THE SCHOLARLY CONSENSUS

In the recent Brill's Companion to Silius Italicus, Ganiban, while considering Sil. Pun. 8.149, a line contained in the Additamentum, asserts that ‘[m]ost scholars consider these lines to be authentic; see, e.g., Santini (1991) 54–6, as well as Brugnoli and Santini (1995)’.Footnote ²² This, as we see it, gravely misrepresents the scholarly consensus, underscoring the fact that a reprise of this issue is overdue. In fact, Brugnoli and Santini, whom Ganiban cites twice, are the only modern scholars who make a full-throated argument for authenticity. They and Heitland form a vocal minority, having written more words in favour than all the combined opinions against.

The lines of the Additamentum Aldinum present a vexing problem. Since Calderini, it has been clear that Anna's story is incomplete without them and so the secondary scholarship has been forced to step carefully around this accretion of uncertainty.Footnote ²³ To examine the evolution of the status quaestionis, we briefly recapitulate the views of editors and translators. Lefebvre (1781) is the only editor who unreservedly accepts the lines: ‘Nec dubito quin Silii sit’. Ruperti is characterized by Heitland as ‘haltingly favourable’,Footnote ²⁴ although some might think him equivocal at best; he certainly notes that ‘the imitation of [Virgil] and Ovid seems too servile’.Footnote ²⁵ Corpet and Dubois note Lefebvre's acceptance but dissent on the basis of the clumsiness of the textual adaptation.Footnote ²⁶ Bauer says: ‘Along with Heinsius and others, I believe these lines were invented in order to fill up the lacuna.’Footnote ²⁷ In the English tradition, Summers's edition appeared not long after Heitland's article, in Postgate's great Corpus Poetarum Latinorum (London, 1905). His notes in such a cramped tome are necessarily brief and refer the reader to his earlier remarks in The Classical Review.Footnote ²⁸ That position is quite clear: ‘Its genuineness is well-proved by Heitland’,Footnote ²⁹ but one wonders whether the note in Postgate's Corpus is deliberately ambiguous—‘Silio non indignos esse luculenter demonstravit Heitland’ (‘not unworthy of Silius’ does not rule out interpolation, only incompetence).

Moving to the modern era, Miniconi and Devallet are guarded, but appear to favour authenticity.Footnote ³⁰ In the 1983 Loeb volume, Duff seems sympathetic: ‘the verses fit in perfectly with the context, and … are such as Silius might have written’.Footnote ³¹ Spaltenstein's 1986 commentary is diplomatic,Footnote ³² but like several others he too finds that borrowings from Virgil and Ovid become both more frequent and more overt. At the turn of the century, Ariemma expressed a similar view: ‘the flavour of pure adaptation … deviates slightly from the Silian norm’.Footnote ³³ Our statistical analysis provides empirical evidence in support of this scholarly intuition. In his 2005 translation, Villalba Álvarez simply acknowledges uncertainty,Footnote ³⁴ but in the most recent translation (2021) Augoustakis and Bernstein, in tune with current thinking, are unequivocal: ‘Lines 144–223 … are considered an interpolation to complete Anna Perenna's narrative’.Footnote ³⁵

In summary, then, we have just Heitland as well as Brugnoli and Santini who argue for authenticity at length. Brugnoli and Santini's arguments are varied and deserve a fuller treatment, which will follow. The only editor or translator who commits unreservedly to authenticity is Lefebvre,Footnote ³⁶ and he offers no support for his position. Delz, Bauer, Sabbadini, and Augoustakis/Bernstein are firmly of the opinion that the piece is an interpolation. Reeve, an expert on the transmission, concurs—convinced on external grounds provided by Summers and internal ones by Delz.Footnote ³⁷ The rest of the opinions fall somewhere in the middle, but even among the neutral commentators most note that the adaptation of Virgil and Ovid increases noticeably in frequency and decreases in subtlety. So, in so far as we have consensus, the prevailing mood is sceptical, with proponents of interpolation outweighing the few defenders.

THE TRANSMISSION OF THE ADDITAMENTVM AND THE IMPORTANCE OF MS C

All theories of transmission that allow for the genuineness of the Additamentum share the following general assumption—that the lines were present in MS S but were lost, somehow, during the creation of Poggio's copy. Then, following the identification of the lacuna, the missing lines were rediscovered, found their way to Guarino and thence to Costanzi. And so, the urgent question is this: assuming that the lines we have received were present in MS S, how, precisely, is it that they are absent from the copies, and how were they then rediscovered? Both Goold and Heitland offer conjectures based on a ‘loose sheet’. Without going into detail, if the codices were bound in such-and-such a way, with so-and-so lines per page, then if the Additamentum had formed the middle leaf of a quire it might have been dislodged and then later rediscovered.Footnote ³⁸ Neither scholar, however, offers an explanation as to how the rediscovery might have happened after so many intervening years. No search can have occurred until the lacuna was noticed, and the earliest such note is after 1440.Footnote ³⁹ Guarino himself (if it were he that recovered them) was not born until 1435.

The most significant challenge to these theories is posed by MS C. In the late sixteenth century an independent manuscriptFootnote ⁴⁰ was discovered in Cologne, which was collated by both Carrio and Modius, the first publishing some readings in 1583, the latter in 1582. We know that those collations were consulted by Heinsius in the 1660s, with the aid of the notes he found in a 1547 Gryphian edition (possibly Carrio's own), and that Heinsius made his own notes in two different editions, a Colinaei and a Dausque.Footnote ⁴¹ These notes of Heinsius were copied ‘quanta fide potui’ by Drakenborch in the preparation of his 1717 edition. Not only is MS C lost, but so too are the collations of Carrio and Modius, the annotated Gryphian relied upon by Heinsius, as well as the Colinaei and the Dausque in which he made his own notes. Now, if MS C contained the lines, then either Carrio or Modius, when performing their collations, should have discovered, and hence recorded, one of two things. Modius, collating against the 1543 Basel editionFootnote ⁴² (without the Additamentum) should have been amazed to see the lines in MS C (Blass uses this point as a key to his claim that the lines were not there).Footnote ⁴³

As for Carrio, collating against a Gryphian (containing the Aldine lines): if MS C had the lines, then it must have had line 157a, which is present in the lines from Costanzi and hence purportedly from MS S, but is not present in the Aldine. The presence of a new line would surely have been noteworthy. This view is also taken by Summers, leading him to dissent from Heitland (‘I think the balance favours the absence of the lines from C.’).Footnote ⁴⁴ However, given this, it is baffling that Summers can accept that the lines’ ‘genuineness is well proved by Heitland’. If MS C did not contain those missing lines, especially given the very close correspondence of MSS S and C in all other respects, then certainly neither did MS S.Footnote ⁴⁵ It is simply impossible that precisely the eighty-odd lines omitted while copying MS S should, coincidentally, happen to be missing in MS C. However, the only way to reconcile their presence in MS C with the silence of the commentators is to assume, via tortuous logic, that they noticed the lines but made no comment (thus Heitland),Footnote ⁴⁶ or to assume that Modius or Carrio did make such a comment but that it was lost owing to the unreliability of Heinsius,Footnote ⁴⁷ Drakenborch, or both of them (considered but eventually rejected by Summers).Footnote ⁴⁸

One final issue to be considered is the cleanliness of the transmitted text of the Additamentum. As Reeve notes, it ‘differs by a single letter (s in 204) from what someone could have written’.Footnote ⁴⁹ Blass uses this as part of his argument to deny that the lines were in MS C,Footnote ⁵⁰ implying that there were no variants because the lines were not there. Heitland presents an alternative—that the lines were clean because ‘as the result of a later search they [were] copied at leisure and under far more favourable conditions than the rest of the poem’.Footnote ⁵¹ This might be plausible as far as it goes, but even if the copy were perfect, the source manuscript was still, it is argued, of the ninth century and in poor condition. Textual problems occur frequently in the transmitted text, despite Poggio's corrections.Footnote ⁵² We have no idea what proportion of these issues stem from problems in MS S and what proportion are due to copying errors, but certainly not all of them can be of the latter sort. It remains an intriguing peculiarity that the only portion of Punica Book 8 that is essentially free from textual problems should be the eighty-one lines of the Additamentum.

For those inclined to accept the view of Blass, Summers, Reeve, et al., who believe the lines to have been missing in MS C, then the matter is already settled—if the lines were not in MS C then they were not in MS S, and if they were not in MS S then we have no existing theory to account for their transmission. However, the evidence from MS C is weak. The manuscript is lost, the collations are lost, even Heinsius's notes based on those collations are lost—we have nothing but Drakenborch, which seems entirely too little. We therefore proceed on the basis that the case from MS C is not proved, intending to show that, even if this is left aside, there is still ample evidence to suggest that the Additamentum was not written by Silius.

EVIDENCE FROM LITERARY ANALYSIS

We now move to a consideration of the Additamentum on philological grounds. It is important to bear in mind that the modern authorship debate is set against the backdrop of a sweeping re-appraisal of the poetic value of Silius.Footnote ⁵³ From his very first sentence, Heitland is deprecating: ‘Silius Italicus is not a poet of the first order. But he has a place of some kind in Latin literature …’. Delz, on the other hand, implies the opposite opinion when, after listing ‘some grammatical, stylistic and metrical observations’ regarding the Additamentum, he concludes that ‘these, and others, I consider to be utterly unworthy of Silius’.Footnote ⁵⁴ Although it is entirely natural for us, as readers, to bring our aesthetic judgement to bear, we must then be aware that we are arguing at one remove from the real question. Whether the Additamentum is good or bad poetry is not relevant—we are asking whether it is Silian. Having said that, it is possible that scholars with a dismissive attitude towards Silius are more liable to accept stylistic anomalies. Heitland, it seems, erred sometimes in this direction with such statements as ‘[w]e may for the present remark that imitation of Vergil can hardly be too servile for Silius’.Footnote ⁵⁵

A greater problem with this manner of analysis is that not only can each small point be rebutted in isolation, but most are presented in terms that are not objectively verifiable or, if they are, are not probative. Heitland, for example, says of line 194 that ‘the rhythm is very Silian’ (whatever that might mean), and at line 187 comments that ‘velamen is common in Silius’ (true, but hardly relevant. There are thirteen occurrences, but fifteen in the Metamorphoses, which is shorter). In any case, if this is to be a comprehensive treatment, then the most important arguments need to be considered. The simplest approach is to work line by line:

145. umbra … magni corporis. For Delz, with characteristic bluntness, ‘ridiculum est’. The model appears to be Verg. Aen. 4.654 magna … mei imago. Heitland offers Luc. 6.720 proiecti corporis umbram, which gives a little support to everything except magni. Spaltenstein is silent, except for a note that magni has been transposed arbitrarily for the ‘more natural’ magna.

146. fors here adverbially (for forsitan) is rare and, as pointed out by Delz, is not used by Silius. Spaltenstein diplomatically reminds us that it is far from the only hapax legomenon in Silius. ‘In any case,’ he continues, ‘the inventiveness of this line and the reference to Vergil are very typical of Silian manner’.Footnote ⁵⁶ In that judgement we bow to his opinion, but of course being ‘typical of Silian manner’ and being of Silian composition are two different things. Heitland has no comment on this line, which is odd (cf. his lengthy note on line 199). These kinds of arguments from rarity are superficially interesting but not terribly useful as evidence. There is no sound statistical test which would tell us whether the use of a hapax legomenon is stylistically ‘Silian’ or not. Philologically, we have yet to see a convincing argument as to why rare words would be more likely from an interpolator (if anything, intuition suggests the opposite). What would be needed here is positive evidence that adverbial fors was more common in humanist poetry.

155–6. These lines transparently rework Verg. Aen. 4.690–1. Delz's verdict is that ‘revoluta, taken from Aen. 4.691, is absurd in this location’. Presumably Delz dislikes the image of Anna flopping back into the lifeless arms of her sister—if so, we agree; it seems bathetic. Neither Spaltenstein nor Heitland offers anything here. Brugnoli and Santini remind us that this is not the only projection of the Aeneadic story of Dido onto Anna, citing Pun. 8.171–3 (also in the Additamentum) and 8.71 (undisputed).Footnote ⁵⁷ The issue, however, is not the projection but the clumsy manner of its execution.

159. devenio. The first word of the line is enjambed, so the clause ends after devenio, punctuated by Delz with a semicolon. What seems initially to be a problem is that the line is scanned with an elision in devenio; hinc which ignores the strong sense-pause. However, Brugnoli and Santini offer at least three more instances of an enjambed initial quadrisyllable being elided across a strong sense-pause: 4.502 Sicania? en; 8.460 Fulginia, his; 13.667 militia. heu.Footnote ⁵⁸ The nascent objection evaporates.

165. Identical to 7.282, and the only time a verbatim repeat occurs in Silius. Noted by all commentators, with the only real defence being mounted by Spaltenstein, who remarks that Virgil reuses part of Verg. G. 2.291 as Aen. 4.445 (not his only repeat—Aen. 4.124 and 4.165 are identical and just forty-one lines apart). Courtney finds this persuasive and suggests, based on several examples, that ‘the composer of the interpolation, having just read Book 7, had that book prominently in mind’.Footnote ⁵⁹

166. Dido aegerrima. Delz, correctly: ‘There is no exemplar for this brutal elision in the name of Dido.’ The name appears thirty-four times in the Aeneid and ten in the Punica, none of which is elided. It is surprising that none of the other commentators addresses this.

179. Numicus. Within the space of twelve lines we have two variant spellings for the name of the river, which are not (per scansion) problems with the text. Heitland concedes that Numicius is the usual nominative form and that its genitive Numici is much more common in literature in general. He defends Numicus with Livy 1.2.6.3 super Numicum flumen, but in fact that is the only other classical instance.Footnote ⁶⁰ However, Numicus, with accusative Numicum, is the form habitually used by Servius in his late antique commentary on Virgil, a text that was well known to humanist scholars. Note in particular that Calderini uses numico in his prescription for the content of the lacuna (see n. 8 above) as well as in his comments on lines 1.666 and 8.358.Footnote ⁶¹

181. rapies. Used here in two senses—Dido instructs Anna to rapies viam (‘set out immediately’) and rapies … tutos receptus (‘take advantage of safe refuge’). Delz is unimpressed: ‘the zeugma seems too daring’, while Spaltenstein is unfazed: ‘Rapies does not have the same sense in the two phrases, but the zeugma explains this.’ Heitland notes a textual problem, but has nothing to say about the zeugma. Delz here is perhaps pushing his case too zealously.

191. abscondidit. Delz correctly observes that the word ‘is foreign to epic diction’. None of the other commentators remarks on this variant perfect (-didit vs -dit) found elsewhere only in comedy.Footnote ⁶² Compare Luc. 4.458 corpora saepe tulit caecisque abscondit in antris.

192. dies … radiis. The first of three lines that Reeve laconically adds to Delz's list of ‘objections on internal grounds’.Footnote ⁶³ To be sure, radiis … solis is much the more common figure of speech. However, contrast: Prop. 4.6.86 iniciat radios in mea vina dies; Ov. Met. 7.411 contraque diem radiosque; Sen. QNat. 5.10.5 aestate incipiunt flare, cum et longius extenditur dies et recti in nos radii diriguntur; and so forth.

195. manifesta. Only here in Silius, but rare in any case. See nn. on lines 146, 199.

196. ab alto is criticized by Delz as ‘obscurum’. This is certainly true, and we can take as evidence the fact that both Heitland and Spaltenstein devote lengthy notes to its construction. The confusion essentially revolves around whether the waters are being drawn back from the sea as in Verg. Aen. 9.125 where the Tiber reverses its course (revocatque pedem … ab alto) or from the deep. In the Fasti, Ovid instead has the river stop still (3.649–52 sustinuit … amnis aquas), which is how Duff, undaunted by the text, has translated this line. Once again, if we argue that the text is not genuine because the meaning is obscure, we would need to show that genuine Silius prizes clarity; that is not a case which anyone should take up with enthusiasm.

199. affarier. An archaic infinitive and a Silian hapax legomenon (in fact, this precise form does not occur elsewhere in classical Latin). This is the second of Reeve's objections. Heitland mounts a lengthy defence and certainly seems successful in showing that Silius ‘is fond of old forms’. In the immediate context of Anna's apotheosis, the solemnity of an archaic form does not seem inappropriate.

209. vigili … voce. Delz, with characteristic terseness: ‘mirum’, presumably in the sense of ‘incomprehensible’. Nobody has a satisfactory interpretation for a ‘wakeful voice’. Heitland offers one semantic conjecture—namely, that Hannibal is ‘awake and talking out loud to himself’—but spends the bulk of his note evaluating proposed emendations before favouring mente. Spaltenstein prefers Bentley's emendation corde for voce, which to him ‘seems quite impossible’.

217. Tirynthius heros. The last of Reeve's additional objections. The reference is to Fabius by lineage, but heros should really refer to Hercules himself. Fabius in Pun. 2.3 is Tirynthia proles. As metonymy, it does not seem impossible. For a full analysis of how Silius connects Fabius to Hercules throughout the poem, see Lee ad loc. with bibliography.Footnote ⁶⁴

Taken on balance, we find the philological arguments persuasive but not conclusive. In our view, the strongest arguments for interpolation are at lines 165 (repeated), 166 (Dido aegerrima), 179 (Numicus) and 191 (abscondidit). We are not persuaded that the quality of the Additamentum is so much better or worse than genuine Silius as to constitute evidence in either direction,Footnote ⁶⁵ but each reader finds something different in each text. This, as much as anything else, motivates our use of computational analysis as an adjunct to scholarly intuition. Before then, however, there is one more consideration.

THE ARGUMENTS OF BRUGNOLI AND SANTINI

Several criticisms of Brugnoli and Santini's L’Additamentum Aldinum di Silio Italico were laid out, in excoriating fashion, by Reeve in his review;Footnote ⁶⁶ while we concur, we will not waste space by repeating them. Leaving most of those flaws aside, the authors bring two lines of argument that merit examination. The first is that there are detectable allusions (riecheggiamenti) to the Punica in Petrarch's Africa (c.1340) and in Walter of Châtillon's Alexandreis (c.1170), including allusions to lines that are contained in the Additamentum.Footnote ⁶⁷ If established as fact, this immediately destroys the theory that the lines are a Renaissance interpolation—there is no need, as the authors attempt, to show that the frequency of allusion to the Punica is somehow consistent between the undisputed text and the Additamentum. So, leaving aside the broader question of those authors’ knowledge of the Punica,Footnote ⁶⁸ all that is required is to evaluate each proposed allusion (to the Additamentum) on its merits. There are only five, so it is swiftly done. We abbreviate some of the passages, but retain the underlining by which Brugnoli and Santini indicate their ‘matches’:

This is the first and best example. Carthaginis arces/urbem is nothing out of the ordinary, but the proximity of construere (struere would be more common) is rare. If there were another four or five matches of this quality, the argument might begin to convince.

Unconvincing. There are dozens of instances of pax near nulla in the classical canon (leaving aside the fact that nihil and nulla are, technically, entirely different words).

These two lines of the Punica are too distant to be considered as a unit. The second line of Silius does not fall within the Additamentum and thus (as discussed) is not relevant to the argument. Considering line 8.201 by itself is no help. Forms of venero near numen are, unsurprisingly, common;Footnote ⁶⁹ no case can be built without the unusual collocation with geminus. Connecting culta to colit seems ambitious.

Alexandreis 5.83 matches only the second line, but in any case the intertext is weak—for example Verg. Aen. 1.371 suspirans imoque trahens a pectore uocem seems at least as good a model. These next lines from the Africa are still cited against Pun. 8.208–9 above:

Again, hardly a convincing intertext—volutans vaguely near vigili. There is just one more:

which seems futile. Not only do the underlined ‘matches’ smack of desperation, the authors themselves provide a more plausible model for the line from the Alexandreis—namely, Ov. Met. 4.213 septimus a prisco numeratur origine Belo.Footnote ⁷⁰

In summary, it simply cannot be accepted that Brugnoli and Santini have proved any kind of connection between either of these two texts and the contents of the Additamentum. Once again, we express no opinion on their claims regarding the Punica in general as an influence on the Africa and the Alexandreis since it is not pertinent to the question at hand.

The other claim, laid out in Chapter II, relates to the way in which Ovidian allusion is handled throughout the Anna Perenna episode (8.44–235). Essentially, the authors argue that allusion is used to tone down the story in the Punica compared to Ovid's racier account in the Fasti, and that this practice (‘l'intento di denaturare il modello ovidiano’) is consistent between the undisputed text and the Additamentum. They then categorize and count allusions in 108 lines of undisputed Silius vs 80 lines of the Additamentum. Statistically, there are many objections. Leaving aside the breakdown into categories, which are completely subjective (the authors themselves identify this as a limitation),Footnote ⁷¹ the total number of allusions cited in each section is not ‘pressoché equivalente’ as is claimed. Sixteen total instancesFootnote ⁷² in 108 lines of undisputed Silius is around 14.8 per cent, whereas eight instances in 81 lines of the Additamentum is 9.9 per cent, although there is no way of knowing whether this variation is signficant. Essentially, the sample is just too small to be worthwhile. In total, about two hundred lines are analysed, of twelve thousand in the Punica. The authors’ argument is interesting from a literary perspective,Footnote ⁷³ but it cannot be made statistically. At this point in the story, anyone, whether Silius or an interpolator, ‘was bound to make ample use of Aeneid 4 and Fasti 3.523–656’,Footnote ⁷⁴ not least because that is precisely what Calderini had said should be done. To build a quantitative picture of authentic Silian style, the authors would have done better to consider Virgilian allusions which occur throughout the Punica and not the allusions to Fasti 3 which are naturally concentrated in this section. The beginning of such an analysis occurs in the very last line of the chapter, where they record the relative proportions of two types of Virgilian allusion. Their data indicates that the Additamentum has a slightly higher proportion of both. This finding—that the Virgilian allusions increase—is consistent with the intuition of many of the commentators (as discussed above) and is, in fact, one of the arguments against authenticity.

A STYLOMETRIC INVESTIGATION

In this section we set out the most novel contribution of this paper.Footnote ⁷⁵ These techniques are drawn from the latest methods in computational stylometry and represent a true cross-disciplinary approach.Footnote ⁷⁶ We employed three different types of analysis to compare the Additamentum to the rest of the Punica. The rationale behind providing three different studies is to explore the nature of the Additamentum from three orthogonal perspectives, examining metre, language and literary allusion. We show that the style of the Additamentum is a statistical outlier in all three terms. As we have discussed, even a very close philological examination is subject to endless debate. Many scholars have expressed reservations regarding the authenticity of the Additamentum, but it has not yet been possible to provide evidence through a unified analysis that considers several factors at once. It is hoped that this section will finally fill that gap.

The first study concerns metrical style. Although the quantitative study of the Latin hexameter is well established in ‘traditional’ Classics and PhilologyFootnote ⁷⁷ and stylometry has been applied to the textual features of Latin prose writers,Footnote ⁷⁸ computational stylometrists have rarely studied the metrical patterns of Latin poets.Footnote ⁷⁹ On the ‘traditional’ side, Duckworth considered the genuineness of the Additamentum in 1967 and concluded that ‘[t]he fact that there are so many similarities between the passage in question and the Punica as a whole argues strongly for the authenticity of the passage’.Footnote ⁸⁰ Duckworth's analysis (and indeed his prolific work on the quantitative analysis of Latin poetry in general) was groundbreaking, but considerable advances have been made in the intervening half-century. His brief investigation compares the percentages of certain hexameter foot patterns, along with some metrics of his own invention (repeats, pattern variety, reverses, etc.), but it has no formal statistical basis.Footnote ⁸¹ We aimed, therefore, to investigate the metrical qualities of the Additamentum using updated techniques. Because this application to Latin metre was novel, it seemed sensible to expose it to formal peer review in a technical journal. A complete description of these techniques and results is now available,Footnote ⁸² and we refer the reader to the full paper for additional detail.

In addition to foot patterns (dactyls and spondees), we analysed pauses (caesurae and diaereses), conflict between ictus and accent, and elisions (the features are described in more detail in Table 1). Because the number of metrical features is reasonably low, our approach provides highly interpretable results (Table 2). To validate this metrical analysis, we first demonstrated that hexameter authors can be distinguished with high accuracy based on their metrical style. In cases where authorial styles are very different, such as those of Ovid and Juvenal, passages as short as ten lines are sufficient. When using passages of at least 75 lines, every classification experiment produced more than 90 per cent accuracy, which supports the application of our methods in the case of the Additamentum (81 lines).

Table 1: A description of feature abbreviations used

Table 2: The two most significant metrical outliers from Silius’ general style. For each feature, we show the squared Mahalanobis distance (Score), the percentage of lines in the sample containing that feature (Samp. %) and the percentage of lines with that feature taken across the entire Punica (Mean %). Higher M² distances are further from typical Silian style. Features are described in detail in Table 1.

To compare the Additamentum with the rest of the poem, we took successive 81-line chunks using a ‘rolling window’. The results show that the metre of the Additamentum differs substantially from typical Silian style (Fig. 1). The specific metrical differences, as compared to the Silian mean, can be seen in Table 2(a). A stretch of eighty-one lines without a single second-foot weak caesura (2WC) is unmatched in classical hexameter,Footnote ⁸³ and presumably this is connected to the marked differences in the first foot (1WC, 1CF, 1DI). The other significant anomaly is the much more circumspect use of fourth-foot ‘bucolic’ diaeresis (4DI). Furthermore, there is only one passage in the Punica whose metrical style is more unusual, that being lines 8.564–644 (during the catalogue of Italian troops).

Figure 1: An analysis of metrical style, sampled as a rolling window throughout the text. Each point represents an 81-line chunk. Chunks with higher scores are more unusual when compared to typical Silian practice.

When the passage from the catalogue (8.564–644) is compared to the Additamentum, it is clear that the metrical qualities in which it diverges are quite different. In the passage from the catalogue (Table 2[b]), most of the distance is created by a single feature—the use of the strong fourth-foot caesura (4SC) is much less frequent than usual. When analysed by hand, thirty-five of the eighty-one lines in this section are built on an identical metrical template: they have a third-foot spondee with a strong third-foot caesura, and the fourth foot is unbroken inside a single word. One possible interpretation of this pattern is that it creates a strongly divided line with a sort of regular rhythm, as if the poet is marching to a martial theme. In any case, it seems that there is a clear poetic device, concentrated in a single feature. However, in the case of the Additamentum (Table 2[a]) there does not seem to be any deliberate poetic effect connecting the five features whose deviances from Silius’ general style make up the bulk of the distance score.

In summary, the metrical technique of the Additamentum differs from the rest of the poem in a statistically significant way (p < 0.001). This result is contra Duckworth, but note that Duckworth analysed only foot patterns, not pauses. Examining Table 2(a), the general proportions of spondees and dactyls in each key position (1SP, 2SP, 3SP, 4SP) have low distances, confirming that, as Duckworth found, they match Silian proportions fairly closely.Footnote ⁸⁴ However, it requires no particular stretch of the imagination to accept that foot patterns are easily counted and imitated. Winbolt offers a well-known and comprehensive guide to the composition of Latin hexameter in which he recommends precise ratios to imitate Virgilian style, and there is no reason to suppose that simple arithmetic methods were beyond a sixteenth-century humanist.Footnote ⁸⁵

For the next experiment, we performed ‘Latent Semantic Analysis’ (henceforth, LSA) on the language of the Additamentum as compared to the language in the rest of the Punica. In this kind of analysis, the text is broken down into either words or ‘n-grams’, but it is the latter method that performs best on this problem.Footnote ⁸⁶ The n-gram approach involves considering fragments of words: for example, ‘punica’ contains the 3-grams pun, uni, nic and ica.Footnote ⁸⁷ By analysing the relative frequencies of every n-gram in the texts it is possible to build extremely effective classifiers. n-grams are sensitive to minute subtleties of authorial style in terms of both lexicon and grammar (because of inflections). An immediate matter for consideration is that this type of stylometric analysis is typically applied to prose and has mostly been validated for much larger pieces of text. Because the Additamentum needs to be analysed as a single passage, this study works with 81-line chunks, which are around 500 words. We hypothesized that the semantic density of Latin poetry would allow strong results to be obtained, even though the samples are small. To this end, it was critical to establish first that we could effectively distinguish different authorial styles at our target sample size. We chose ten works (not restricted to hexameter): Aeneid, Eclogues, Georgics, Pharsalia, Punica, Thebaid, Juvenal's Satires, Ovid Amores Book 3, Fasti and Metamorphoses. To perform the validation, we used ‘supervised’ classification algorithms. In a classification experiment, the computer model is ‘trained’ on a subset of the data (commonly 80 per cent) and then attempts to predict the classes of the remaining 20 per cent, which it has never seen (in this case, it tries to predict the work).Footnote ⁸⁸ The overall accuracy for the supervised classification tests was over 95 per cent, indicating that it is reasonable to apply LSA to the data we are examining—in particular, reliable results may be achieved even working with these seemingly small chunks.

The result presented here uses ‘unsupervised’ clustering, in which the chunks are arranged into clusters by the computer algorithm, and the individual points are then labelled by work.Footnote ⁸⁹ The results of this clustering are shown in Fig. 2. The clustering performance is extremely strong, and it is encouraging to note that different works by the same author cluster together but retain individual identity. The Punica, as can be seen, has a slightly messy stylistic border with the Aeneid (as we would expect), but the Additamentum itself is markedly more similar to the lexico-grammatical style of the Aeneid than to any other passage in the Punica.Footnote ⁹⁰

Figure 2: ‘Latent Semantic Analysis’ on the language of the Additamentum as compared to the language in the rest of the Punica.

It is noteworthy that a lengthy section (Pun. 14.300–584) is detected as being stylistically close to Luc. 3.514–673.Footnote ⁹¹ The passage from Lucan relates the naval attack on Massilia, while the section in Punica Book 14 deals with a sea battle near Syracuse. Both passages make rich use of technical language concerning warships and there are multiple synonyms for ‘ships’, ‘sailors’, ‘water’ and ‘fire’. It seems that the specific language of naval combat is distinctive enough to dominate the general differences in authorial style between Silius and Lucan. This raises an important point. The battle at Syracuse is deliberately modelled on Lucan,Footnote ⁹² so it is reasonable to wonder (given that intentional allusivity can pull a passage so far towards the cluster representing a different author) whether the Additamentum is simply being shown as highly allusive. Without intending to dismiss the concern (this is, after all, why we chose to perform three different studies rather than to rely on a single approach) we make two points. The first is that after the application of TF-IDF stylistic similarity scores, by design, are more affected by uncommon words than by common ones, and so this rare naval vocabulary has a disproportionately large effect; there is no such specialized lexis in the Additamentum. The second point is made in two parts. First, the Additamentum is shown as strongly Virgilian, but the surrounding text is not. This seems odd given that the extended engagement with Aeneid Book 4 begins at around line 8.40. Second, as so well demonstrated above (n. 73), allusion in the Additamentum is as much (or more) to Fasti Book 3 as to Aeneid Book 4, and yet the lexico-grammatical style as detected by the clustering appears slavishly Virgilian. None the less, it should be made quite clear that the problem of differentiating ‘true’ allusivity is certainly a limitation of this technique.

The third and final experiment was designed specifically to investigate the question of Virgilian reuse.Footnote ⁹³ As mentioned elsewhere in this paper, many commentators have noted that, although imitation of Virgilian lines is common in Silius, the level of borrowing within the Additamentum is unusually high. To perform this experiment we began with data from the well-established tool Tesserae which ‘aims to provide a flexible and robust web interface for exploring intertextual parallels’.Footnote ⁹⁴ We configured the tool to search for parallels between the Punica and the Aeneid, restricting the output to high-quality matches, and then post-processed the results. To cover the technical minutiae would be tiresome; however, certain important limitations must be identified and explained. Tesserae finds parallel lines that share two or more words. The software has the ability to match words which are different forms from the same lemma, so struxit will match strueram, but in some cases this can produce false matches where morphological forms overlap. Each Tesserae match is assigned a score based on its custom algorithm, which generally lies in the range of 6 to 10 (higher being better). Qualitatively, the Tesserae authors have found that matches with a score of 7 or higher tend to be genuinely relevant when reviewed by a human,Footnote ⁹⁵ although some matches might be missed at this threshold. For our purposes, since the matches could not be individually reviewed (there are around thirty-five thousand in total), we preferred an even higher threshold to avoid false positives. From there, we summed the scores for each chunk of eighty-one lines and considered this as a general score of ‘Virgilian Intertextuality’ for that chunk. We then graphed this score for a rolling window of sequential chunks taken throughout the poem (Fig. 3). A full philological exploration of the results is beyond the scope of this article, but it is comforting that we can observe some expected dips in reuse, for example at the end of Book 8 (a catalogue of Italian geography with no parallel in Virgil) and of Book 14 (the naval battle which we have already discussed as being stylistically closer to Lucan's Pharsalia Book 3). In other words, the method appears to produce sensible results. This analysis confirms that the whole Anna Perenna episode is unusually Virgilian—entirely expected given the densely woven echoes of Aeneid Book 4. However, the Additamentum itself has a markedly higher score than the rest of the Punica and is a clear outlier both locally and in terms of the poem as a whole (p < 0.01).Footnote ⁹⁶ This analysis suggests that, although Silius is undeniably attracted to Virgilian style, it is (pace Heitland) ‘possible for the imitation of Virgil to be considered too servile’, even for Silius.

Figure 3: Virgilian borrowing, sampled using a rolling window through the text. The score for each chunk is the sum of the best Tesserae score for each line. Higher scores are more Virgilian. The Additamentum is more than three standard deviations from the Silian mean.

In summary, these three experiments measure style in three quite different ways:

1. 1. Lexical/Grammatical Style

   The most orthodox analysis is the ‘Latent Semantic Analysis’ (LSA) approach using TF-IDF normalized n-grams. This type of analysis has been applied to many texts in a variety of languages and is widely considered the most robust of the general stylometric techniques. We demonstrated that LSA can be applied to Latin poetry with small sample sizes while still yielding extremely accurate classification results. Our visualization (Fig. 2) displays meaningful and well-separated clustering behaviour, both at the level of authors and at the level of works. The LSA experiment shows that, in lexico-grammatical terms, the Additamentum is an outlier from the rest of the Punica, and the clustering results suggest that the style of the Additamentum is more similar to Virgil's Aeneid than to Silius—just as many scholars have already observed.

2. 2. Metrical Style

   The metrical analysis (Fig. 1, Table 2) shows the highest-confidence margin of the three results, but is also the most novel technique. As with the LSA approach, it was shown to provide highly accurate classification on small samples and offers the most interpretable results. In the metrical analysis the Additamentum is one of two extremely strong outliers (p < 0.001). The patterns of dactyls and spondees employed in the Additamentum are a reasonable match to Silian style (something that is quite feasible to imitate), but the handling of pauses in the hexameter is clearly different. We believe that this metrical fingerprint is the most difficult for an interpolator to conceal.

3. 3. Virgilian Borrowing

   The final experiment measures direct reworking of Virgilian lines and is based on data from an external tool, Tesserae. The results confirm the intuition of Spaltenstein, Delz, Ariemma and others by showing that the Additamentum displays significantly more direct borrowing from Virgil than Silius does in general (p < 0.01), even allowing for the deep connections between the Anna Perenna episode and Aeneid Book 4.