vergil and the computer -...

VERGIL AND THE

Fourth Foot Texture

COMPUTER

in AENEID I When, in 1940, O. Skutsch cited the need for a XaJ...K.iVTt.poç inthestatis

tical study of Latin poetry, 1

he may not have realized how prophetie his

words were. "Brazen bowels" is an epithet which can be applied to the

computer even more suitably tban to the grammarian. Didymus. We describe

here one instance of how the computer has been càlled upon to accomplish

quickly and easily types of analysis which would otherwise be too arduous to

justify their undertaking. When Oberlin Col lege recently installed a com

puter facility, we took the occasion to program the machine_to scan Latin

hexameter verse. This complex task was facilitated by using a text with no

hidden quantities. The text used was that of Pharr. 2

This text is conve

nient because ali long vowels are marked and ali consonantaiJ.'s are indica

ted by l_. ln accordance with general usage, !:!. and~ are likewise differen

tiated.

The text of Aeneid 1 was punched into IBM cards, one line to a card. The

first three columns of the card were reserved for the li ne number. Due to

1. ln his review of W .F .J. Knight, Accentuai Symmetry in Vergil, (Oxford, 1940), in CR 54, (1940), 93-95,

2. Pharr, C., Vergil'sAeneid Books l-VI, (D.C, Heath, rev.ed.copyright 1964).

Extrait de la Revue (R.E.L.O.) III, 1 à 4, 1967. C.I.P.L. - Université de Liège - Tous droits réservés.

2

the paucity of characters avai Jable, the following conventions were obser

ved:

a) Capital letters were indicated by a prefixed dollar-sign.

b) Long voweis were indicated by a slash (/) following the letter:

c) Single apostrophe was used for ali quotation marks.

Semicolon was i ndicated by +.

Colon by =. Question-mark by * .

This for exemple, was the form assumed by li ne 1

$ARMA VIRUMQUE CANO/,$ TRO/JAE QUI/PRI/MUS AB 0/RI/S

Punching the 756 !ines of Book 1 into 756 IBM cards was the most laborious

and ti me consuming of ali tasks involved. ln addition, it was necessary to

check the accuracy of the punched text. These were the sole reasons for

limiting our venture to only one book of the Aeneid. There is one redee

ming feature, however : the job need be clone only once. The cards, once

punched, are easily duplicated, and may be used in ali sorts of ways.

The program for metrical scansion instructs the computer to print a 2 under

the vowel of a long syllable, a 1 under thot of short syllables, and a 3under

a short vowel followed by mute + 1 iquid. The program a Iso takes into


1 "--__/

3

account standard diphthongs, ~nd allows elision and ecthlipsis wherever pos

sible. Rather than attempt a program that wou Id cope with instances of hia

tus, semi-hiatus, diastole, systole, synapheia, or synizesis, a cheching rou

tine was instituted wherein the computer prints the numbers 1 through 6 under

the initial syllables of the metrical feet. This routine recognizes either

dactyls or spondees, and. can translate the 3 (i.e., the short vowel before

mute + 1 iquid) into a long or short syllable according to the context. If

unacceptable combinations occurred, the computer simply noted an errer,

which was a signal to us that one of the above metrical "licenses" was pre

sent. These were repaired by hand, but it is quite possible to devise a pro

gram which could deal automatically with most, if not ali, of these "licen

ses." Here is an example of our output at this point :

$ALBA /NI /QUE PATRE /S ATQUE ALTAE MOEN lA$ RO / MAE.

2 2 2

2

3 2

3

2 2 2

4

2 11

5

2

6

2

We now proceeded to the replication and testing of sorne of W.F.J. Knight's

speculations in his Accentua 1 Symmetry in Vergi 1 (Oxford, edition of 1950),

First, we devised a program for indicating prose accent. lt is, of course,

distressing that the "questions connected with the accent of Latin are among


4

the most debated in ali scholarship ." l After considerable reflection, we

applied a strict penultimate rule, i.e., (1) ali monosyllables receive stress.

(2) Ali bisyllabic words are accented on the first syllable. (3) Words of three

or m,ore syllables receive only one stress, on the penult if long, otherwise on

the antepenult. Some other possibilities will be discussed below. Our pro

gram had the computer print an asterisk under the vowel receiving the prose

accent. An example of our composite output thus far follows :

$MU/SA, MIHI/CAUSA/5 MEMORA/, QUO/NU/MINE LAESO/

2

*

2 2 2

2 3

*

2

4

2

*

2

5

2 2

6

* Perusal of the above example reveals thot wherever our numbers 1-6 (signi

fying the first syllable of a metrical foot) coincided in vertical column with 2

asterisks, we had an instance of a "homodyned" foot as defined by Knight;

elsewhere an instance of "heterodyne." Thus, in the example above, feet 1,

5, 6 are homodyne; 2, 3, 4 are heterodyne. The computer was instructed to

print !!:_ under cases of heterodyne, and~ under cases of homodyne. Aga in,

an example of output :

1. Beare, William, Latin Verse and European Song, (London, 1957), 49. lncidentally, it should be noted thot Knight nowhere clarified his own system of prose accentuation.

2. Op. cit., p. 13


5

$ URBS ANTI/QUA FUIT($ TYRII/TENUE/RE COLO/NI/)

2 2 2 1 2 1 12 12 2 2

2 3 4 5 6

* * * * * * c c A A c c

Our initial task was now complete. Following our directions, not only had

the computer generated the series of~ 1s and .s_•s for each of the six feet in

the lines of Aeneid 1, it had produced this materiel in a form amenable to

further analysis by mechanical means, Although our sole concern was the

examination of fourth foot texture, the procedure could just as easily hàve

been repeated fot any foot of the Vergilian line. Similarly, we could have

replicated easily, accurately, and quickly such statistical compilation as

those of Sturtevant and Duckworth • 1

Knight's major claim reads : "For you are asked to believe that hundreds of

passages of Vergil have a reguler rhythmic scheme never till quite lately

suspected to exist at ali; that Vergil's hexameters are constructed together

into elaborate but symmetrical systems, thirty verses long or more, domina

ted by two sorts of pattern, very variously blended, ... "2 Knight 1s

1. ln TAPA 54 (1923) and TAPA 95 (1964) respectively.

2, Qe.. cit., p. 1,


6

words re fer to fourth foot texture, i .e ., to the distribution and arrangement

of homodynamic and heterodynamic fourth feet. The two sorts of (ll!lttern

referred to are the released movement and the alternat ion. 1 A released

moyement is a series of lines with heterodyned fourth feet followed by a line

with a homodyned foùrth foot. An alternation is simply a sedes of !ines

whose fourth feet are alternated homodynes and heterodynes. Patterns of

this sort were easi ly discerned by the computer procedures described below.

Another aspect of Knight's procedure needs clarification. He seems to havE:.

fixed his attention upon discrete portions of Vergil as defined by sense, i.e.,

sentences, paragraphs, etc., and then to have selected as significant those

sense-units which exhibited the patterns he had in mind. 2 This procedure

is statistically suspect. lt seemed tous preferable to deal with the entire

series of fourth foot homodynes and heterodynes in Aeneid 1 without taking

'~

note of sense-units. Inspection of the series of homodyned and heterodyned

fourth feet in Aeneid 1 without cognizance of sense-units reveals that there ~~~

are thirty-six released movements of six or more !ines in length. The~e are.

the patterns ending at lines 7, 14, 51, 60, 67, 91, 119, 134, 155, 164,

183, 221, 249, 285, 322, 329, 349, 365, 389, 403, 432, 447, 500, 509,

1 • These are defined by Knight, op. cit ., p. 48 and p. 59.

1

2. Objections have been advanced against sorne of these sense-units, e .g ., " ••• leaving oside the fact that he chooses to end his sample where editors print a semi-colon, nota full stop " L. P. Wilkinson, Golden LatinArtistry, (Cambri<lge, England, 1963), p.l2~,~


1 ~)

1

-7

518, 528, 599, 614, 625, 634, 658, 681, 693, 7CJ7, 720, 749. Of these

thirty-six, the endings of only ten coïncide with the end of a sense-unit.

Considerable doubt is thus cast on the thesis that Vergil ever associated such

a pattern with a sense-unit.

The case for alternations is more difficult to deal with, since any part of an

alternat ion is itself an alternat ion. Aeneid 1 contains ten alternations of six

linesormore in length, Theseare 136-142, 170-177,203-208, 227-236,

285-290, 307-312, 355-360, 476-484, 657-664, 748-756, Sense-unitscan

be found within ali of these but one (307-312), but there is only one good

fit, that is 748-756, Once a gain, doubt is cast upon Knight 1s thesis.

The computer techniques used to isolate these and other patterns may now be

described, We first instructed the computer to print out the entire series of

_s•s and (21s (i ,e, 1 homodynes and heterodynes) for the fourth foot, This

appears as a long string of _s•s and (21s1 753 to be exact, (Li nes 534, 550

and 636 are incomplete 1 a lthough it could be argued that 636 is heterodyne

in the fourth foot. These three were taken as _s•s in our computations for the

runs test described below, but were of little statistical importance no matter


8

how treated .) Given this string of 753 (modified to 756) interspersed .S.'s

and ~'s, it was possible to carry out a number of operations.

The first of these was cal led forward block comparison, ln this operation,

we instructed the computer to inspect the pattern of C's and A's in a block

of arbitrary size and to list ali other blacks containing the seme arrangement.

Our arbitrary block lengths were six lines and twelve lines, Thus, in the

latter case, the computer inspected the series of .S.'s and ~'s in 1 ines 1-12,

and reported that the seme series is found in li nes 503-514 and 701-712. lt

then inspected the series contained in lines 2-13, 3-14, and so on, repor

ting in each case ali similar blocks occurring in Aeneid 1. This is an exhaus

tive procedure which no sene man would use unless he had a computer at his

disposai. lt was this procedure, using a block size of six, which allowed us

to discern quickly ali exemples of released movement or alternation in

Aeneid 1. lt would also have been quite possible to instruct the computer to

pick out those patterns whose limits coincided with the limits of sense-units,

and to compare their number with that of those which did not so coïncide.

The second procedure was cal led reverse block comparison. This procedure 1

(~

\


(

9

is exact ly that described in the preceding paragraph except that the compu

ter was instructed to report ali blocks containing exactly the reverse of the

series contained in the given block, (By reverse, we mean the same series

in reverse order, i, e., backwards,) Thus, using a block size of twelve, we

were told that the blocks ending in lines twelve and thirteen were the rever

ses respectively of the blocks beginning with lines two and one. This pro

gram allowed us to discern symmetrical patterns, Thus, the sequence in li

ne 1-13 is six A's, aC, and six A's, which is, of course, symmetrical.

Cursory inspection of our results allowed us to pick out over a dozen rather

ornate symmetrical schemes in Aeneid 1. For example, the sequence 396-

445 is quite elaborate : lines 396-409 are the exact reverse of 432-445; a

central group, 415-427 is symmetrical; the gaps are 410-414, a symmetrical

group, and 428-431, a series of unrelieved heterodynes. This sequence, we

submit, is as ornate as anything to be found in Knight, and more complex

ones can be found. Unfortunately, in the case of 396-445, while line 445

coïncides with the end of a sentence, 396 does not coincidewith the begin

ning of one. Now, it is obvious that an equal number of li nes may be sub

tracted from beginning and end of such groups and they will remain symme

trical. They can thus, quite often, be made to coïncide with sense-units,


10

and this, in effect, is what occurred in Kn ight 's speculations.

With regard to our next procedure, it is opposite to quote Wilkinson's verdict

on Knight's work : "Accentuai patterns related to meaning are vital. Short

ones may even be pleasing in themselves. But long ones, though they may

be symptomatic of a feeling after variety, can more easily be set out as such

on the page than taken in by the ear. They exceed the 'psychische Presens

zeit,' and are probably fortuitous. "1

With this verdict we agree, but our

present concern is with the word "fortuitous." Our entry is the hypothesis

that the series of .S.'s and ~'s generated by the fourth feet in Aeneid 1 (or

any other Latin dactylic hexameter poetry) may be considered analogous to

the series of "heads" (H) and "tails" (T) generated by repeated tosses of a

coin. A similar but closer analogy for our situation follows: Aeneid 1 con

tains 521 heterodyned fourth feet and 235 homodyned fourth feet. Let us

imagine that we have a large jar fil led with 521 red balls and 235 white

ba lis. A blindfolded man picks them out one at a time. What sort of se

quence would cause us to believe that our blindfolded man is peeking ? Si

tuations of just this sort have been dealt with by statisticiens, although the

topic has by no means been exhausted. 2

The procedure we describe is

1. Ibid.

2. See note 1 p • 13 •


11

cal led the runs test. A run is an unbroken sequence containing one or more

elements. Thus, the series RRRWW consists of two runs; the series RWRWR

consists of five runs; the series RRWWR consists of three runs. The stat istical

procedure at this point is to imagine a listing of ali the possible sequences

containing 521 red balls and 235 white balls together with a listing of the

number of runs found in each sequence. Then, the statisticien speaks as

follows :We will assume that a specifie sequence is random unless itcontains

a number of runs either greater or fesser than that contained by 95% or 99%

of ali the possible sequences. ln such cases, we reject the hypothesis of

randomness at the particular leve( of significance specified in advance,

This is customarily set at either the 5% or the 1% leve(, This, then, is the

runs test, and a discussion of it may be found in any textbooks on statistics.1

The mathematical formula for the test statistic is the following:

z =

1 • E .g ., W .J. Dix on and F .J. Messey, Introduction to Statistical Ana lysis, (Mc Graw-Hi Il, 1951), pp. 254-256.


12

where N1

and N2

stand for the number of red and white belis respectively (or

homodynes and heterodynes}, and ~ signifies the number of observed runs. At

the 5% level of significance, the hypothesis of randomness is to be Cilccepted

if- 1 .96 (z (1 .96, At the 1% level, the figures are- 2.645 (z (2 .645.

Aeneid 1 contains 521 heterodyned fourth feet and 235 homodyned fourth

feet. The number of runs observed is 329. We fou nd z = 0 .351' very com

fortably within the confines of the hypothesis of randomness. ln order to

check the possibi 1 ity thot a bias in one part of the sequence may be com

pensating for an opposing bias elsewhere, we divided the sequence into

seven equal parts and computed z for each part. The results follow :

Li nes 1-108 z = 0.51

109-216 1,61

217-324 0.87

325-432 -0.78

433-540 -0,07

541-648 -0.42

649-756 0.75


13

These are a Il to be accepted as random sequences. Th us, we conc lude from

the runs test that Vergil's sequence of homodyned and heterodyned fourth

f • A 'd . d l'b. l eet rn ene1 1s not e 1 erate •

One significant result was revealed by the runs test. Knight said : "The al

ternation at the end of Aeneid 1 is of special interest partly because the

book begins with a released movement. But anyhow the texture at the end

of a book is genera lly worth examination. "2

Although confining our major

investigations to Aeneid 1, we took a cursory look at the beginning and

ends of ali the books. Combining the first five !ines of each book into a

single sequence of sixty units and performing the runs test produced the fol

lowing result : z = -1 .3 which is not significant at the 5% level. Combi

ning in similar manner the last five !ines of each book produced the follo

wing interesting result: z = 2,39, which is significant at the 5% level, but

not at the 1% leve!. lt is a Iso noteworthy that here homodynes outnumber

heterodynes, contrary to Vergil's usual practice. The significantly high

number of runs indicates a tendency toward a lternation on the part of Vergi 1

at ends of the books of the Aene id.

1. The runs test is not the last word in statistical analysis. A couple of examples will illustrate : The sequence THTHTH ••• is quickly perceived as non-random by the runs test. But the runs test will not perceive the non-randomness of TTHHTTHH ••• This constitutes a real difficulty since there are apparently innumerable non-random schemes that would not be discerned by the runs test. Sorne of these, however, would have been perceived by the forward and reverse block comparisons described above. They were not so perceived.

2. Op. cit., pp. 59-60.


14

With the exception of the finding noted above, every test we have employed

does not contradict the hypothesis that the arrangement of fourth foot homo

dyne and heterodyne in Aeneid 1 is random. As noted above, e .g ., of the

released movements in Aeneid 1, only about one third have endings coinci

ding with the. ends of sense-units. When one adds to this the observation

(which can be made by examining 100 lines at random) that about one third

of~ the lines in Vergil end in a period, semi-colon, or colon, it becomes

clear that the so-called released movement is of no significance whatever.

Si mi lar conclus ions are probably justified for a Il the other patterns discerned

by Knight. Still, it remains true 1 as noted by Knight 1 to his everlasting

credit 1 that only about 30% of the 1 ines in Aeneid 1 have a homodyned

fourth foot 1 wh ile about 50% of the lines do in Lucretius 1 De Rerum Nature 1

and in Ovid 1 Metamorphoses 1. Why this sizable difference should occur 1

we do not know. Y et the difference seems large enough to demand explana

tion.

The findings of sorne supplementary procedures are appended here. Confi

ning our observations to Aeneid 11 the only material we had under mechani

cal control, we paid close attention to the fifth and sixth feet of the line.

lt has a lways be en c lear to ali sc ho lars that the prose accent has a huge


15

tendency, for whatever reason, to coïncide with the initial syllables of the

sefeet, i.e., they are almost always homodyned. An inspection of the

exceptions in Aeneid 1 provided sorne interesting possibilities. Aside from

lines 65, 105, and 151 which end in monosyllables, line 72 which ends with

the name Deiopea and thus constitutes the only evidence for secondary

accent 1

in Aeneid 12

, and line 617 which caused problems because the

fifth foot is spondaic and contains hiatus, the following li nes are of interest:

177 Tum Cererem corruptam undis Cerealiaque arma

569 Seu vos Hesperiam magnam Saturniaque arva

332 iactemur, doceas. lgnari hominumque locorumque

448 aerea cui gradibus surgebant limina, nexaeque

601 non opis est nostrae, Dido, nec quicquid ubique est

Unes 332 and 448 are hypermetric with synapheia. These in conjunction

with lines 177 and 569 suggest that elided -~ had no effect on the prose

accent of the word to which it was attached •3

Une 601 would seem to be

a counterexample, but, presumably, ubique is not to be read as ubi plus the

enclitic. To be sure, these may simply be cases of poetic license. After

ali, lines 332 and 448 are hypermetric, and the.!._ in Cerealiaque and Satur

niaque could be sorne sort of semivocalic. Still, the evidence was intriguing

_1. "The existence of secondary accent on polysyllables is disputed. The evidence for it is given by W.M. Lindsay, The Latin Language (1894), pp. 159-161." Wilkinson, op. cit., p. 257.

2. This ignores the possibility of using the first metrical foot in the line as evidence. The first feet contain too many instances of apparently unassailable heterodyne, e .g ., 1 Italien, 10 insignem, 11 impulerit. ---

3 • Although arrived at independently, this notion is not new. See R .J. Getty 's survey in Lustrum 8, ( 1963) 1 p • 122 •


16

enough for us to devise a program for discerning elided enclitics in the

fourth foot of the line. Elided -que is present in the fourth foot in lines 14,

27, 43, 69, 84, 103, 137, 152, 155, 176, 196, 208, 270, 309, 357, 410,

422,· 491, 570, 588, 645. Elided -ne is in line 39, and elided -~in line

682. This variant was not employed in our forward and reverse block compa

risons. The variant does not affect the runs test in any significant way. 1

Nathan A. Greenberg,

Oberlin Col lege.

1 • No man is an island when he works with a computer. 1 take the credit and the blame for initiating this study. 1 wish to express my gratitude to the following: to my students, Miss Dianne Haley, Miss Margaret Lamberti, and Mr. Theodore Tarkow, who punched the text and concocted many of the flow diagrams necessary for the various programs; to Oberlin Col lege and to Mr. Robert Bushnell, director of the computer center here; to Mr. Warren Esty, a student in mathematics, who did more than merely interpret our wishes to the computer; to Professor Samuel Goldberg of the Department of Mathematics, whose knowledge of statistics was placed at my disposai.


vergil and the computer -...

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