University of Virginia Library

The Analysis of Open Traditions
by
Michael Weitzman

1. Stemmatic analysis and its aims.

1.1. The stemmatic method involves the following assumptions:

• (i) the author nowhere left variant readings;
• (ii) every manuscript (except the original) was copied from a single source;
• (iii) no two copyists originated the same error independently;
• (iv) errors were not removed by conjecture;
• (v) every relevant manuscript (i.e. a manuscript that survives or leaves extant progeny) except the original introduced at least one new error, at a point where no relevant manuscript had yet erred;
• (vi) of the errors introduced by a given relevant manuscript, at least one can be identified by critics as an error.

These assumptions concern the original (i), the genealogy (ii), scribal behaviour (iii-v), the length of the text analysed (v) and the investigator's judgment (vi). Assumptions (v) and (vi) can usually be relaxed but never wholly dropped.[1]

In any passage where the manuscripts are divided between the truth and one false reading, the set of manuscripts presenting the false reading may be termed the "error set". On the above assumptions, the error is due to an ancestor[2] common and exclusive to the error set. In two passages that exhibit different error sets, consider the relationship between the two ancestors responsible. Either one derives from the other, or they are collateral. In the former case, the error set due to the earlier ancestor

includes the whole error set due to the later ancestor. In the latter case, the two error sets have no manuscript in common. Two error sets are therefore called "consistent" either if one includes the other or if they share no manuscript.[3]

From a series of mutually consistent error sets, the stemma is reconstructed thus. We list all the manuscripts across the page, and arrange the error sets underneath, so that any error set(s) contained in a larger error set appear(s) below it. Every error set is joined to that immediately above.

Of each manuscript we then delete every occurrence except the lowest. This procedure is applied in fig. 1b to the error sets generated by fig. 1a, namely AB, CD, A, B, D.[4]

The text of ω, the latest common ancestor of the extant manuscripts, is reconstructed on the principle that two manuscripts which agree reproduce the reading of their latest common ancestor. In fig. 1, the agreement of AC or BC suffices.

So far, P. Maas's approach[5] has largely been followed, but an alternative method was developed by J. Froger. We may regard any stemma as suspended from its topmost point, which represents the latest common ancestor of the extant manuscripts. Were it suspended from any other point, Froger observes (pp. 80, 118), the new stemma would generate the same patterns of agreement and disagreement, as long as the notion of error is left aside. These patterns thus admit a range of possible stemmata, which present the same enchainment[6] (i.e. network of lines connecting extant manuscripts and lost branch-points) but differ in orientation (i.e. choice of topmost point).[7] Froger therefore first seeks the enchainment,

on the basis of agreement patterns in two-way splits alone (p. 119). One extant manuscript is arbitrarily chosen as a fictitious original (p. 83). The "error" set in any passage now comprises all manuscripts disagreeing with that manuscript. Over different passages, these sets too are consistent,[8] and so Froger can proceed (pp. 84, 95) as in fig. 1, obtaining an enchainment suspended from the fictitious original. With the tradition of fig. 1, and with C as "original", the "error" sets become AB, A, B, D, whence the enchainment of fig. 2ab, arbitrarily orientated

with C on top. He now re-orientates, on the principle (p. 88) that if a group of manuscripts (or one manuscript) is caught in error, the topmost point cannot lie on their (its) side of the line that separates them (it) from the remaining manuscripts. An identifiable error in AB, and another in CD, would suffice to locate the topmost point; in fig. 2c dotted curves surround the areas eliminated. Fewer identifiable errors are thus required under (vi). This is an advance, because passages (which we may call determinate) where intrinsic criteria identify the original reading may be rare.

The remaining assumptions are no less necessary. Without (v) different manuscripts would appear identical. As for (i), if certain variants stood as alternatives in the original, unrelated manuscripts could agree in their choice between them. The basic principle that an error set has an exclusive common ancestor is ensured by (ii)—(iv), which imply that any error set comprises all the descendants of the manuscript responsible for the error and them alone. If (iii) fails, however, the error set may be augmented; if (iv) fails it may be diminished (Froger, pp. 108 ff.). The failure of (ii) has the same effect as that of (iv) or (iii), according as good readings or bad are transferred from the secondary source. Two or more such shifts may occur in a single passage. In different passages the error sets may be distorted in different ways, and cease to be mutually consistent. If few consistent variants remain, the above construction methods break down. The largest error sets are the likeliest to be distorted. In all

too many traditions, therefore, some small groups remain recognisable, but the passages where the manuscripts are more evenly divided exhibit a bewildering variety of inconsistent patterns of agreement, each occurring just once or twice.

In most traditions, authorial variation, coincidence in error and successful conjecture are exceptional, and instances can often be suspected on intrinsic grounds and excluded. It is therefore primarily the level of contamination that determines whether a stemma can be constructed. In the total absence of contamination there are but a few possible error sets, all mutually consistent. At the opposite extreme we could imagine a totally contaminated tradition, where the truth may survive in any one of the manuscripts uniquely and a fortiori in any combination, and the possible error sets are correspondingly numerous and in the main mutually inconsistent. (Such a tradition, comprising just three manuscripts, is considered in §4.1.) Real-life traditions fall between these extremes. Contaminated traditions were less pejoratively termed "open" by G. Pasquali.[9] Here an open tradition will be defined empirically as one for which no stemma can be constructed.

1.2. Before devising an alternative to the stemma, one must ask what the stemma ideally achieves. The answer seems obvious: the stemma sketches the history of the extant manuscripts, and that history establishes priority between rival readings. In other words the stemma has two functions, historical and evaluative; and the latter would seem to depend on the former.

Yet once the possibility of contamination is accepted, the history sketched by the stemma becomes just one of many possibilities. In 1928 J. Bédier complained that the same distribution of agreements and errors in manuscripts of the Lai de l'Ombre admitted either of the pedigrees in fig. 3.[10] Indeed for any stemma, however well it fits the patterns of agreement and error, any number of alternative pedigrees can be devised. The stemma may present a simpler history, argued Bédier, but not necessarily the true one, and therefore formed no sure basis for evaluation of rival readings (pp. 354 f). This objection to the stemma is weightier than Bédier's well-known argument that among the stemmata constructed by editors the proportion having just two branches is impossibly high; in

fact a heavy preponderance of two-branched stemmata is entirely to be expected.[11]

Here the answer to Bédier is that the evaluative policy stands even if the history falls. Consider how a stemma evaluates variants. In any variant passage, each rival reading is attested in a group of one or more manuscripts, and traced back to the latest common ancestor of that group. Suppose that one of these ancestors derives from another; we may call the manuscripts whose reading is traced to the earlier ancestor the superior group, and those manuscripts bearing the reading traced to the later ancestor the inferior group. Then the superior group prevails, the divergence between the groups being attributed to error in the later ancestor. This is the essence of stemmatic evaluation. In fig. 3a, for example, let ABDE agree against CG. The latest common ancestor of CG (=y) derives from that of ABDE (=v); hence ABDE's reading is older, and CG's may be put down to error in y. Now the reason that an exclusive common ancestor was posited for the inferior group at the construction stage is that that group were somewhere caught in an exclusive common error. Bédier's objection is that such an error is not conclusive proof of an exclusive common ancestor.[12] True; but the fact remains that the superior group has been known elsewhere to preserve the truth against the inferior group,[13] through whatever historical process, while the converse has never been observed. Hence, in passages (called indeterminate) where intrinsic considerations fail, readings exclusive to the inferior

group deserve no priority. This conclusion bypasses historical reconstruction and Bédier's objections thereto, and rests on direct induction from determinate to indeterminate passages.[14] The history and the evaluative policy must be derived from the determinate passages independently, and not, as commonly thought, in succession.

2. Historical methods in open traditions

2.1. The genealogy, if known, would make evaluation easy even in a contaminated tradition. Suppose that the manuscripts disagree. If we can find a common ancestor for the group that attest one reading, and at the same time a path bypassing that ancestor can be traced from each member of the (or a) rival group back to the original, the former reading is attributable to error in that ancestor. Every group can be tested thus against every other, and unless every reading is found attributable to error, the original (or rather the oldest recoverable) reading will be identified.

Now the only way to know that a group of manuscripts share an ancestor on which the remaining manuscripts are not wholly dependent is to have caught that group in an exclusive error elsewhere. Open traditions, however, exhibit a multitude of two-way splits (to go no farther), mostly rare or even unique. Over Cyprian's De Unitate, for example, there are 346 passages where the eighteen manuscripts collated by M. Bévenot survive and divide into two groups; these show no less than 198 different agreement patterns, of which 164 occur just once.[15] Many agreement patterns among the indeterminate passages occur in no determinate passage; none of their constituent groups, therefore, will have been observed in exclusive error. Such patterns cannot be illuminated by the partial genealogy derivable from the determinate passages. Among four manuscripts ABCD, for example, suppose that we detect unique errors in each, as well as some common errors in AB and some in CD. The stemma of fig. 4a results. Suppose in addition an indeterminate split AD:BC. According to fig. 4a, AD have no common source but the original, nor do BC; but in fact either AD or BC must have a common source, as one of the readings must be wrong.[16] The existing genealogy does not

aid evaluation here. On the contrary, an evaluation would fill out the genealogy: if we decided after all that AD were correct, we would ascribe to BC a common source (which fig. 4b takes simply as B); if we preferred to follow BC, we would link AD.

It may be noted that the same apparatus criticus admits more than one genealogy in an open tradition (§1.2). Suppose four manuscripts EFGH, each bearing unique errors, and suppose further some common errors in EF, some in GH, some in EH, some in FG. We might infer fig. 5a. However, the links E-H and F-G could be differently orientated (fig. 5b). Or, instead of ascribing common error to "intrastemmatic" contamination, we should perhaps ascribe common freedom from error to an "extrastemmatic" source (i.e. a lost source not derived from the latest common ancestor of the extant manuscripts);[17] in fig. 5c, μ accounts for the shared errors both of GH and of EF (which had no access to μ to correct λ's errors). In an open tradition it is not always obvious which of the alternative pedigrees has the dubious advantage of being the simplest.

2.2. For a genealogical approach to evaluation, then, one determinate specimen of every attested two-way split is prerequisite. Dom H. Quentin, however, claimed that a full genealogy could be constructed with far less information. He argued that if three manuscripts were related in any of the ways shown in fig. 6, the outer pair (AC) would never agree against

the intermediary (B).[18] All the diagrams comprise the same enchainment, variously orientated. Quentin supposed conversely that if the number of agreements of two manuscripts (AC) against a third (B) were zero, the three were related according to one or other of the diagrams in fig. 6 and stood in the enchainment A-B-C. On comparing by threes all the manuscripts of a tradition, Quentin expected to discover enough zeros to form the complete enchainment, which would merely require orientation. Conflation would be revealed through the last case in fig. 6, though in fact zero agreement in AC against B will occur only in the atypical case where B simply amalgamates AC and never errs.

Now in all six cases in fig. 6, at least one of the three manuscripts derives directly from another. It follows that if, after standard practice,[19] every manuscript which derives from another extant manuscript is eliminated, the remaining manuscripts will exhibit no zeros at all. Yet Quentin did obtain zeros, by restricting the field of variants. Suppose three independent descendants of one ancestor. Before the count begins, the number of agreements of any pair against the remaining manuscript is of course zero. If the text is long enough, all three manuscripts will eventually err and all three zeros will be breached. However, if the text is so short that one of the manuscripts did not err, a spurious zero will remain. Quentin used short texts, and further increased the likelihood of the survival of a zero by eliminating readings which "attirent l'attention des copistes".[20] He also regarded a low figure as a quasi-zero, equivalent to zero; but in fact a quasi-zero may result not only from intermediacy (e.g. if the two outer manuscripts occasionally agree by coincidence) but also from wholly different relationships.[21]

Quentin also eliminated unique readings. Any manuscript standing at the end of a branch was thereby replaced by the nearest extant manuscript

or branch-point; in fig. 7b, for example, a should show A's text apart from A's unique readings. Once an enchainment was established between these surrogates, the manuscripts themselves could be shown branching off it. For example, the enchainment Hub-Bern-Anic-Theo, reached after the removal of unique readings, was modified to fig. 7a

(Mémoire, p. 257). With this adaptation, Quentin's method detects zeros in a wider range of enchainments but by no means in all. In fig. 7b, A without its unique readings becomes a, as does B; C becomes β, and so on; but no zero reveals the relations between αβγδ.

The variants therefore had to be kept few. One of Quentin's genealogies rested on a passage of under 250 words—hardly long enough for every copyist to have committed an error meeting Quentin's conditions. All his analyses involve fewer than 100 variants and he considered twenty sometime sufficient (Essais, pp. 124, 65). Those who took larger samples of the same works found no zeros. For example, whereas Quentin used 91 variants from the Vulgate Octateuch (Mémoire, p. 328), Dom J. Chapman found, on the basis of some two thousand from Genesis and Exodus alone, that "comparison by threes will no longer produce zeros".[22] Again, the zeros which Quentin found on the basis of a sample from the Lai de l'Ombre were breached elsewhere, as Bédier noted (Romania, LIV [1928], 328). Similarly a test on hundreds of variants in Mark yielded "but one zero line among eighty-four groups of three manuscripts".[23]

Quentin's approach has been continued by G. P. Zarri, who uses even fewer variants. In a section of some one hundred lines of the Chanson de Roland he reduced the field to just thirteen, by eliminating on the suspicion of polygenesis the variants that prevented the appearance of the requisite zeros.[24] Another study concerned a text so tiny that Zarri found

too many zeros: the Copa in the Appendix Vergiliana, comprising thirty-eight lines, yielded sixteen admissible variants among six manuscripts, and no less than fourteen zero lines among the twenty groups of three manuscripts.[25] His rules for combining the lines of intermediacy are questionable. For example, in fig. 8a he expects a zero in C against BE,

among many others. In fact, however, two manuscripts will not show zero agreement against a third if a path exists between the two manuscripts—other than a path leading downwards from both—which bypasses the third. Some agreements of BE against C are therefore expected, where C innovates and E follows D. Again he wrongly supposes that the pattern of zeros allows a convergent enchainment to be re-orientated. Fig. 8b will exhibit one zero, namely in BD against A; if B is instead placed uppermost, the only zero now stands in AC against B.[26]

2.3. Instead of a contaminated genealogy, some are content to reconstruct an outline stemma on which every manuscript is derived from its main source alone. One method is to list the two-way splits in decreasing order of frequency until we meet one that is inconsistent (§1.1) with some predecessor.[27] If contamination is slight, this selection will include most passages, and a stemma accounting for them follows through the methods of Maas and Froger. Where contamination is more extensive, different procedures are proposed by P. Buneman,[28] V.A. Dearing,[29] D. Najock[30] and E. Poole[31] for selecting variants on which to base a tree that traces

main sources. In this situation, however, the cumulative neglect of subsidiary sources, which in some cases might be almost as important as the main sources, compromises both the historical and evaluative functions of the tree.

In open traditions, it may be impossible to identify any genealogy of main sources as the correct one. A single apparatus criticus admits many equally plausible histories, which may differ even if secondary sources are overlooked. For illustration, suppose three manuscripts ABC which err together five times; let each manuscript also bear ten unique errors; in five more places, A alone is correct, and, in seven more places, C alone. One possible genealogy is fig. 9a:ω committed five errors, and so on, while B adopted seven of a's errors and five of β's and added ten of its own. B thus departed from α in 15-7+5+10=23 places, and from β in 8-5+7+10=20 places. Hence its main source is β, and the genealogy of main sources is fig. 9b. However, the genealogy of fig. 9c equally fits the

facts. Here A used λ to avoid five of γ's errors and one of δ's, but accepted two of λ's errors and added eight of its own. As A departs from λ twenty-five times and from δ only sixteen times, its main source is δ, whence the tree of fig. 9d. Now any procedure to recover a divergent tree from the apparatus criticus will yield either (b), which is false if (c) is the true history, or (d), which is false if (a) is the true history. The tree yielded by any particular procedure can therefore be no more than one out of many possible genealogies of main sources.

Evaluation can be falsified by disregard of subsidiary sources. Fig. 9b implies that AB's agreements are correct, but they may in fact be errors inherited from the neglected a; similarly fig. 9d gives unwarranted priority to BC's shared readings. Again, as shown in §2.1, contradictions result if the stemma is applied to evaluate variants discarded in its construction as inconsistent. If fig. 4b were the true genealogy, with C following β more often than B, and the stemma of fig. 4a were recovered, then in the splits AD:BC, resulting from C's secondary use of B, the stemma could not decide priority. Such discarded variants would abound, in open traditions. The first chapter (about 160 words) of Cyprian's

De Unitate yields, for the eighteen manuscripts abBDeGhHJkmOp-PRTWY, the following five splits, among others:[32]

• 1. DHJkP: rell. (induimur)
• 2. bhHmpRT: rell. (subruendis)
• 3. GhHJmpRT: rell. (grassatur)
• 4. DhJmT:GY: rell. (crudelitate)
• 5. aJHT: rell. (conatus)

Of these five, no stemma could accommodate more than one. Generally, no stemma can provide an evaluative policy in a seriously contaminated tradition. V.A. Dearing's application of stemmata to evaluation require the discarded variants to be "treated as something different from what they really are" (see n. 29, pp. 87 ff.). The present writer has elsewhere criticised in detail the logic of Dearing's approach to history and evaluation. A model tradition, representing in miniature two parallel families that influence each other (fig. 10a), supplied a test: Dearing's procedures yielded a quite different tree (fig. 10b) and led to the wrong choice of reading in 44% of passages.[33] Dearing replies that a test problem which

contradicts his method involves different assumptions on textual transmission, and that a tradition which violates his own assumptions is not "likely to occur in real life";[34] but real life seems more varied than Dearing allows. He further objects that, in any case, "hypothetical cases are always hypothetical"—rather as if the manufacturer of a drug which in experiments on rats proved fatal protested that rats were merely rats.

3. History-free approaches

3.1. Diagrams that resemble but do not constitute stemmata result from cluster analysis. Here an index of similarity (or conversely of distance) between every possible pair of manuscripts is required. Initially each manuscript constitutes a "group" of one. The two groups most similar according to the index are amalgamated, and this step is repeated until there is but one group, comprising all the manuscripts. The obvious

index of similarity is the number of agreements, but, as Patricia Galloway explains, other indices exist and, where two groups each comprise many manuscripts, there is more than one way of defining the index between the groups in terms of the indices between the constituent manuscripts.[35] The resulting diagrams, unlike stemmata, cannot show one manuscript above another, or a branching into three or more lines, and many cluster analysts rightly distinguish them from stemmata.[36]

A. Kleinlogel, however, after a complex argument based on lattice algebra,[37] proposes that we provisionally select the original reading in every variant passage, and thence count, for every manuscript pair AB:

Three-way splits may be left aside. A similarity index which will supposedly reveal the stemma through cluster analysis is Yet in a simple example this method gives the wrong stemma. In fig. 11a,

α erred five times, and so on, and all forty-five errors arise in separate places. For all pairs we tabulate:

TABLE 1

             

	s	t	u	v	τ
AB	10	20	5	10	0.00
AC	25	5	10	5	0.35
AD	25	5	15	0	-1.00
BC	10	5	25	5	-0.35
BD	10	5	30	0	-1.00
CD	30	5	10	0	-1.00

Cluster analysis yields fig. 11b, which falsifies the history, and also the evaluation: if β and D erred simultaneously, whence a three-way split AB:C:D, with C alone correct, fig. 11b would wrongly condemn C's reading.[38]

Other investigators propose similarity indices not involving the distinction between true and false readings, apply cluster analysis, and call the results stemmata. Were this valid, one could obtain a stemma on the basis of mere similarity, without ever deciding between readings[39] — which is absurd, since, without the notion of error, one cannot even draw a stemma for two manuscripts AB, showing whether A derives from B or B from A or both from a lost source. The distinction, already stressed by Greg (see n. 3, p. 59) between similarity and historical relationship is illustrated by fig. 12a: AD are the most similar pair, but not the most

closely related, and cluster analysis yields the very different tree of fig. 12b. Yet P. Tombeur (loc. cit., see n. 36), and V. Wendland[40] attempted to found stemmata on the number of agreements as a similarity index.

Similar but more elaborate is P. Malvaux's treatment of fifteen manuscripts of Theodoret of Cyrrhus.[41] Five groups were immediately apparent from the apparatus criticus, each departing unanimously on between

nine and eighty occasions from the agreement of the others. Together these groups covered all fifteen manuscripts (AYZ; BR; CFHP; ENT; GQW). Malvaux posited for each group an ancestor responsible for its distinctive readings, and a more distant ancestor free of them. To study the relations between those remoter ancestors, Malvaux discarded unique readings and the distinctive readings of the five groups, on the ground that they originated subsequently.[42] The disagreements between the extant manuscripts were counted over the reduced field of variants. Cluster analysis linked most closely AYZ and BR, between which the fewest disagreements occur, and then linked the two with ENT; meanwhile CFHP were linked with GQW; hence the main lines of fig. 13a. The contrary findings of his collaborator the philologist

P. Canivet, however, imposed the contamination line. Canivet produced no common error in CFHPGQW, and found in CFHP alone some readings that were undoubtedly correct.[43] This situation is better explained by fig. 13b, which rests on Canivet's findings plus Froger's method applied to the agreement patterns.[44] It rehabilitates one "séduisante" reading that Canivet abandoned in deference to the stemma (p. 405)[45] and accommodates 403 of the 447 variants reported (out of a total of 585). In any event, as Canivet concluded (p. 413), this is not a particularly contaminated tradition.

In yet another approach that excluded the criterion of error, Carmélia Opsomer-Halleux counted for each manuscript pair the number of

common departures from the text of the majority, and on that index founded a stemma.[46] But the majority need not be correct; an error may have infected a fertile family. The notion of error cannot be sidestepped.

3.2. Some investigators find similarities informative, even though they yield no genealogy. J. G. Griffith has used them to arrange the manuscripts in a spectrum, i.e. a sequence in which manuscripts that are similar textually stand close together.[47] In a study of Juvenal's Satires, the sincerest witnesses came out at one end and the most interpolated at the other. The textual worth of a manuscript could thus be inferred from its position along the spectrum. Between eight spectra for different sections of the Satires, Griffith found some variation, which indicated shifts of allegiance, as he confirmed by traditional methods. Within each spectrum groups were discerned which showed especially high similarity figures among themselves. In a second study, covering fourteen or fifteen manuscripts over four samples from Luke and John, the spectra did not prove interpretable as scales of textual purity. The groups, however, followed accepted divisions, appearing in the order: Byzantine, Caesarean, Alexandrian, Western.

A spectrum can be viewed as a one-dimensional map where the distance between successive manuscripts is not quantified. Griffith and others have experimented with maps in two or even more dimensions. Each manuscript is represented by a point on the map, such that the distances between points reflect the degrees of textual divergence between the corresponding manuscripts. Manuscript maps were first proposed by the monks of Solesmes, in their edition of the neumic text of the Roman Gradual.[48] These maps bore obvious but not total resemblance to geographical maps of provenance of the manuscripts, and facilitated the comparison of textual with political and linguistic affinity. The map also served to divide into eighteen clusters the four-hundred-odd manuscripts collated, and whichever reading was attested by the majority of these clusters prevailed.[49] Despite the obvious risk that an

error might have infected the majority, this evaluative policy was as reasonable as any, for one can hardly detect errors in a neumic text.

While the monks of Solesmes drew their maps freehand, other investigators use factor analysis. D. Najock[50] and F. G. Berghaus (op. cit., see n. 36, pp. 102 f, 110) analysed thus the tradition of Old English glosses on the Psalter, obtaining maps which demarcated clearly the two classes distinguished by conventional methods. Again, the main accepted groupings of New Testament manuscripts were confirmed, with some fresh insights, in J. Duplacy's map.[51] In a map compiled by P. Monat of nine manuscripts of Lactantius' Divinae Institutiones IV, the manuscripts located to the 'west' carried a longer version of the whole work, and those to the 'east' a shorter version, both attributed to the author; the oldest manuscripts appeared in the 'south'; Monat concluded (p. 322) that any reading attested jointly by the most 'southwesterly' manuscript and the most 'southeasterly' should prevail.[52] Griffith's maps of passages from Horace, Juvenal, the Gospels and Aeschylus confirmed and refined earlier groupings, while variation between results from passages by one author suggested shifts in the textual history.[53]

The deficiency of all these approaches, including cluster analysis, is that the main aims of textual criticism—an evaluative policy and a history—are not attained. Admittedly, into one spectrum series (Juvenal) and one map (Lactantius) the notion of error, or at least priority, was readily imported, and led to an evaluative policy; but the contrasting performance of the remaining spectra and maps casts doubt even on those evaluative policies which intuitively emerge.[54] Many interesting results remain, especially the groupings, and the differences in transmission between different sections of one work or between different types of variant (e.g. whether they involve a whole word or not) (Galloway, see n. 35, pp. 4 ff).

3.3. We turn finally to approaches that involve no genealogies or other diagrams. M. Bévenot set forth a principle applicable to any tradition, however contaminated: a reading attested by two manuscripts never or seldom caught erring together prevails over a reading that lacks such attestation (op. cit., see n. 15, pp. 133 ff, 147 ff). In his edition of Cyprian's De Unitate, Bévenot had set up a 'Resultant Text' presenting at each point his choice of reading on intrinsic grounds. He then counted, for each manuscript pair, their agreements in readings not accepted for the Resultant Text. The pairs showing the lowest totals were termed "opposed". He identified some instances of three mutually opposed manuscripts, and argued that their shared readings were almost certainly correct. Using this principle to check the text, he found that triply opposed manuscripts hardly ever agreed in a reading earlier rejected; but this confirmation of his original choice of readings is suspect, since the underlying statistics of agreement in error themselves depend on that choice. More soundly, he applied his results from the De Unitate to another Cyprianic treatise, the De Lapsis, whose textual history could be presumed identical. He had meanwhile noted in the De Unitate a group (which he later called a 'team') of four mutually opposed manuscripts, and, in the evaluation of variants in the De Lapsis, "the agreement of any three of the four almost invariably carried the day."[55]

M. L. West too counts common errors within every manuscript pair, to identify manuscripts that never err together when the truth anywhere survives.[56] Like Bévenot again, he constructs a 'team', but better defines it as the smallest group to contain all the ancient readings anywhere preserved. Bévenot's formulation (minimum agreement in false readings) might have admitted a group of manuscripts that were deficient, or exhibited separate errors, in places where the truth survived elsewhere. West's team does not rest on his statistics of common error. Instead, he lists all identifiable ancient readings.[57] Any manuscript that uniquely preserves such readings is adopted. Any ancient reading attested by the existing team members is struck from the list, and whichever manuscript contains the most of the remaining readings joins the team. The procedures in the last sentence are repeated until the list is exhausted.

The approach of Bévenot and West seems the most promising. It is logically sound and attacks directly the goal of evaluation. It reduces the bulk of the apparatus criticus, and the labour of collation in works whose history may be presumed identical. It does not, however, yield a textual history.[58] The evaluative policy is clear, but only when the team is unanimous. Unfortunately it is often divided; in the De Unitate, for example, Bévenot's team of four (aepY) is divided in some twenty passages in Ch. 1 alone. Bévenot, as stated, would follow the majority, but this is to ignore the common phenomenon of unique preservation.[59] West is silent; but if the approach is indecisive wherever the team divides, its role in evaluation is limited indeed. The following sections ask whether these gaps can be filled.

4. The inductive approach to evaluation

4.1. In an open tradition, the agreement patterns are too confused to illuminate directly the history and evaluation, but the principle of opposed pairs (§3.3) remains valid. To develop the argument we require what will be termed the bipolar assumption.

If we collate many manuscripts, we can identify a relatively small 'team' of manuscripts which together attest all the good readings anywhere preserved (§3.3). Let us now define the team differently as the smallest set of manuscripts never to exhibit a common error when the truth anywhere survives.[60] Team members may on that account be termed 'poles'. What determines the size of such a team? A team of one results, of course, if only one manuscript is collated or is the source of all the others. Any other uncontaminated tradition yields a team of two, or rather many alternative teams. Any pair independently derived from the archetype form a team, and every manuscript belongs to at least one team. Fig. 3a, for example, yields eight teams (AD, AE, BD, CE, . . .). On the original definition, multiple splits could extend the team: in fig. 3a, if in one place xz erred separately, in another yz erred separately, and in a third w erred, we should need a team of three, namely (1) C or G, (2) A or B, and (3) D or E. With the modified definition all eight teams stand, and team size depends not on scribal behaviour but on genealogy alone.[61]

A group of manuscripts can suffer some contamination but still have just two poles. If one manuscript (γ in fig. 14a) adopts good readings from a lost extrastemmatic source (§2.1), then any original team (i.e. a team that would have been valid had no contamination occurred) not containing that manuscript or a descendant thereof is eliminated. In fig. 14a, only the teams AC and AD would survive. Two lines of extrastemmatic contamination, however, might eliminate all the original teams

(e.g. if the lines led to B and γ), and result in a team of three. As for intrastemmatic contamination, if one member of an original team (or an ancestor thereof) transfers error to the other member (or an ancestor thereof) the team is invalidated; but as long as one team stands (AC in fig. 14b) the tradition remains bipolar.

Consider a team of three members ABC. Each is on occasion correct against the agreement of the other two. There are many possible pedigrees, all rather complex, which could bring this about. In fig. 15a, each

pair shares a source and thence errors, but the only source common to all three manuscripts is the original. In fig. 15b, some of B's errors mar BC but not A (thanks to a), some of C's reach A but arose after B, some of α's reach AB but not C (thanks to β). In fig. 15c, B consulted λ in some passages where ω was corrupt, C consulted λ in other such passages, and A is sound where BC bear β's errors. Teams of four or more betoken even more complicated genealogies. If such intricacy seems far-fetched, one need only recall that in the Aeschylean triad the question is whether the team numbers eleven or twenty.[62]

Evidently not every tradition is bipolar. Moreover, even if the set of all manuscripts collated is bipolar, not every sub-group is necessarily so: for example, the group ωλβABC (all for a moment supposed extant) in fig. 15c is bipolar, but the sub-group ABC is not. Nevertheless, the assumption that manuscript groups are bipolar is far less restrictive than that of total absence of contamination.

4.2. The method here proposed begins with a list of the determinate two-way splits. Hence the errors in every manuscript and the errors common to every manuscript pair are counted. Multiple splits are excluded from the list, since manuscripts which elsewhere err together may there err separately and cause anomalies, as in fig. 16. Suppose that β and D

each erred, so that BC show one error and D another; it would be misleading to ascribe one common error to BC and none to BD or CD and thereby suggest an exclusive relationship between BC.[63] In any case multiple splits are rare, if each independent point of variation, however great or small, is separated. Thus the readings to you I tell: to you I say: I say to you entail two variations: word order and tell/say. Similarly composed: composing: reposing comprises two variations: comp-/rep- and -ed/-ing. The readings amorous AB: loving CD: lufand EF yield two variations: (1) amorous/[loving] AB:CDEF, and (2) loving/lufand CD:EF (with AB unavailable). Some multiple splits (e.g. say:tell:sing) are, however, irresoluble.[64] The criterion of independence is usually easy to apply; for example, see and hear: hear and see yield not two independent variations, but one. (Contrast Dearing, see n. 29, p. 32.)

An error unique to any manuscript cannot affect the totals of shared errors, and as for the error total for that manuscript, all that matters (cf. §4.3) is whether unique errors occur or not. Unique errors can (rather than must) therefore be excluded, though their carriers should be noted. Unique preservation of the original reading, however, does affect the error totals, and any variant for which this possibility exists must remain.

Probable cases of coincidence in error or successful conjecture should be excluded, since the figures are intended for extrapolation to indeterminate passages, where such non-genealogical causes of common error are not especially liable to generate the same agreement patterns.

4.3. We obtain, then, a table of error totals. Each total can now be expressed as a percentage of the number of determinate passages. This yields the average number of errors observed per hundred variant passages. (The problem of missing readings is ignored for the moment.) It is now assumed that, over the indeterminate variants too, every manuscript or pair of manuscripts yields a similar percentage of errors. This assumption turns on the number and accuracy of our determinate variants, and ultimately on our critical judgment; compare assumption (vi) in §1.1.

At any indeterminate variant passage, the manuscripts divide into two or more groups. Even if such a group contains more than two manuscripts, its error percentage can still be defined as the average number of errors common to the group over a field of one hundred variants. The obvious course is, as before, to express the number of common errors detected in the group as a percentage of the total of determinate passages; but the results, at least for larger groups, may be unhelpful. In a tradition where scribes constantly compared sources in order to improve the text, readings that penetrated a good proportion of the extant tradition and yet can be confidently identified today as errors are rare. If (say) eight manuscripts agreed against ten in an indeterminate passage, it is all too likely that we could identify no instance of all the eight agreeing in error, nor of all the ten, and comparison of the two error percentages would be fruitless.

The error percentage for a larger group is instead estimated through the bipolar assumption. Of all the pairs that can be formed from the group, let the pair PQ (say) show the smallest error percentage. The error percentage for the entire group cannot be greater; PQ plus others cannot agree in error more often than PQ alone. Can the error percentage be smaller for the group than for PQ? Let us suppose the group bipolar. PQ are then poles: wherever PQ err together, the truth survives

nowhere in the group, which either shares PQ's error or is divided between two or more separate errors. The latter event being exceptional, most of PQ's shared errors will be common to the entire group, whose error percentage will approach that of PQ, the pair yielding the lowest percentage.

For a group comprising just one manuscript, the error percentage will have been tabulated; if the manuscript bears unique errors, one will note that the true figure is higher.

If the error percentage for the group attesting one variant reading is zero, that reading will prevail—unless a rival also shows zero, implying that our determinate variants formed an inadequate sample. If the error percentage for one group is low, and that for the rival group is far higher, say by a factor of four or more, that factor will indicate the odds in favour of the first reading, which of course prevails.[65] If there is no overwhelming imbalance between the error percentages, however, no decision is possible, as either group might well have erred.[66]

As the error percentages for groups depend on those for pairs, this procedure comes back to the principle of opposed pairs: a reading attested by a pair never caught agreeing in error prevails over a reading not attested by any such pair. The replacement of 'never' by 'relatively seldom' adds a probabilistic version of that principle.

4.4. Let us examine further the logical role of the bipolar assumption. Two different lists of variants, requiring two different critical policies, could yield the same array of error totals (and percentages). Suppose that among ABC the error totals are two for each individual and one for each pair. This would result not only (i) if each manuscript erred once alone and all three erred once together, but also (ii) if AB erred once against C, AC erred once against B, and BC erred once against A.[67] These possibilities lead to different genealogies (the former to fig. 17, the latter to such genealogies as fig. 15abc) and imply respectively that readings common to ABC might, or cannot, be errors. The bipolar assumption, reasoning

from constituent pairs to parent group, chooses whichever possibility posits the least contamination—here, the former.

The consequences if the assumption fails appear from fig. 18. Thirty-two determinate passages (excluding unique readings) reveal eight common errors in AB, ten in AC, twelve in BC and two in DE. These were inherited from the lost manuscripts λ, μ, ν and ξ respectively, unbeknown to the investigator. The bipolar assumption, however, would impute

eight common errors to ABC, and admit the genealogy of fig. 18b. Consider now a split ABC:DE. The smallest error percentage amongst ABC is 25%, yielded by AB (100% x 8/32), while DE show 61/4% (100% x 2/32). Our investigator would find odds of 4:1 (=25:61/4) in favour of DE's reading. In fact, however, the agreements of ABC must reproduce Ω, and the split ABC:DE indicates an error in DE.

4.5. To adjust for missing readings, the error total for any manuscript (or pair) should be expressed as a percentage not of the total of determinate passages, but of the number of determinate passages where the manuscript(s) is (are) available. Should this new denominator appear inadequate, the percentage must be treated cautiously or even discounted. Otherwise we might come to follow the agreement of a certain pair of manuscripts on the ground that they have never been caught in error

together, when in fact there was little opportunity of catching them, either because they hardly overlapped or because the critic lacked the knowledge to recognise many errors. The adequacy of any particular denominator can only be assessed by someone expert in the tradition.

With this revised definition, the error percentages can be tabulated and utilised as above to assess the credibility of the manuscript groups attesting the rival readings. The use of these procedures is illustrated in §6.

5. A complementary approach to evaluation and history.

5.1. The main drawbacks of the above approach are the need to compare a large array of error percentages in each variant passage and the failure to suggest a textual history. The following complementary method aims to fill these gaps.

Suppose a two-dimensional map of manuscripts, on which the distances between points reflect the degrees of textual divergence between the corresponding manuscripts (cf. §3.2). To such a map we might add hypothetical manuscripts. Imagine, for example, a manuscript which always follows either A or B. We may expect to locate it along the line AB, in a position reflecting its relative indebtedness to its two components. Similarly, a hypothetical manuscript conflated from ABC should lie within the triangle ABC, and a mixture of many manuscripts should lie within the largest polygon that can be formed from the corresponding points (cf. fig. 19). These expectations are merely intuitive, and we shall see that they need modification; but for the moment let us accept them.

The best text recoverable from the extant manuscripts is a hypothetical mixture ω which selects the true reading wherever that reading survives, but follows the manuscripts where all err together.[68] In an uncontaminated tradition, ω would be the archetype, which term denotes

a manuscript that once existed. In an open tradition, however, that combination of good and bad readings which comprises the best recoverable text might never have stood in any manuscript; in the pedigree of fig. 14a, for example, ω's errors will be those of a minus those which γ avoided with λ's aid. From the determinate passages we may assess the degrees of divergence between ω and each extant manuscript, and hence locate ω on the map. This step introduces the notion of priority, which is essential for the derivation of an evaluative policy, but lacking (or at least not systematically included) in existing maps of manuscripts.

Consider a group of manuscripts represented by points which span a polygon that contains ω. Then ω is a mixture of those manuscripts; that is, ω could be constructed from those manuscripts alone. Wherever that group of manuscripts agrees, so must any mixture of them. Hence their agreement gives the best recoverable reading. This principle evaluates variants: in fig. 20, for example, the reading of OPQX prevails over that of NRSTVYZ.

5.2. To construct the map, we require measures of 'distance' between all the manuscripts involved, i.e. between every pair of extant manuscripts and between ω and each extant manuscript. To adjust for missing readings, the 'distance' between two extant manuscripts is defined as the number of textual differences, expressed as a percentage of the number of variant passages where both manuscripts are available (cf. §4.5). Since at the outset ω is known in determinate passages only, the 'distance' between ω and an extant manuscript is taken as the error percentage of that manuscript, i.e. its total of identifiable errors as a percentage of the number of determinate passages where it is available. In all but the smallest traditions, unique errors are best omitted, as shown in §5.7.

To be readily grasped the map should be two-dimensional. It is usually impossible, however, to draw a two-dimensional map on which the distances between points equal the distances between the manuscripts. One can only draw up a map that minimises the discrepancy, and different definitions of discrepancy lead to different methods. The technique here adopted is multidimensional scaling (MDS), which aims to preserve the rank ordering of the textual distances; that is, if one pair of manuscripts shows greater textual divergence than another, the first pair should be farther apart on the map than the second pair.[69] Although most manuscript maps have rested on factor analysis, MDS is preferred here. Firstly, factor analysis yields, in the first instance, a map in many dimensions, and aims for no specific correspondence between the data distances and the distances on the map obtained by neglecting all but the first two dimensions;[70] and without such correspondence, as §5.4 will show, the map cannot reliably assist evaluation. Secondly, MDS copes better with missing readings[71] and even with missing distances (Lingoes and Roskam, p. 73). The latter result if a lacunose manuscript survives in too few determinate passages, or if two such manuscripts overlap too little, to yield a reliable percentage. That entry could then be omitted, and a map could still be constructed from the remaining percentages.

5.3. The relationship between the measures of common error in §4.2 and the above statistics deserves clarification. The variants where any

two manuscripts AB survive fall into five categories, as Kleinlogel remarked (§3.1):

• (i) AB agree in the correct reading, s times.
• (ii) A is correct and B errs, t times
• (iii) B is correct and A errs, u times
• (iv) AB err together, v times
• (v) AB err separately, w times

The classification holds whether the errors are detectable or not. There are (u+v+w) errors in A and (t+v+w) errors in B, and AB diverge (t+u+w) times. The identity v=1/2 [(u+v+w)+(t+v+w)-(t+u+w) -w] implies that:

If we neglect the atypical event of separate error, and express the other items as percentages of the number of passages where AB survive, the general formula results:

Strictly speaking, all three terms on the right-hand side should be calculated over the field of all variants where AB both survive. In practice the first term rests on a different field (namely all determinate variants where A survives), as does the second; but if the determinate variants form a representative sample (§4.3), the figures should not differ greatly.

5.4. We must now examine more rigorously the proposition that the agreement of manuscripts which on the map surround ω gives the best recoverable text. If two manuscripts alone surround ω, they subtend there an angle of 180°. If more than two together surround ω, they include at least one pair subtending an obtuse (or right) angle at ω. In

any triangle, an angle of 90° or more must be the greatest and stand opposite the greatest side. Therefore the distance between two manuscripts (say AB) subtending an angle between 90° and 180° at ω exceeds the distances Aω and Bω, on the map. The same holds of the textual distances, if the map preserves their rank ordering. Now it was shown above that

The distance AB is the largest term on the right-hand side. The greater the angle, the further ahead it will stand in the rank ordering and the more it will predominate. Hence the error percentage of AB should be low—but not necessarily zero.[73] This suggests a more general but more tentative formulation: an angle between 90° and 180° subtended at ω by a pair of manuscripts suggests that they rarely if ever agree in error.

5.5. Some possible pedigrees for three extant manuscripts will exemplify the map. For simplicity, unique errors are included and all errors are supposed to originate in different passages. In fig. 22, A miscopied ω

twice, and so on, whence ten variant passages altogether. All the textual distances can be reproduced on a map in just one dimension (fig. 22b): d(A,B), i.e. the distance between A and B, is 3/10 x 100 = 30; d(B,ω) = 3+2/10 x 100 = 50; and so on. The numbers 2, 3, 5 are of course arbitrary. The pairs AC and BC each surround ω, and the agreement of either pair indeed gives ω's reading. Note that a line of descent (A→B) appears on the map as a path radiating outwards from ω.

In fig. 23a, each of ABC miscopied ω once. The distance between ω and any copy is 1/3 x 100 ÷ 33; that between any two copies is 2/3 x 100 equalsdot 67. Were the map to reproduce those distances, ω would stand midway

between AB, but also midway between AC and midway between BC—which is impossible.[74] We can only preserve the rank ordering, as in fig.

23b. Here what should have been the lines AωB, AωC and BωC are bent away from one another, and the range of the distances has been reduced (from 33:67 to 37:63).[75] The pairs AB, AC, BC each subtend an obtuse angle (120°) at ω, and the agreement of any pair indeed gives the best recoverable reading. As in later examples, the numbers of errors were chosen to produce ties, since with so few manuscripts rank ordering is otherwise insufficient to define a unique map.

In fig. 24, the textual distances AB and AC equal 4/5 x 100 = 80, while Aω and all the rest equal 40. The pairs AB and AC each subtend an obtuse angle (150°) at ω, while BC subtend only 60°; correspondingly, the

best recoverable text is given by the agreement of AB or AC but not necessarily by that of BC.

Fig. 25a introduces conflation. If B reproduced all errors of A and C, the distances Bω and AC would equal 4/4 x 100 = 100, and the rest 2/4 x 100 = 50, whence fig. 25b. Alternatively, if B adopted just one error from each of AC, the distance Bω too would equal 50, whence fig. 25c. In either case, the only pair to subtend at ω an angle in the 90°-180°

range is AC (90° or 120°), while the remaining pairs subtend only 45° or 60°. The genealogy confirms that AB could agree in A's errors, and BC in C's, but that AC agree only if both reproduce ω.[76] Note that the distance of a conflate manuscript from ω reflects its total of errors, while its direction thence is a compromise between those of its sources, reflecting their proportionate contributions.

5.6. The principle that paths radiating outwards from ω indicate descent, together with this remark on conflation, help to derive a textual history from the map, even though a unique history cannot be recovered (§§1.2, 2.1). We may indeed experiment with alternative histories, positing, for example, a lost common ancestor of two manuscripts (say AB) at the incentre of the triangle ABω.[77] Thus the map of fig. 25c could be reinterpreted by supposing a lost common ancestor α for AB (ωαA and ωαB becoming somewhat bent (see n. 77) lines of descent) and regarding C as conflated from B and a lost source β (C's direction from ω lying between those of B and β). This pedigree (fig. 26b) wholly differs from fig. 25a, but explains equally well the survival of the truth now in A alone (untainted by B's errors), now in C alone (thanks to β), but never in B alone. External clues, such as dates, may help to choose between alternative histories.

5.7. One limitation of the method is that it may be impossible to draw any two-dimensional map that reflects the rank ordering adequately.

The rank orderings of the textual and map distances are in fact unlikely to correspond exactly (unless the manuscripts are few), but the discrepancy is sometimes so extensive that the map is inapplicable. Suppose, for example, five independent copies of ω. No possible map can provide

that every pair of manuscripts subtend an obtuse angle at ω. A compromise like fig. 27b, where some pairs subtend an obtuse angle and others do not, creates illusions, e.g. that B is conflated from AC.[78] Such cases could be detected through the measures of 'badness of fit' output together with the map.[79]

An implication of the last case is that unique errors should (rather than may—§4.2) be omitted here, in all but the smallest traditions. In most traditions at least five manuscripts bear unique errors. A map based on those errors alone would be at least as cramped and misleading as fig. 27b, and even a map based only in part on those passages might partially retain those defects.

The map is also limited in its capacity to convey complex relationships. Consider, for example, the addition to fig. 23b of a conflate manuscript drawn 40% from A, 40% from B, 20% from C. Its bearing from ω must lie between those of A and B, its main sources; but then it is

indistinguishable from a mixture of AB alone. Again, in any tradition comprising three manuscripts ABC, such as those of fig. 22-25, suppose that we inserted for each manuscript five (say) instances where that manuscript was correct against the agreement of the others. Then the number of divergences between AB would rise by 5+5=10, as would the number of divergences between Aω, and similarly for all other pairs. The rank ordering, and therefore the map, would remain unchanged. However, any evaluative policy founded on the map would fall, since any manuscript even singly might now preserve the truth. Hence even when a map has straightforward implications for evaluation and history, the risk remains that some important relationship has been overlooked. A partial answer is that checks may exist. The former complication (regarding the manuscript conflated from ABC) might be traced through the entry for C and the conflate manuscript in the table of common error percentages (§4.5); the latter (each manuscript alone preserving some true readings) might be suspected from the incidence of unique preservation among determinate passages. If such danger signals are absent, however, and the map gives reasonable results, it seems over-cautious to posit further complications.

A problem in applying the map to evaluation is that the same error may arise by coincidence in two manuscripts which happen to subtend an obtuse angle at ω. A similar difficulty limits the stemma. Intrinsic considerations may indicate the likelihood of polygenesis of a given reading.

The map, then, must be used not in isolation but in conjunction with the error percentages. Where either method is indecisive, caution is necessary, as §6.3 illustrates.

In some respects the map is more limited than the stemma, but in other respects less so, whence the hope that the new methods may illuminate some traditions where the stemma fails. The virtue of the map is that of statistical procedures in general, namely the capacity to reveal fundamental trends, even though random fluctuations may disguise them, amid a mass of data. The genealogical relationships, however entangled, are fundamental in that they abide throughout the text. They are disguised by a host of sporadic (if not random) factors, e.g. coincidence, conjecture, physical damage and critical misjudgments among the supposedly determinate passages. The following experiment shows what the map can recover and apply to evaluation and history.

6. An experiment

6.1. Dom Quentin, to test his own theory, cleverly imagined how twenty-one imaginary scribes (B-Z), after the genealogy of fig. 28, might

copy a Latin passage by Florus of Lyons.[80] Let us suppose that manuscripts N-Z alone survive. The apparatus criticus presents 49 independent (though nos. 36 and 38 interact) variants, cited against the lost original:

An investigator was now imagined who, finding almost half these passages determinate, made twenty correct and four wrong decisions. The correct decisions were in passages nos. 3 (Publio), 4, 5, 10, 11, 14, 17, 22, 23, 25, 30, 32, 35-38, 40, 42, 43, and 47, and the wrong decisions in passages nos. 9 (atque), 21, 34 and 48. The locations are randomly chosen. These decisions mean merely to reflect a particular level of performance, which one hopes will seem realistic: the critic is right in 41% of passages, hesitant in 51%, confident but wrong in 8%. How credible each decision might seem to real-life specialists on Florus' writings is beside the point.

6.2. The determinate passages yield the following error percentages:

TABLE 2

                       

	N	O	P	Q	R	S	T	V	X	Y	Z
N	38[+]	0	4	4	29	33	33	33	12	29	29
O		25	17	17	12	4	4	4	12	17	17
P			25	25	17	8	8	8	4	21	21
Q				25	17	8	8	8	4	21	21
R					42	25	25	25	8	38	38
S						42	42	42	17	33	33
T							42[+]	42	17	33	33
V								50	17	42	42
X									25[+]	17	17
Y										58	58
Z											58[+]

Note the distortions introduced by the four wrong decisions.

In the construction of the map the few unique variants were included despite §5.7, as T and Z would otherwise be indistinguishable from S

and Y.[81] The measures of distance (not tabulated here) between the manuscripts (including ω) yield the map of fig. 29.

6.3. Would these results yield correct decisions in the indeterminate passages and detect the four wrong decisions? The first pair of rival readings are diram NOPQRX, duram STVYZ. While diram is attested by NO, never caught erring together, the lowest error percentage among the pairs formed from STVYZ is 33; moreover, NOPQRX surround ω while STVYZ all stand 'west' of it; hence diram is rightly chosen. The truth is identified no less readily in thirteen other indeterminate passages: nos. 7, 8, 13, 18, 20, 24, 26, 28, 29, 33, 44, 46 and 49.

In passage no. 2, N stands alone. While the lowest error percentage for any pair among OPQRSTVXYZ is 4 (OS), the figure for N exceeds 38; the odds favour the majority reading, especially since the percentage of 4 results from a single passage (no. 48). In confirmation, O-Z surround

ω on the map. Great imbalances in error percentages, and the fact that one group surrounds ω, similarly identify the correct reading in four other indeterminate passages: nos. 12, 15, 27 and 31. In passage no. 15, the group thus preferred are in the minority. OPQX surround ω (see fig. 20), while the majority (NRSTVYZ) lie within the wedge NωR, which spans only 66° at ω; OPQX also yield a better error percentage (4PX versus 25RS). In one wrongly determinate passage (no. 48), where the investigator followed NR against the rest, the error percentage of NR (29) and the fact that they subtend only 66° at ω should make him think again.

So far the error percentages and the map have favoured the same reading. Where they are contradictory, or even where either is equivocal, the decision is doubtful. No. 6 splits between NRSTVYZ, OPQ and X. The error percentages (25RS, 17OP, 25+) and the angles subtended at ω (66°, 40°, 0) are indecisive. Fig. 28 confirms that any of the groups could agree in error—e.g. NRSTVYZ in L's, OPQ in O's, X in its own—so that one is right to hesitate. Again in no. 19, NSTVX and PQRYZ show similar error percentages (12NX, 17PR) and neither subtends an obtuse angle at ω. Here too the genealogy shows that the agreement pattern is indecisive, since NSTVX might reproduce an error of C, and PQRYZ an error of P.

Sometimes the percentages seem decisive but the map suggests caution. In passage no. 45, OX depart from the majority, whose error percentage is far lower (4NP against 12OX). Yet OX subtend 154° at ω, an angle large enough to suggest that they never err together, which is in fact true. Their error percentage of 12 reflects three wrong decisions among the determinate passages (nos. 9, 34 and 48). The map, however, which utilises all the distances, in effect rejects the high error percentage of OX as inconsistent with the overall structure. This will give pause to the investigator both here and in the three misjudged determinate passages. Again, in the split NPQRSTVYZ:O:X at passage no. 41, the error percentages strongly favour the majority (4NP:25:25+), which are in fact correct. On the map, however, the decision is less certain: the majority span at ω an angle (<NωP) barely obtuse at 96°. This should alert us to the possibility, with this pattern of agreement, that O or X might be correct and NPQRSTVYZ might reproduce an error of D (see fig. 28).

Conversely, the error percentages may modify the conclusions of the map. In the split OPQR:NSTVXYZ at passage no. 16, the angles subtended at ω (69° and 120°) favour the latter group, but the error percentages are equal (12OR, 12NX). The pattern is therefore equivocal. Indeed, over its two occurrences, NSTVXYZ err (through C) in no. 16, while

OPQR err in no. 21. Even clearer, on the map, seems the choice between NRSTVXYZ and OPQ in passage no. 39, the angles subtended at ω being 136° (>RωX) and 40° (<OωQ). The error percentages, however, do not differ overwhelmingly, being 8RX versus 17OP, or, if no. 48 has by now been dropped from the determinate passages, 9RX (= 2/23 x 100) versus 13OP (= 3/23 x 100). This pattern too is best treated as equivocal. Over its three occurrences, NRSTVXYZ are correct in no. 39 but err (through C) in nos. 25 and 36.

Altogether, nineteen of the twenty-five indeterminate passages are now correctly decided, while six (nos. 6, 16, 19, 39, 41, 45) show an agreement pattern favouring no one reading. Of the four wrong determinate readings, one (no. 48) is discredited, but the agreement pattern will seem indecisive in the other three (nos. 9, 21, 34). Equivocal patterns are commoner in open traditions, as new cross-currents normally mean that new combinations of manuscripts share a source and are therefore liable to err together. Whereas an uncontaminated tradition could show at most one indecisive two-way split pattern, three appear here, namely OPQ:rell., OPQR:rell., and OPQRYZ:rell. The split OX:rell. will also seem ambiguous, as already stated, but in fact is not: OX deserve priority, as they have no common source except the original, while D is a source of the remainder.

6.4. For one who knows the genealogy, it is hard to imagine how much the investigator might reconstruct. He would note that O lies to the 'north-east' of ω, X to the 'south-east' and the remainder to the 'west'. Within the 'westerly' group, RYZ and especially PQ share a 'northerly' tendency with O, and NSTV a 'southerly' tendency with X.[82] Provided that he is no longer certain that OX err together, he may draw fig. 30a. While the apparatus criticus sometimes confirms the division PQRYZ: NSTV of the 'westerly' manuscripts (nos. 4, 10, etc.), R or YZ or all three often join some or all of NSTV in what the critic now sees as error (nos. 1, 3, 15, 38, etc.); hence some adjustments (fig. 30b). The inferred manuscripts aβγε prove to be the lost E, D, C and L respectively.[83] While a

complete reconstruction could not be expected, this outline does explain the main patterns of agreement in error.

6.5. Dom Quentin's manufactured tradition does not provide an ideal test. A controlled experiment with many subjects copying according to a contaminated genealogy withheld from the investigator would have been more realistic. But extensive trials with hypothetical examples are essential to the development of text-critical methods. Failure in such a trial indicates at the very least a limitation, if not a fatal flaw. It should be obvious that any method must start from a statement of the assumptions limiting it, and be derived logically from these. Too many investigators, however, compose or borrow procedures whose intricacies so absorb them that they lose sight of the underlying logic. The justification for every result—the priority accorded to this combination of manuscripts, the common ancestor posited for that group, and so on—must be clear. An elaborate technique is no substitute for a sound rationale.

Notes