B. Frischer, Shifting Paradigms: New Approaches to Horace's Ars Poetica. Atlanta: Scholars Press, 1991. APA American Classical Studies, No. 27. Pp. xiii + 158; 2 black and white plates. ISBN 1-55540-619-X (hb). ISBN 1-55540-620-3 (pb). $24.95 (hb). $16.95 (pb).
Reviewed by Edward Sacks, Bryn Mawr College.
Second Review by Paul Keyser (below)
For Frischer, Horace's Ars Poetica [AP] is typically read under the paradigm (hence the title) of a straight-forward didactic treatise. But for F., the poem, so taken, seems to be nothing more than "tedious ramblings on poetics" (p. 61) and the "speech of a very unauthoritative dullard...." (p. 87). F. proposes a new reading of the AP as parody. Read this way, the AP may be seen as a witty send-up of ancient literary criticism, and "brilliantly amusing fiction." The speaker of the poem is now not Horace, however, but some ignorant grammaticus, the butt of Horace's satire.
As underpinnings for this interpretation, Shifting Paradigms considers four basic problems of the AP -- title (Chapter 1); date of composition (Chapter 2); personae in the poem -- the Pisos and the speaker of the poem (Chapter 3); and, finally, genre (Chapter 4).
In Chapter 1, F. shows that the ancient testimony strongly favors the title Ars Poetica or Liber de Arte Poetica, rather than Epistula ad Pisones. While F. may ultimately be correct in his conclusion (of interest to F. for guidance in interpreting the work), the problems, as F. notes (p. 16), are that at best Ars Poetica is a name applied about a century after Horace's death (by Quintilian), and the ancient titles given to works are sometimes unreliable. We thus still cannot be certain what Horace called the work (p. 51), so that any interpretative guidance from the title would be tentative, but F. does at least challenge the view of those who insist the AP is a literary epistle.
In Chapter 2, F. argues for a compositional date of 24-20 B.C., rather than one closer to the end of Horace's life in 8 B.C., as is sometimes asserted. F.'s arguments for this dating, based on stylometric grounds, are discussed by Paul Keyser in the following review.
Chapter 3 proceeds from the conclusion in Ch. 2 that the poem can be dated to 24-20 B.C. This permits F. to argue that the Piso père of the poem is L. Calpurnius Piso Caesoninus (cos. 58 B.C.) rather than Caesoninus' son, L. Calpurnius Piso Pontifex (born 48 B.C.; cos. 15 B.C.; city prefect 13 A.D.). In 24-20, Caesoninus would be about 80 years old, and still a possible addressee (if alive), while a compositional date nearer 8 B.C. would almost certainly demand Pontifex. According to Porphyrio, our only ancient source to identify Piso père, Pontifex was himself a poet. He also was the patron of Antipater of Thessalonica, who composed an epic about the war Pontifex had waged in Thrace (PIR2 Calpurnius 289). (This latter fact is surprisingly not mentioned in the discussion of Pontifex's life, pp. 53-4, yet it bears on the issue which F. raises later, namely why the AP focusses on epic.)
In addition to noting that in 24-20 B.C., Pontifex would be too young to be a father with children described as iuvenes, F. rejects Pontifex because he thinks Porphyrio's and Horace's Piso père are two different individuals: in the AP, the father seems to be a critic to whom the younger Pisos are to show their work, whereas Porphyrio describes his Piso pere (Pontifex) as a poet. But cannot poets be critics? Horace himself would be an example in point, as would Philodemus, the critic/poet patronized by Caesoninus.
F.'s first hurdle is to provide evidence that Caesoninus was even alive in 24-20 B.C. Earlier scholars had assumed that Caesoninus did not survive the triumviral period, but F. cites three inscriptions from Pola (p. 55) for evidence of his existence ca. 33 B.C. However, there are serious difficulties in connecting these inscriptions with Caesoninus.1
F. argues that all three inscriptions refer to the same man, L. Calpurnius Piso Caesoninus, cos. 58. But in Inscription 1 (an official document of a duumviral commission), it is unlikely that Caesoninus, a man of senior consular and censorial rank, would find himself ranked second to L. Cassius Longinus (tr. pl. 44; RE #65), a man much his junior. In fact, it will be noted that the L. Calpurnius Piso of this inscription is not given the agnomen "Caesoninus," while the L. Calpurnii Pisones in the second and third inscriptions are. A more plausible explanation is that the Piso in Inscription 1 is the L. (Calpurnius) Piso who shows up as a legatus Antoni in 43 B.C. (Cic. Phil. X 13; RE #81 = #73a in Supp. III). He would be a near contemporary of L. Cassius Longinus, and a much more appropriate colleague.
Inscriptions 2 and 3 are also problematic. The Caesoninus in Inscription 2 is called "consul." But, as F. points out, the earliest year in which the inscription could have been erected is 33 B.C. Caesoninus, as we know, was consul in 58 B.C., and at no time thereafter. As far as I know, an inscription describing a man as cos. outside his year of consulship would be unique in Roman official documents (F. does not adduce any parallels). Surely, we must assume that Inscription 2 refers to a L. Calpurnius Piso Caesoninus in his year of consulship, some time after 33 B.C. We know this other Caesoninus as Pontifex (cos. 15, the son of F.'s Caesoninus), because he is described as such in our literary sources (composed after his death), but he could not have received that agnomen until he had become a pontifex, sometime later in his career. Until he was known as Pontifex, his agnomen was undoubtedly Caesoninus, as had been the agnomina of his forefathers before him. Inscription 2 thus provides important evidence that Pontifex used his ancestral agnomen, Caesoninus, prior to taking on his new agnomen at a later time. Inscription 3 most likely refers to the same "Caesoninus" as Inscription 2, i.e. Pontifex.
F. suggests that the educated reader immediately would have assumed that Piso pere was Caesoninus, since Cicero had pilloried him in the In Pisonem, facetiously calling him a grammaticus.2 But in view of the fact that both Caesoninus and Pontifex had literary pretensions, the educated reader could reasonably have considered either one the addressee. The choice between them would have depended in large measure on when the AP was composed.
F. argues (p. 61) that the AP is a parody, because Horace undermines the authority of the speaker of the AP, when that speaker makes statements discordant with Horace's remarks in other works. But the examples cited by F. are not so very discordant. For example, AP 385-90 (spend time refining your work before you publish it) is not antithetical to Horace's remarks at Ep. II.1.34-35 (classical poetry is not better than modern poetry simply because it has been around longer). The first remark relates to the time and care to be spent on a work before publishing it; while the second relates to the esteem a work should receive, based on the time after it has been published.
F.'s second argument for the parodic nature of the work -- that the speaker of the AP puts himself into dubious literary-critical company (p. 62) -- is also unpersuasive. The three critics whom the AP cites with approval are Quintilius, Sp. Maecius Tarpa, and Piso pere. Since Horace himself revered Quintilius (as F. notes, pp. 67-68) and the AP also cites Quintilius as a worthy critic, the views of Horace and the speaker of the AP coincide and Q. can in no way be deemed dubious company. F. notes, too (p. 67), that the speaker of the AP was, like Q., arrogant towards poetasters, so again any distance between Q. and the speaker of the AP is minimized.
This brings us to Sp. Maecius Tarpa. Here, Horace tells the young Piso that if he is writing tragedy, he should show his work to Tarpa (AP 387), who had been a licenser of plays in 55 B.C.3 F. states that the authority of the speaker of the AP in recommending Tarpa is undermined by the facts that (1) Cicero had belittled Tarpa's taste in Ad Fam. 7.1.1; and (2) Horace reveals his negative opinion of Tarpa in Sat. I.10.36-39. But what Cicero may have said about Tarpa in 55 B.C. has little bearing on what Horace may have felt about Tarpa more than 30 years later. It is true that Horace in Sat. I.10.36-39 states that he will not be writing drama which will end up on the stage, with Tarpa as judge. But this is because the genre is not congenial to his artistic powers -- he is not necessarily trying to avoid Tarpa. Indeed, in Ep. II.1.208 ff. Horace states that even though he is not a dramatic writer, he does admire the talent of someone who can write tragedy well. In the very different context of the AP, there is nothing inconsistent in using Tarpa's name as an example of the kind of critic an aspiring tragedian should approach.
What of Piso père? Remember that he is one of the addressees of the poem, perhaps the very one who commissioned the work. Unless Horace is taking extreme liberties, or is out of his mind, he will not be mocking his patron (80 years old, in F.'s theory), or characterizing him as "dubious ... company". Now, if Piso père is Caesoninus, Horace probably admired him early in his career (as F. notes, p. 64). Evidence of Caesoninus' poor literary taste, then, comes not from anything Horace says, but here F. resorts to a wholly different source, namely the jibes which Cicero, a political enemy, had aimed at Caesoninus. F. suggests (p. 65), as part of the "fun" of the AP, that its genesis arises from Cicero's reproach of Caesoninus in the In Pisonem (quid nunc te, asine, litteras doceam). Thus, Horace would then (most tastelessly) be alluding to, and carrying on, Cicero's attack (over 30 years old) and precisely teaching Caesoninus literature. One problem with this argument is that F. does not show that the literary views in the AP were consonant with Cicero's. There is also no convincing evidence of verbal allusion from the AP to Cicero.
Other arguments which F. adduces for his thesis that the speaker of the AP is a hopeless conservative (because, F. says, these genres had died 50-100 years earlier, p. 63), and to be distinguished from Horace himself, are similarly open to question. That the writer of the AP draws his rules of poetry from comedy, tragedy and epic is not so much evidence of his conservative taste, as F. argues, as due to the importance these genres held in the rhetorical and philosophical tradition from which the rules of the AP are drawn. Since the "real" Horace speaks of these genres in Epistles II.1, we do not have to invent a persona to explain their occurrence in the AP. In addition, these genres had certainly not died in Rome around the time of Horace.4 Finally, we know that at least one of the dedicatees of the poem, viz. Pontifex, appreciated epic, because he was the protagonist in one, written by his client Antipater.
F.'s parodic reading of the introductory lines of the AP will perhaps cause readers the greatest surprise. Among the inconsistencies (leading to his characterization of parody) which F. argues are present in these verses are as follows:(1) The speaker of the AP is inconsistent with his own advice, because, e.g., he begins with a descriptio, while he condemns descriptiones in AP 14-19 (p. 73). But as the AP condemns only irrelevant descriptions, and since the description at the beginning of the poem is certainly relevant to the issue of coherence in poetry, there is no inconsistency.5
(2) The poet of the AP botches the introductory metaphor of the disjointed monster, and thus engages in excessive poetic license, even though the point of the AP here is that the poet should not engage in excessive license. But the botching for F. consists of the fact that he can conceive of two ways in which to understand the monster metaphor. Yet that does not qualify the metaphor as either "botched" or as excessive license.
(3) The AP is a monstrous book, like the monster decried at its beginning, since it lacks a conventional conclusion. But the conclusion of the AP (describing the mad poet) is relevant to the last section of the poem (whether a poet is made or born) and is unlike the randomly formed monster at the beginning of the AP. F. notes that "the AP is open-ended like many of Horace's poems" (pp. 93-94). Thus, if the AP is open-ended and "monstrous," so are other Horatian poems. Thus, open-endedness is not a feature by which the speaker of the AP can be distinguished from the "real" Horace.
(4) The speaker of the AP shows himself to be a conservative ignoramus about the excesses of contemporary painting, since there really were (according to F.) paintings of the sort which the AP criticizes at the beginning of the poem. But the monster which the AP condemns is a concoction of a great many species: a woman's head, horse's neck, bird's body and fish's tail (AP 1-5). Further, the feathers are of different colors (varias, AP 2 -- perhaps even taken from different kinds of birds) and the limbs are taken from many different types of animals (undique collatis, AP 3). None of the actual paintings which F. cites in Table XVII (pp. 78-79) approaches the confusion of the monster in the AP. Moreover, Horace in the AP is going out of his way to describe an inappropriately mixed creature -- he does this with turpiter and undique collatis membris (AP 3). Whatever the permissible bounds of artistic variation might be (and Horace in AP 9-11 emphasizes that a good deal of license may be accorded artists), Horace drew his monster so as to exceed those bounds. Now, either the "real" Horace believed in artistic limitations or he did not. If he truly believed in no limitations on the artist, then perhaps we can read the opening of the AP, with F., as not rep resenting Horace's own views, but rather those of some other persona. But Horace is not, it seems, a poet of the fantastic, or one who feels that anything goes. (Cf. e.g., Ep. II.1.114-17, 166-67, 189-96, 232-37; Ep. II.2.109-14.) So, if the "real" Horace did believe in bounds, the monster image at the beginning of the AP is an adequate and appropriate way of criticizing a work run amuck.
Finally, in Chapter 4 (pp. 87-100), F. defines the genre of the AP. The argument proceeds from F.'s initial assumption (p. 87) about the parodic nature of the work -- in form, F. claims, it is more a satire than an epistle (pp. 90-95). But the formal aspects on which F. relies to disprove the epistolary nature of the AP are paralleled in other Horatian epistles, either directly, or with slight modifications. F. claims that:(1) The AP fails to name the addressee(s) in the first sentence. This, however, is paralleled in Ep. I.7. And in fact, the Pisones are embraced within the amici of the first sentence of the AP, then identified by name at the very beginning of the second sentence, in v. 6.
(2) The introduction of the AP is not a standard one for an epistle. But similar introductions appear in Ep. I.6 and Ep. II.2 (which, like the AP, begins with a hypothetical condition in medias res).
(3) The AP does not have a standard epistolary closing, but is open-ended. But the open-ended moralizing at the end of the AP is paralleled, inter alia, in Epp. I.16, I.17, and II.2.
(4) The possible motivation for the AP does not become clear until vv. 385-390 (we assume that the elder son of Piso is thinking of writing a poem and has asked Horace for advice). This is paralleled in Ep. I.19 and Ep. II.1.
Rejecting the AP as a standard letter, but also conceding that it contains some characteristics of the epistolary form (p. 96), F. also concludes that the AP is not wholly a didactic poem either. Therefore, it must be some tertium quid, which he finds in the genre sermo (p. 97). But if sermo is a genre which includes epistles, F.'s concern about whether the AP should be classified as satire, or epistle, seems somewhat moot. And given F.'s concern in Ch. 1 with titulature as pointing the way to interpretation, it is possibly significant that Horace did not entitle the AP a sermo, either. Even if the AP's genre is some tertium quid, the sermo does not exhaust the possibilities of such mixed genres. In fact, the AP may very well be sui generis with its own poetic rules, and some effort should be made to interpret it on its own terms.
We must always keep in mind what kind of parody F. deems the AP to be. F. has not shown that the AP violates all the standards of poetry which Horace expresses elsewhere.6 Nor has he shown that the principles in the AP are ones to which Horace could not in any way have ascribed. Similarly, he has not demonstrated that the principles in the AP humorously exaggerate (parody, if you will) contemporary theories of poetry. Indeed, to the contrary, the AP's parody for F. consists of precisely the fact it so well represents straight-forward ("dull", to F.) contemporary literary theory. Where, then, is the parody?
For F. it consists not so much of the actual substance of the work, but rather the circumstances surrounding the composition of the work -- namely that a great poet should deign to produce "rules" of poetry which sound so commonplace. While we may be disappointed in the remarks Horace has to offer about writing poetry, we should remember that Socrates in the Apology was similarly disappointed when he questioned Athenian poets about their art. While Shifting Paradigms raises an interesting parodic interpretation -- one which does make sense for some other Horatian poems -- it does not seem to work here.
 I wish to thank Prof. T. Corey Brennan for pointing this out. The three inscriptions are as follows:(1) L·CASSIUS·C·F·LONGIN(US) | L·CALPURNIUS·L·F·PISO· | IIVIR(I)... [CIL V 54 = ILLRP 639 = Inscr. Ital. X.i.81] (2) L·CALP[URNIUS·L·F] | PISO·CA[ESONINUS]· | CO[S] [CIL I.22512 = ILLRP 423 = Inscr. Ital. X.i.65] (3) [L·CAL]PURN[IUS]·L·F· | [CAE]SON[INUS] [ILLRP 424 = Inscr. Ital. X.i.708]  F. also suggests that four scattered Horatian lines (three in Epistles I; only one in the AP) allude to some metaphors in Cicero's orations against Caesoninus (p. 58) (at least two of these metaphors are unremarkable, e.g. "remove the cloud from one's brow"). From this F. argues (p. 59) that Horace identified with Caesoninus as an Epicurean, and this carried over to the AP. But, wholly apart from the tenuous nature of these possible allusions, under F.'s theory there should be no linkage between the Horace of the Epistles (who speaks in propria persona) and the (to F.) alien persona of the speaker of the AP, whom F. says Horace is satirizing.  Tarpa would be perhaps in his 60's in 24-20 B.C. If the AP was composed closer to 8 B.C., and if Tarpa was not an active critic then, the line should be taken more as "show your plays to someone like a Tarpa."  See J. W. Duff, Literary History of Rome (New York 1960) pp. 446 ff.  Incidentally, the speaker of the AP is certainly consistent with himself in advising the aspiring poet to use the in medias res technique (AP 148), and in using it himself at the beginning of the AP.  F. does promise to show this in another publication (p. 19). Yet, even if F. does show some inconsistencies, that by itself would not establish parody. But in fact many key concepts and themes about poetry in the AP do parallel those which appear in other Horatian works. Just to cite a few: the poet gives examples for life, promotes the education of the young and serves the cause of religion (Ep. II.1.126-38 ~ AP 391-407); the poet should know his limitations (Ep. II.1.259-60 ~ AP 38-40); the poet should accept criticism from others, and should revise his work with the same spirit as a censor (Ep. II.1.221-2, Ep. II.2.110-14, Sat. I.10.73 ff. ~ AP 386-90, 419-52); the poet will use old words and coin new ones (Ep. II.2.115-19 ~ AP 46-72).
Also Reviewed by Paul Keyser, University of Alberta.
In an attempt to reinterpret the Ars Poetica, F. seeks to redate it (to 24-20 B.C., from the generally accepted 28-8 B.C., or the "currently fasionable late dating to the end of Horace's life," p. 3), and turns to stylometry to aid him in his quest. I here consider only that portion of the book (roughly one third: pp. 17-49, 109-114, 143-58).
His point of departure is the work of Duckworth on the metrical patterns of Horace's hexameters.7 In essence Duckworth examined the frequencies of the sixteen possible patterns of the first four feet of the line (from dddd to ssss, where d = dactyl and s = spondee). Duckworth's assumption was that any changes were monotonic in time (and that, e.g., Epist. I predates Epist. II.1). The results were, as F. argues, ambiguous in that for some patterns (or groups of patterns) the Ars seemed sometimes to predate Epist. I, sometimes to fall between the two, and sometimes to postdate Epist. II.1 (pp. 20-2). F. applies various more rigorous statistical tests to Duckworth's data; although his explanations are rarely clear, he correctly concludes (based on his figures) that a connection between metrical pattern and date is unlikely.
More important however are his own results. He briefly uses the rate of hapax legomena (i.e. words occurring once only in a given work, e.g., Sat. I), but focuses his effort on the changing rate of use of certain "function words." To this we shall return below. He rejects the use of average word-length (p. 41 and Table N, p. 153) as it does not vary from poem to poem greatly. He is probably quite right, though he never notices the extensive bibliography. He rejects the use of sentence-length (pp. 41-2, and Table O, p. 153), which he calls "the ratio of words per strong stop," as it gives results which are different for the hexameters and the lyrics, and as punctuation is "notoriously arbitrary." Again he is probably quite right, but again omits the extensive bibliography. His treatment of hapax legomena is woefully inadequate. In counting words one may count instances of a given grapheme ("string" or "token," thus pater and patres are two words), or instances of a given lexeme ("type," thus all forms of pater are added together), or instances of a given meaning (thus pater might be counted as any of several categories). In a highly inflected langauge such as Latin, probably the poorest choice would be graphemes (cp. the English case: if go appears multiple times in a text but going only once, could that possibly be statistically significant let alone meaningful?). Yet that is F.'s choice, on the grounds that "it is impractical to study a corpus as large as Horace's" via lexemes (p. 42). It is not at a ll impractical if one uses the lexicon to Horace by Domenicus Bo (1965) -- there is no need to bewail "the current lack of a parser for Latin" (p. 42). Further -- he is a bit hasty to conclude that the counting of hapaxes (however done) is "our last hope" (p. 42) for establishing chronology -- what of parts of speech, uses of various grammatical forms, word-order, etc.?
But given that he elects to count graphemes, he ought to go about it properly, which he does not. First of all, both the rate of words occurring twice only, thrice only, etc. as well as the rate at which words occurring a given number of times (zero, once, twice, etc.) in poem A are found to appear in poem B, are also significant. Vocabulary studies are far more complex than F. makes out.8 Second, he treats the data he does take abysmally. He first applies the chi2 test (described above) which would tell him if there is likely an association between the 'variables' of (a) the nine poems (all hexameter and lyric) and (b) the categories unique and non-unique strings. But this is a most peculiar procedure -- it is perhaps possible to treat sets of poems as a set of disjoint categories representing some sort of nominal (not arithmetical) variable (as above with metrical patterns), but I do not believe it is defensible to treat as a variable the pair of disjoint categories "unique strings" and "non-unique strings." What, pray tell, is varying? Furthermore, by failing to make clear how the expecteds are calculated, F. here obscures the point that the 'expected' percentage of "unique strings" is the same for all poems in his calculation (62.8% as it happens). Indeed the variations from this are larger than would be expected if merely random (they are 52.8%, 55.2%, 56.9%, 72.4%, 73.0%, and 66.5% for the six hexameter poems in order as above, and are 68.0%, 70.4%, and 73.2% for the lyrics), but to assign that variation to some aspect of the nine poems is to beg the question. It may be that whatever "percentage of unique strings" measures is something which varies a lot. So far from a "statistically significant pattern ... confirmed by chi-square ... tests of the data," F.'s tests here prove just nothing. He then assigns to the poems numerical dates as given by Vretska in Der Kleine Pauly (s.v. Horatius ), p. 44, and plots the percentage of unique strings (hapax legomena graphemes) in the three sets of lyrics (Epodes, Odes I-III, and Odes IIII). This seems to show a linear increase, but of course with only three points and a modest difference of a few percent (from 68% to 73%) it is almost inevitable that the data appear linear. Furthermore, if the proper uncertainties on the counts (of a few percent each) and on the dates (of a year or two each) were to be included, the line would appear very fuzzy indeed (none of these percentages or uncertainties is given by F.).9 For the hexameter poems he has five more or less firm dates and when the percentage of unique strings is plotted versus the A. U. C. date for these five (Sat. I, etc. as above, less the Ars of course), the result (despite F.'s claims) is not much like a line (Table XV, p. 46). (He reports the result with misleadingly excess precision; a reasonable report would be: Y = - (610±256) + (0.92±0.35)X, where Y = percentage of unique strings and X = date given as years A.U.C., based on his figures.) The less linear character of the data can be seen in the larger uncertainties on the parameters. He interprets this formula as giving a date for the Ars of 21/20 B.C., but in fact, when the uncertainty on the slope parameter (0.92±0.35) is included in the calculation, as is necessary,10 the result is a date of 733 ± 5 A.U.C. (or 20 ± 5 B.C.) -- more or less the status quo ante (cp. F. pp. 17-18, where the range of dates is 28 to 8 B. C.).11 And if the uncertainties on the five 'firm' dates and on the percentages of unique strings were to be included, the uncertainty on the result would be somewhat larger than ±5 years. So F. is far from the mark when he describes his result of 21/0 B. C. as of "high reliability" (p. 47).
What about F.'s study of the changing rate of use of certain "function words" (pp. 26-40, 47-8, 109-114, 143-52, 155-8)? Despite focussing most of his effort here, his results are even worse. He starts well (pp. 26-7) by citing what may be the only generally accepted stylometric result (on the Federalist Papers), in which the relative frequency of "function words" turned out to be the most reliable discriminator between two possible candidates for authorship. F., with a wild hope, transfers this to the problem of chronological discrimination among a handful of works in two genres of one author in Latin.12 He seeks to establish trends in the frequency of use of these words (which may differ numerically between the lyrics and the hexameters, but should show the same pattern within each set: p. 30). He examines 51 words (Table, p. 31), prepositions, conjunctions, and adverbs, most (35) of which turn out to be too infrequent to be useful as statistics. Of the remaining sixteen , he claims that twelve display no consistent pattern (atque, aut, cum, et, iam, in, non, nunc, si, sic, ut, and uel) while four display a pattern consistent between lyric and hexameter (ad, nec, per, and sed).
How has he established this claim? The argument is simply mad. In Appendix II (pp. 109-114) he examines the probability that four pairs of trend lines would match out of a sample of sixteen. But the matching itself was established by eyeball, no more. He uses some rather over-subtle mathematics (the binomial distribution gives the probability of finding X positive results in a sample of n if the a priori expected probability is known),13 and combinatorics (the various ways one can classify three-point three-level trend lines and five-point three-level trend lines), but the fundamental problem is never addressed: just how did he decide that the four pairs matched while the others did not? The fact that four of sixteen is more than would be expected by chance (that part I grant he has established) is probably telling us that F. examined the trend lines through rosecolored glasses. When we look at those trend lines (pp. 143-52) it is very difficult to see how they could be modeled as three-level lines (in fact the three or five points vary in level freely). Moreover, the match of the lyric and hexameter trends for his chosen four is really very poor (see Tables K-L, pp. 151-2), as is the claimed match between the trend of ad and that of per (Table K). Though the latter by itself does not destroy his argument, it does show how flexible his standards are; the first observation by itself renders nearly all the remainder of his discussion moot. He finds that for ad the lyrics display a positive-curvature (U-shaped) parabola (p. 36 -- really it is just a V, and of course any three points determine a parabola), and claims that the hexameters show the same thing -- if we disregard Sat. I "in accordance with the principle of parsimony in modelbuilding." Well, if we disregard Epist. I on the same plot we get a relatively smooth linear rise (and not such a bad one even retaining Epist. I), and linear models are generally to be preferred on the principle of parsimony. I would further argue that for example the lines of et, iam, in, and nunc show at least as good a match between lyric and hexameter (Tables C, D [iam and in], and E); furthermore et and nunc are at least as similar to one another as ad and per are to one another.
Finally, the whole approach of matching trend lines by visual appearance (on a three-level model) is methodologically very suspect. The proper thing to have done would have been to use the otherwise so oft-applied chi-square test (and the conventional dates of the poems other than the Ars) to see if indeed the rate of use of ad, etc. is consistent between the groups lyric and hexameter. F. does almost this test, but finds that although the two 'variables' (a) poems and (b) the set ad, per, sed are not independent, they are only weakly associated (pp. 32-3). He tries various dubious statistical tricks to show that the weak association is not so weak (pp. 33-4). F. fills rather too much space (pp. 34-40) looking for associations of the Ars with other poems which maximise the resultant chi-square (computed, for the two 'variables' [a] poems and [b] the set ad, per, sed or [b] the word nec), on the hypothesis "that poems grouped together belong to the same period of composition" (p. 34). Better is the attempt using as the first variable the relatively firm dates of the other poems (pp. 47-8, 155-8). Here he has fitted the trends of the hexameters in rate of use of ad, per, sed, and nec to a parabola (of rate versus date), while varying the date of the Ars from 24 B.C. to 8 B.C., and he selects the best fit in each of the four cases as giving the most likely date.14 But in fact the goodness of fit (measured by F, using R2, the coefficient of variation) does not greatly vary (p. 47). A plot of R2 versus date in each of the four cases would have been helpful; further -- why restrict oneself to 24 B.C. or later? Why not as early as 28 B.C.? If the method works at all, it should not turn up spuriously early dates. F.'s conclusion (p. 49) that his results here confirm his date of 24 to 20 B. C. simply does not follow -- he never checked anything earlier.15 But crucial is the fact that none of his fits are very convincing (pp. 155-8): the 'best' model of sed seems to me to be fitted just as well by a line, while the others look more or less like randomly scattered points. The conclusion ought to be that the five or six points (rates of use of one of the four select "function words") do not fit a parabola well.
All in all a disappointment. An incoherent sorites of sophistical mathematics, an unreflective and enthusiastic use of chi-square tests in inappropriate situations, an insistence on seeing patterns where likely none exist -- all this is no paradigm shift but shifting sand on which no reliable view of the Ars can be built.
 George E. Duckworth, "Horace's Hexameters and the Date of the Ars Poetica," TAPA 96 (1965) 73-95 (F. consistently cites as vol. 66).  I cite only one protreptic example from a vast almost two-century-long bibliography: R. Thisted and B. Efron, "Did Shakespeare write a newly-discovered poem?," Biometrika 74 (1987) 445-55.  The values graphed in Table XIV, p. 45 do not quite agree with the values obtained from the figures in Table XI.  And when the correct value of Y = 66.5% (percentage of unique strings) from Table XI is used instead of the wrong value (66.1%) given in Table XV.  The uncertaintly designates the range withing which there is a 68% chance that the true value falls (based on whatever assumptions went into the calculation of that uncertainty). Thus, if we would like to know what is the range within which it is, say 95% likely that the true value (here the correct date) falls, we must multiply the computed uncertainty by some factor (as it happens, for 95% the factor is 1.96, or roughly 2.0), so that in this case we have for a range of dates 30 to 10 B.C., i.e., as stated, more or less the status quo ante. For this factor see Spiegel 71-2, or Taylor 114-7 (as cited in BMCR 2 (1991) 426 n.1).  In fact another study of "function words" suggests that they usually vary randomly: F.J. Damerau, "The Use of Function Words as Indicators of Style," Computers and the Humanities 9 (1975) 271-80. He concludes that they are not satisfactory as markers of style.  Correct a misprint, p. 109: P(X) = [n!/X!(n-X)!]piX(1-pi)n-X (The first ! omitted). Note that by setting the a priori probability pi low enough, P(X) may be made microscopically small for any reasonable n and X.  In every graph which I checked several points were plotted wrongly (errors of a year or two), no doubt by a kind of graphical misprint.  For example, and only by eye (the data are scarcely worth greater effort), it seems to me that for sed a date of 33 B.C. would give a fit as good or better, for per 37 B.C., for ad perhaps even 45 B.C. These scattered (and scarcely likely) dates for the Ars underscore the weakness of the method.