[image ALT: Much of my site will be useless to you if you've got the images turned off!]
mail:
Bill Thayer

[image ALT: Cliccare qui per una pagina di aiuto in Italiano.]
Italiano

[Link to a series of help pages]
Help
[Link to the next level up]
Up
[Link to my homepage]
Home

This webpage reproduces an article in
The Classical Journal
Vol. 23, No. 8 (May 1928), 588‑593.

The text is in the public domain.

This page has been carefully proofread
and I believe it to be free of errors.
If you find a mistake though, please let me know!

p588 De Loquela Digitorum
By Eva Matthews Sanford
The College for Women, Western Reserve University

The Disputatio regalis et nobilissimi iuvenis Pippini cum Albino scholastico, with the wide variety of material included in its brief questions and answer, contains almost endless suggestions for investigation and comment on the workings of the Carolingian mind at school. Since its inclusion by Professor Beeson in his Primer of Medieval Latin (pages 169‑73) has made it accessible to an increasing number of readers, it seems pertinent here of the comment on one at least of the many matters it involves. The topic of finger notation has been more thoroughly discussed elsewhere,1 but not, I think, in a classical periodical, and not with emphasis on the later Latin materials.

Albinus puts the question, "I saw a man holding eight in his hand, and from the eight he took seven, and six remained."2 It is apparently so easy a question that Pippin scorns to give a direct answer, in words at least, and merely remarks, "The boys in school know that." I say "in words" because it is very likely that a rapid bit of finger movement accompanied his answer. The ancient Romans were doubtless the more proficient in finger reckoning because of their fondness for the game of morra. One recalls, too, Quintilian's strictures on the orator who shows his lack of education, not by hesitating over the sum, but by an ignorant awkwardness in the motion of his fingers during p589the reckoning.3 Martianus Capella's description of Arithmetica paying Jove a pretty compliment by spelling out his name on her fingers would lose too much of its picturesque rhetoric in the translation — "digiti vero virginis recursantes et quodam incomprehensae mobilitatis scaturrigine vermiculati."4 In passing, it is noteworthy that Philosophia fails to understand the action, and Pallas, who apparently had a better education or more native intelligence, had to explain it to her.

Since Albinus' riddle is not explained in the Primer it might be well to go into some detail here, basing my suggestion on an authority whom Albinus would gladly have recognized, the Venerable Bede. He began his work De Temporum Ratione by pointing out the value of a thorough knowledge of finger notation for all who intended to read his account, that they might the better keep account of the chronology.5 He then gives careful instructions for counting on the fingers, instructions which correspond to the scattered information we have about the Greek and Roman methods, to the complete method as described by Nicolaus Rhabda of Smyrna in the same century, and to those of the diagrams in the mathematical works of the Renaissance.6 Truly a worthy industria, which had proved itself in so many centuries and over so wide a territory as this.

For the numbers from one to ten his instructions may be briefly stated as follows: for one, using the left hand, as for all numbers under a hundred, bend the little finger at the middle joint with p590the tip of the finger touching the palm; for two bend the fourth finger also; for three add the middle finger; for four raise the little finger, keeping the other two bent; for five raise the fourth finger, leaving the middle finger bent. This brings us to the point of Albinus' riddle. For six the fourth finger alone is pressed against the middle of the palm, for seven the little finger is bent well down over the palm, with the others extended; and for eight the fourth finger is also closed on the palm. So quite literally one may take seven from eight and have six left. For the sake of round numbers, bend the third finger also against the palm for nine and press the nail of the index finger against the middle joint of the thumb for ten.7 For higher reckoning I refer you to the Venerable Bede or to his modern debtors.

Since I am being rather discursive than systematic I cannot resist a digression for the sake of Bede's quotation from Jerome on the number thirty. In his account of the numerals he instructs us, "When you say thirty, join the nails of the index finger and thumb in a gentle embrace." On the significance of this number he has already quoted Jerome's statement, made most inconsistently in his famous diatribe against matrimony, that the number thirty is connected with marriage, "for the very joining of the fingers, as if embracing and allying each other with a tender kiss, depicts the husband and wife."8 What a delightful contrast this is to other parts of the same book "agayn Jovinian" and to the p591many books of "wikked wyves" descended from it to vex the Wife of Bath and others perhaps less able to defend themselves. Surely the authors of such books must have suffered some compunctions when their pages numbered the conjugal thirty.

It is a pity that the introduction of the less cumbersome Arabic numerals and the ever useful zero have caused the art of finger computation to be reduced to its lowest terms. Dr. Smith lists among its purposes the aid it gave in bargaining, especially when the buyer and seller spoke different languages. In this connection the Greek and Italian vase-paintings showing the merchant and customer bargaining for oil, wine, or other good, and indicating the prices on their fingers, are of interest.9

For the phrasing of Albinus' question we may refer to Bede's discussion of the use of finger notation for secret conversation. He reminds us that this computation may be used also as a sort of "manual speech," as much for the sake of practice as for amusement, by substituting the numerals in turn for the letters of the alphabet and so being able to carry on a conversation even at a distance with any who know the art, meanwhile mystifying those ignorant of it. "When you wish to indicate the first letter of the alphabet," he says, "hold one in your hand," a phrase corresponding closely with Albinus' octo in manu tenentem. But how much of human interest there is in the rest of the passage quoted.10 Should we need any more to remind us how well Bede understood his younger pupils and what pleasure could be added to arithmetic by the chance to show off one's cleverness and mystify the unskilled in collaboration with anyone else who knew hanc industriam? p592Bede's example for this industria is suggestive also of its more serious uses, for he shows how the express the words Caute age on the fingers.

Indeed, another passage may be found in the Primer to illustrate the use of finger language in a serious crisis. In the extract given from Ermoldus Nigellus, De rebus gestis Ludovici Pii,11 Zadun the Moor has been captured by the Franks and forced to bid his men surrender to them. He obediently shouts to them to open the long-closed gates, meanwhile, though pretending it an empty gesture, signalling to them on his fingers to continue their resistance. Unfortunately one of the Franks recognized the ruse and struck him, "admiring the Moor, but even more his cleverness."

Isidore of Seville shows that the military use of finger speech was known in his day, and characteristically quotes several lines of description of a most modern young person to illustrate one of its other uses; for the last of the admirers by whom the "Girl from Tarentum" is surrounded have to content themselves with the words, kind ones we hope, that she forms for them with her fingers. Perhaps her other lovers had never learned to talk in this fashion.12 Isidore shows somewhat more fairness to the p593ladies than some of his successors, for he caps the example of the Tarentine girl, who, however ancient the Punic Wars may seem to our modern maidens, might have given them points on how to handle several men at a time, by a quotation from Solomon about the wicked man who "walked with a froward mouth" — Annuit oculo, terit pede, digito loquitur (Proverbs 6:13).

One of the most potent reasons for the importance of finger speech in the middle ages was, of course, the monastic rule of silence, especially at meals, where some means of communication might seem essential to a hungry monk. The extremes to which this might go are lamented by Giraldus Cambrensis, who cites conditions at Canterbury in 1177.13 The prior had so many gestures to make to the monks who served him, and the servers and monks at the lower tables found frequent communication so necessary that Giraldus thought their gestures of fingers and hands and even arms, and their whispering, far more frivolous and licentious than was becoming to their order. Indeed, he fancied himself among actors and jesters rather than cloistered monks. It is no wonder that he thought to speak "human words" with due modesty would be more consonant with their position and respect than to use signs and whispers so merrily in "mute garrulity." In the insula domus Ailbei, on the other hand, where the monks suffered none of the infirmities of flesh and spirit that hover about the human race, they talked only by signs made with eyes or fingers.14


The Author's Notes:

1 Cf. Smith, D. E., History of Mathematics, II, 196‑202; Richardson, L. J., "Digital Reckoning among the Ancients," American Mathematical Monthly, XXIII (1916), 7‑13. Further bibliography will be found in each of these. The article digitus (c), in computatione, in the Thesaurus, is particularly rich in suggestions to the classical student.

2 Beeson p172, line 30: Vidi hominem octo in manu tenentem et de octonis rapuit septem, et remanserunt sex.

3 Quintilian Inst. Or. I.10.35; In causis vero frequentissime versari solet; in quibus actor, non dico, si circa summas trepidat sed si incerto aut indecoro gestu a computatione dissentit, iudicatur indoctus.

4 Martianus Capella De Nuptiis VII.729.

5 Giles, J. A., Ven. Bedae Opera quae supersunt omnia, VI, 141. De Temporum Ratione, Cap. i. De computo vel loquela digitorum. De Temporum Ratione (Domino iuvante) dicturi necessarium duximus, utilissimam primo, promptissimamque flexus digitorum, paucis praemonstrare solertiam, ut cum maximam computandi facilitatem dederimus, tum paratiore legentium ingenio ad investigandam dilucidandamque computando seriem temporum veniamus. Neque enim contemnenda, parvive pendenda est regula, cujus omnes pene sacrae expositores Scripturae, non minus quam literarum figuras monstrantur amplecti.

6 Cf. Richardson, op. cit., p8.

7 Giles, VI, 142: Primo fit indigitatio in laeva manu, tali modo. Quum ergo dicis Unum, minimum in laeva digitum inflectens, in medium palmae artum infiges. Quum dicis Duo, secundum a minimo flexum, ibidem impones. Quum dicis Tria, tertium similiter afflectes. Quum dicis Quatuor, itidem minimum levabis. Quum dicis Quinque, secundum a minimo similiter eriges. Quum dicis Sex, tertium nihilominus elevabis, medio dumtaxat solo, qui Medicus appellatur, in medium palmae fixo.

Quum dicis Septem, minimum solum, caeteris interim levatis, super palmae radicem pones. Juxta quam quum dicis Octo, medium, quum dicis Novem impudicum e regione compones. Quum dicis Decem, unguem indicis in medio figes artu pollicis. Cf. the diagrams in Smith, II, 198.

8 Giles, VI, 142: Quum dicis Triginta, ungues indicis et pollicis blando conjunges amplexu. Jerome, adv. Jovinianum i.3, ap. Bede, Giles, VI, 141: Triginta referuntur ad nuptias; nam et ipsa digitorum coniunctio, quasi molli osculo se complectens et foederans, maritum pingit et conjugem.

9 Cf. de Walle, F. J. M., "La Représentation de la Vente de l'Huile à Athènes," Revue Archaeologique,º Vme Série, XXIII (1926), 282‑295, esp. figures 3 and 6.

10 Giles, VI, 143: Potest autem et de ipso quem praenotavi computo quaedam manualis loquela, tam ingenii exercendi quam ludi agendi gratia figurari; qua literis quis singillatim expressa verba, quae isdem literis contineantur, alteri qui hanc noverit industriam, tametsi procul posito, loquenda atque intelligenda contradat, vel necessaria quaeque per haec occultius innuendo significans, vel imperitos quosque divinando deludens. Cujus ordo ludi vel loquelae talis est: Quum primam alphabeti literam intimare cupis, unum in manu teneto; Quum secundum duo; Quum tertium, tria; Et sic ex ordine caeteras.

11 Beeson, p330, lines 177‑82, quoted from Dümmler, Poetae Latini Aevi Carolini, II, "De rebus gestis Ludovici Pii," lines 483‑92.

Tum manus ad muros tendens vocitabat amicos:

"Pandite iam, socii, claustra vetata diu."

Ingeniosus item digitos curvabat, et ungues

Figebat palmis, haec simulanter agens,

Hoc autem indicio signabat castra tenenda.

Sed tamen invitus, "Pandite" voce vocat.

12 Isidore Etymologiae I.26:º Sunt quaedam et digitorum notae, sunt et oculorum, quibus secum taciti proculque distantes loquuntur. Sicut mos est militaris, ut quotiens consentit exercitus, quia voce non potest, manu promittat. Alii, quia voce non possunt, gladiorum motu salutant. Ennius de quadam impudica (Naev. Com. 75):

— Quasi in choro pila

ludens datatim dat sese et communem facit.

Alium tenet, alii adnictat, alibi manus

est occupata, alii percellit pedem,

alii dat anulum exspectandum, a labris

alium invocat, cum alio cantat; adtamen

aliis dat digito litteras.

13 Giraldus Cambrensis De rebus a se gestis ii.5, ed. Brewer, Rolls Series, I, 51: Tot etenim prior ad monachos servientes, et illi e contra ad mensas inferiores exenia ferendo, et hi quibus ferebantur gratias referendo, digitorum et manuum ac brachiorum gesticulationibus et sibilis ore pro sermonibus longe levius atque licentius quam deceret effluebant; ut quasi ad ludos scenicos aut inter histriones et joculatores sibi viderentur constitutus. Esset itaque magis ordini consonum et honestati verbis humanis cum modestia loqui, quam muta in hunc modum garrulitate signis et sibilis tam joculariter uti.

14 Peregrinatio S. Brandani, ed. C. Schroder, Sanct Brandan, p17.


[image ALT: Valid HTML 4.01.]

Page updated: 20 Aug 06