolution (updating of grammar, style,vocabulary)
5) data loss (individual copies inevitably containing errors)

These factors however, do nothing to explain the actual situation as found in the surviving manuscripts. None of the basic sub-processes above predict the formation of special, pure dead lines in special "pockets" of early manuscripts and the simultaneous failure of the majority of copies to preserve the readings.

As a result, textual critics diverge on just how much data loss occurred and where this data loss happened in various stages of transmission, and consequently how to evaluate the surviving evidences.

Some are optimistic that the essential message of the NT is preserved in its entirety among the multitude of witnesses to the text, in spite of individual errors and minor corruption throughout the manuscript corpus. In this view, the early manuscripts may reflect an unfortunate 'wildness' of text in some quarters, but that such inconsistent witnesses and the minority readings they contain have little real weight in the big scheme of textual transmission.

Others are skeptical and doubt that the true text can be found in the mass of witnesses. They feel rather that substantial corruption took place, and that the "true readings" will be found in a minority of surviving ancient manuscripts from dead transmission-lines, in particular the Alexandrian texts.

The case then boils down to this: Alexandrian or Byzantine. No serious textual critic suggests any other candidates for the original or early text. The whole debate is over the specific differences between the two basic text-types, and this is obvious from the two basic 'critical texts' offered by text-critical parties.

Although there are other early 'text-types' (like the 'Western') and other early witnesses (e.g. the Old Latin version), no large parties of textual critics are backing other horses.

Introduction - The King James Version Debate

We felt that the KJVOnly? Debate was very successful, and generated much intellectual discussion and interest. The only problem was, the pro-KJV camp(s) were a bit outflanked and left rather powerless when it came to refereeing the debates.

In the interests of fairness, we have invited several pro-Traditional text debaters to post their own articles freely, and let the chips fall where they may. This should prevent any charges of bias or censorship on the administrative side, and any also any blame or excuse for unconvincing arguments or failed communications.

Sincerely, Joe Layman.