Testing the structure/page link
Scope
In most cases the structure/page link verification has been applied to single archetypes. However in the case of the three original archetypes behind 2 Corinthians, and the three original archetypes behind Philippians, there is not enough data in some of them to treat them all individually. Therefore for testing purposes each set of three archetypes has been treated as a single unit.
[1]
1 Timothy, 2 Timothy and Titus were not real letters. I have labelled them 'The Pastorals', but originally they were written together on a codex. This was essentially a pseudonymous tract masquerading as three genuine letters of Paul in the sequence: 1 Timothy, Titus, 2 Timothy.
Application
My twenty structure/page arrangements based on the documents in the table have all passed the three tests set out below.
| Matthew |
Romans |
Philippians |
James |
| Mark |
1 Corinthians |
Colossians |
1 Peter |
| LukeEdn1 |
2 Corinthians |
1 Thessalonians |
2 Peter |
| JohnEdn1 |
Galatians |
The Pastorals |
1 John |
| Acts |
Ephesians |
Hebrews |
RevEdn1 |
Definitions
tot_letters = total mumber of Greek letters in the archetype
pp_in_model = posited number of pages allocated for the archetype
mean_lsperp = tot_letters / pp_in_model
base_sectns = number of base sections in the hierarchical structure
deg_freedom = base_sectns - 1
mean_letdev = mean deviation of such sections from the model
[2]
worst_letdev = worst deviation of the base sections from the model
Formulae devised for testing
mean_lsperp
ρ = --------------
4*mean_letdev
worst_letdev
ξ = ------------
mean_lsperp
deg_freedom * base_sectns
η = --------------------------
pp_in_model
How I verified the structure/page links
There were three basic tests for each structure/page arrangement. The first two test the accuracy of a link and the third tests the firmness of a link.
- ρ >= 4
- ξ <= 0.125
- η >= 6
How my verification is related to tests the original author/scribe might have carried out
The ξ test could easily have been a self-imposed constraint for the writers/scribes of the NT archetypes. The 'pass mark' represents 1/8 of a page. For example for an early manuscript, if they penned a typical 25 letters to a line and wrote 24 lines per page, then 1/8 page would have represented 3 lines. For a codex, where a section boundary would have been intentionally close to a page boundary, the writer/scribe would have known to make each section boundary within three lines of the designated page boundary.
The arithmetic involved in the ρ test would have been far too cumbersome in pre-computer days. But of course a high ρ would have occurred naturally as a result of ensuring a low ξ.
The η test would also probably have been too cumbersome. However it happens that the condition η >= 6 would have been achieved incidentally in most if not all of the single-archetype arrangements if the author/scribe had followed a rule which required at least 7 single-page sections in his planned structure.
Notes
1.
More than twenty years ago I had found that all six of these smaller letters appeared to have had close to 800 letters to the page.
2.
Given the idea that a writer/scribe could have planned his space usage by allocating one or more pages to each base section, there are two slightly different ways in which this could have been implemented.
In separate section mode, when near to the end of a section and therefore near to the end of a page, the writer/scribe would be able to finish the section and the page with a few more or a few less lines than he would have done had there been no constraint.
letdif = ABS( lets_in_sectn - (no_of_pages_in_section * mean_lsperp) )
mean_letdev = SUM(letdif) / base_sectns
Guideline mode involves assessing the cumulative letter count from the beginning of the document to the end of each base section except the last (where the deviation is taken to be zero and is therefore not counted):
letdif = ABS( tot_lets_to_sectn_end - ( tot_pp_to_sectn_end * mean_lsperp ) )
mean_letdev = ( SUM(letdif) ) / deg_freedom