Simple counting was done on the fingers. “Reckon on your fingers,” says a character in Aristophanes,[275] “not with pebbles.” A common word for counting was πεμπάζειν, “to reckon on the five fingers”; the division of the month into three periods of ten days can be traced to the same custom. But by various devices it was possible to count up to very large numbers on the fingers. Pebbles were also employed to assist in arithmetic. In the case of complicated accounts a reckoning board (ἄβακος or ἄβαξ) was used, on which the pebbles varied in value according to their position. Such boards go back to early days at Athens, for Solon compared the life of a courtier to a pebble upon them, since he was now worth much and now little.[276] A character in a fourth-century comedy[277] sends for an abacus and pebbles, in order that he may do his accounts. The pebbles were arranged in grooves, being worth one or ten or a hundred and so forth, according to the groove in which they were placed. If they were put on the left-hand side of the board, their value was multiplied by five.[278] The various games of πεσσοί, which somewhat resembled chess, were played on a somewhat similar board to this, and these chess-boards were known as ἄβακες. Now the art of playing with πεσσοί is more than once coupled by Plato with arithmetic or mathematics generally in such a way as to show that the game must have involved mathematical skill.[279] As was usual in Athens, instruction went hand in hand with amusement, and, in playing games, the boys learned arithmetic willingly. A similar value seems to have attached to the game of knucklebones, which the boys in the Lusis are found playing during their whole holiday. Each boy carried a large basket of knucklebones, and the loser in each game paid so many of them over to the winner. The art of playing this game is also coupled with mathematics by Plato;[280] so it must at any rate have encouraged the study of arithmetic, in his opinion. In the school scene of the British Museum amphora, a little bag, usually supposed to contain knucklebones, is figured: so they may even have been used in schools for teaching arithmetic. In another school scene this bag is present with a lyre and ruler; so it was evidently part of the school furniture.

After such revelations of Hellenic educational methods, it is natural to suppose that the ingenious devices by which the “Egyptians,”[281] according to Plato, “make simple arithmetic into a game” for their children, were really used in Attica. One of these devices[282] was as follows. The master took, say, sixty apples. First he divided them among two boys, who were made to count their share, thirty each; then among three boys, twenty each; then among four, fifteen each; then among five, twelve each; and then among six, ten each. This would teach the system of factors. Then, again, a real or imaginary competition in boxing or wrestling[283] was arranged, say in a class of nine. The boys would work out, by actual experiment, how many fights would be necessary, if each boy had to fight all the others one by one, and how many if a system of rounds and byes was introduced. This might even teach Permutations and Combinations.

In another case a number of bowls, some containing mixed coins, gold, silver, and bronze, some all of one sort, would be handed round the class. The boys would have to count them, add and subtract them, and so on. Thus they would learn addition and subtraction of money, and would also gain a clear knowledge of the national coinage.

Plato was immensely impressed with the educational value of Arithmetic. “Those who are born with a talent for it,” he says, “are quick at all learning; while even those who are slow at it, have their general intelligence much increased by studying it.”[284] “No branch of education is so valuable a preparation for household management and politics, and all arts and crafts, sciences and professions, as arithmetic; best of all, by some divine art, it arouses the dull and sleepy brain, and makes it studious, mindful, and sharp.”[285]

The question of the more advanced stages of Mathematics, which were taught to older boys, may be left for the chapter on Secondary Education.

* * * * *

The chief and often the sole instrument taught in the music school was the seven-stringed lyre,[286] with a large sounding-board originally made of a tortoise’s shell.[287] It might be played either with the hand or else with the “plektron” or striker; the boy Lusis had learnt to do either.[288] The boys were also taught how to tighten and relax the strings by turning the pegs till the proper degree of tension was obtained. They brought their own lyre with them from home, the paidagogos carrying it behind his charge. This was a wise regulation from the master’s point of view; for the boys seem to have usually ruined these instruments by their early efforts.[289] Like the piano, the lyre required great delicacy of touch and very agile fingers, and these qualities could only be obtained by continual practice.[290]

As would naturally be expected, individual tuition was usual in the lyre-school; instrumental music cannot be learnt in class. The vases make this point quite clear. The master has a single boy seated in front of him; both hold lyres in their hands, to which they are singing, the words of the song being sometimes represented by a string of little dots. In Plate IV., on the left of this group, a boy is coming up to take his turn, lyre in hand, while behind him stands his paidagogos, leaning on a reading-desk and following his charge with his eyes. On the right is a boy just taking up his flute-case and preparing to depart, while another sits in the corner, wrapped in his cloak, waiting for his turn to take a lesson. In Plate III.,[291] the master is playing a barbitos and apparently singing, while the pupil plays the flute. On the left is a flute-master playing, and a pupil just leaving him, flute in hand. Another pupil, with a lyre, is waiting to take a lesson from the master in the centre, and is amusing himself meanwhile by playing with an animal that is probably a leopard,[291] like that which figures in Plate IV. Another pet, a dog, is howling in disgust at the music. On the right, a pupil with a flute is advancing to take a lesson from the flute-master in front of him. Behind him follows a young man, who may be an elder brother replacing the customary paidagogos for the nonce, or an admirer. In the background sits a small child, sucking his thumb, probably the younger brother of one of the pupils, who has come, in accordance with Aristotle’s advice, to look on, although still too young to learn.

As soon as his pupils knew how to play, the master taught them the works of the great lyric poets,[292] which were not taught in the school of letters. These were set to music, and the boys sang them and played the accompaniment. Every gentleman at Athens was expected to be able to sing and play in this manner when he went out to a dinner-party. The custom, however, began to become unfashionable during the Peloponnesian War. When old Strepsiades, in the Clouds,[293] asked Pheidippides to take the lyre and sing a song of Simonides, his new-fashioned son replies that playing the lyre was quite out of date, and singing over the wine was only fit for a slave-woman at the grindstone. Whether this state of feeling continued and whether it had a prejudicial effect on the music-schools cannot be decided. Sometimes the guests brought their boys to sing to the company: in the Peace the son of the hero Lamachos is going to sing Homer, while the coward Kleonumos’ boy has a song of Archilochos ready. Alkaios and Anakreon were also favourites;[294] the lyric portions of Kratinos’ comedies, too, are mentioned as sung at banquets:[295] no doubt, the same was true of the other great comedians. As the iambic parts of Aeschylus and Euripides were recited at the dinner-table, it is natural to suppose that their songs were also sung. The aged Dikasts in the Wasps sing the choruses from Phrunichos’ Sidonians. Old songs like Lamprokles’ “Pallas, dread sacker of cities” and Kudides’ “A cry that echoes afar” were popular in earlier times. No doubt there was plenty of variety in accordance with the master’s taste. At the music school, too, may have been taught the metrical version, set to music, of the Athenian laws, which was ascribed to Solon,[296] and that of the legislation of Charondas, which Athenian gentlemen sang over their wine.[297] Athenian boys were expected to know the laws by the time that they were epheboi, and may well have been taught them in this convenient and attractive way at the lyre-master’s. To know how to play the lyre became the mark of a liberal education, since every one learned letters, but the poorest did not enter the music-school. “He doesn’t know the way to play the lyre,” became a proverb for an uneducated person, who had not had so many opportunities in life as his wealthier fellow-citizens. So, as a plea for a defendant we find—

To this the Dikast retorts that he has not learnt the lyre either, so he must be forgiven if he is so stupid as to condemn the accused.[299]

At the beginning of the fifth century the Hellenes were stimulated, according to Aristotle,[300] by their growing wealth and importance to make many educational experiments, especially in music. All manner of musical instruments were tried in the music-schools, but were rejected on trial, when the moral effects could be better appreciated. Among the instruments thus found wanting was the flute. At one time the flute became so popular at Athens that the majority of the free citizens could play it. But its moral effect proved to be unsatisfactory; it was the instrument which belonged to wild religious orgies, and it aroused that hysterical and almost lunatic excitement[301] which the Hellenes regarded as a useful medicine, when taken at long intervals of time, for giving an outlet to such feelings and working them off the system, in order that a long period of calm might follow. But such a medicine was most unsuitable to be the daily food of boys. The flute had two other disadvantages. It distorted the face sufficiently to horrify a sensitive Hellene.[302] It also prevented the use of the voice: the boys could not sing to it, as they sang to the lyre. So Athena, in the old legend, had been quite right in throwing the instrument away in disgust: it was only suitable for a Phrygian Satyr, for it made no appeal to the intellect, but only to the passions.[303]

This is Aristotle’s account. It may be objected that the vases which represent scenes in the music-schools show the flute and the lyre being taught side by side, and apparently equally popular. But these vases can mostly be traced more or less certainly to the first half of the fifth century, and so they bear out Aristotle’s statement. Moreover, the flute did not, of course, die out in Hellas by any means; it only became an extra, instead of the regular instrument in schools. The most notable Athenians, Kallias and Kritias and Alkibiades, are said to have played it.[304] It always remained popular at Thebes. But at Athens, in the banquets, while the guests usually played the lyre themselves, the flute was as a rule only played by professional flute-girls,[305] although on the vases the guests are sometimes found performing on this instrument also.[306] Probably the Athenian attitude may be summed up in the “ancient proverb”:[307]

It was usual to play on two flutes at the same time. Such a pair has been found,[308] together with a lyre, in a tomb at Athens. The flutes are somewhat over a foot in length, and have five holes on the upper and one on the lower side. Each has a separate mouthpiece. Besides this, flute-players sometimes wore a sort of leathern muzzle[309] over their mouths; but this does not appear in the schools. The pair of flutes were carried in a double case, made of some spotted skin; it had a pocket on one side, to hold the mouthpieces,[310] and a cord attached by which it could be hung up when not in use. The two flutes seem to have corresponded to treble and bass, “male” and “female” as Herodotos calls them. The treble was on the right, the bass on the left.[311] Flutes could be set to different harmonies, apparently by some rearrangement of stops. In the case of the flute, as in the case of the lyre, individual tuition was the rule. First the master played an air, and then the boy had to repeat it, while the master criticised.[312] Or the master played the air on a barbitos and sang to it, while the pupil accompanied him on the flute. This method had two advantages. The master was able to play at the same time as the boy, and give him instruction while playing, which the flute prevented him from doing. The song, too, which he was enabled to sing obviated one of the chief disadvantages of the flute: for the Hellenes objected to instrumental music as meaningless, unless it was accompanied by words.

There seem to have been music-schools scattered throughout Attica, besides those established in the capital: the description of the village boys marching off to the lyre-master’s in a snow-storm without overcoats has already been quoted. The names of a few masters are extant. Lampros taught Sophocles the poet.[313] Sokrates[314] recommends Nikias to send his son to the famous Damon, who “is not merely a first-class musician, but also just the man to be with boys like this.” But whether these musicians kept regular schools cannot be ascertained. Sokrates himself in his later years attended the music-school of Konnos, and learned among the boys. “I am disgracing Konnos the music-master,” he says, “who is still teaching me to play the lyre. The boys who are my schoolfellows laugh at me and call Konnos the ‘Greybeard teacher.’”[315] The same Konnos adopted the common but iniquitous custom of bestowing his chief attention on his more promising pupils, while neglecting the backward.[316] Aristophanes caricatures Kleon’s school-days as follows: “The boys who went to school with Kleon say he would often set his lyre to the Dorian (= Gift-ian) harmony alone. Finally, the lyre-master lost his temper and told the paidagogos to take him away, saying, “This boy can’t learn anything but the Briberian (Dorodokisti) mode.”[317]

The attitude of the philosophers towards music will be discussed elsewhere. Plato’s view may be summed up in the words which he puts in the mouth of Protagoras the Sophist.[318] “The music-master makes rhythm and harmony familiar to the souls of the boys, and they become gentler and more refined, and having more rhythm and harmony in them, they become more efficient in speech and in action. The whole life of Man stands in need of good harmony and good rhythm.” Aristotle’s attitude is briefly this. “Music is neither a necessary nor a useful accomplishment in the sense in which Letters are useful, but it provides a noble and worthy means of occupying leisure-time.”[319]

* * * * *

Aristotle mentions that in his day some added drawing and painting to the three parts of the course.[320] It was not universal, like these, and it does not seem to have started till the fourth century. In the Republic and Laws Plato does not attack and criticise it among the other educational subjects; but it plays so prominent a part in the Republic that it is obvious that the philosopher regarded it as a dangerous enemy to the views which he wished to spread. It is noticeable that the discussion of Art comes in as an after-thought, in Book X. May it not be inferred that when Plato wrote the earlier books, drawing and painting were not yet in vogue in the schools, but they became popular before he had finished his great work?

In Periclean Athens the possibilities of artistic training had certainly existed. In the Protagoras,[321] as an instance in some argument, it is suggested that the lad Hippokrates might “go to this young fellow who has been in Athens of late, Zeuxippos of Heraklea. Every day that he was with him he would improve as an artist.” Earlier in the same dialogue Sokrates remarks that his friend might go to Polukleitos or Pheidias, and pay to be taught sculpture.[322] The large numbers of boys who became apprentices to the potters at Athens must have learned line-drawing and designing and painting from the earliest times. But art probably did not become a usual part of a liberal, as distinct from a technical, education till the middle of the fourth century.

This date is fixed by a passage in Pliny.[323] According to him, its introduction was due to Pamphilos the Macedonian. At his instance, first at Sikuon, where he lived, and afterwards in the rest of Hellas, free boys were taught before everything painting on boxwood, and this art was included in the first rank of the liberal arts. Now Pamphilos’ picture of the Herakleidai is mentioned in the Ploutos of Aristophanes, which appeared in 388 B.C. Apelles, his pupil, began to come into prominence about 350: Pamphilos himself seems to have lived on till the close of the century. The introduction of painting into the schools at Sikuon may therefore be dated, roughly, about 360 B.C., and from there the custom spread over Hellas. By 300 B.C. no doubt art had become a regular part of the educational curriculum; for the philosopher Teles,[324] who probably lived about that time, mentions the gymnastic trainer, the letter-master, the musician, and the painter as the four chief burdens of boys. A trace of the new art-schools, with their technical vocabulary, is found in the Laws, the work of Plato’s old age:[325] “paint in or shade off,” he says, “or whatever the artists’ boys call it.”

Of the methods used in drawing and painting in Hellas little trace is left. Polugnotos and his contemporaries had produced idealised pictures, taking points from many beautiful men and women and uniting them to make one perfect man or woman. When Idealism gave way to Realism in Hellas, the change affected painting also. The artists tried to create a real illusion in their works, taking subjects like chairs or tables and making the spectator believe them to be real. They were helped by the developments of perspective and foreshortening, which were discovered at this time. It is against this exaggerated realism and the choice of homely subjects that Plato’s attack is directed: he hates such illusions as shams.[326] In the diatribes of the Republic the possibility of idealised painting seems to be forgotten. Whether the boys in the art-schools also suffered by this change and were condemned to draw chairs and tables only cannot be decided.

The pupils, of course, did not have paper to draw and paint upon, nor was canvas employed. Ordinarily they used white wood, boxwood for preference, owing to its smoothness. Lead or charcoal would serve for drawing; for erasures, instead of india-rubber a sponge was used.[327] They may, perhaps, have practised on their wax tablets. One process was σκιαγραφία “shadow-drawing,” which produced rough sketches in light and shade: these seem to have been only intelligible when considered from a distance. Plato regarded them with distrust, as a sort of conjuring.[328]

In ordinary painting, which might be either watercolour or encaustic,[329] the first thing was to sketch in the outline (ὑπογράφειν, περιγραφή); the artist then filled in (ἀπεργάζεσθαι) the picture with his colours, with perpetual glances, now to the original, now to the copy, mixing his paints the while. Beginners would, no doubt, rub out (ἐξαλείφειν) frequently, and paint in again.

Aristotle,[330] in discussing artistic education, notices that it gave boys a good eye for appreciating art, and enabled them to exercise good taste in buying furniture, pottery, and other household requisites, which, to judge from the scanty relics, must have been masterpieces of beauty in the house of a cultivated Athenian. But still more important, it gave them “an eye for bodily beauty”:[331] which suggests that the human form, especially its proportions, formed the chief study of the art-schools. Proportion was the essence of Hellenic art; the great sculptors, as is well known, spent much time in drawing up a canon of perfect proportions for the human body. The boys may well have used their companions in the palaistrai for models, and the canons of physical proportion which they were taught by the art-master would serve to stimulate them with a desire to attain to such a perfection of body by their own athletic exercises.

[207] Lucian, Loves, 44-45.

[208] Aischin. ag. Timarch. 12; Thuc. vii. 29; Plato, Laws.

[209] Lucian, Paracite, 61.

[210] Aischin. ag. Timarch. 12.

[211] Anthol. Palat. x. 43 has been quoted as evidence that six hours’ work a day was a maximum. The epigram runs: “Six hours suffice for work; rest of the day, expressed in numerals, says ζῆθι, ‘enjoy life.’” But the point is the joke that the numerals for 7, 8, 9, 10, the later hours of the day, are ζʹ, ηʹ, θʹ, ιʹ, which spells ζῆθι. The epigram does not mean to state a fact; the joke is its only raison d’être. In any case schools are not mentioned.

[212] Herondas, Schoolmaster (iii.) 53.

[213] Mahaffy, Greek Education, p. 54.

[214] Lucian, Nekuom. 17.

[215] Dem. de Cor. 315.

[216] Theoph. Char. 30.

[217] Ibid. 30.

[218] Herondas, iii. 3.

[219] Demos. ag. Aphobos, i. 828.

[220] Demos. Crown, 312.

[221] Demos. Crown, 270. This is the most probable restoration of the facts from the statements of the opposing orators.

[222] Ibid. 313.

[223] Aelian, Var. Hist. xii. 9 (at Klazomenai).

[224] Benches do not appear on vases, because a row of boys involves elaborate perspective; the artist preferred to take single boys on stools, as a sort of section of a class, just as he gave the stools only two legs. Xen. Banquet, 4. 27, shows two boys sitting side by side. It is not necessary to reject benches, with Girard.

[225] Alexis, Linos (in Athen. 164 B.C.). See Illustr. Plates I. A and I. B.

[226] Plut. Alkib. 7.

[227] Herondas, iii. 83. 96.

[228] See Illustr. Plate No. I. A.

[229] Plato, Protag. 326 D.

[230] In Clement of Alexandria, who gives two others. Strom. v. 8 (p. 675, Potter). A writing copy set by a master, though not of the alphabetical kind described by Clement, is actually extant on a wax tablet in the British Museum (Add. MS. 34,186). It consists of two lines of verse written out by the master and copied twice by a pupil.

[231] Aeschylus, Choeph. 209.

[232] Illustr. Plate I. A.

[233] Xen. Econ. xv. 5.

[234] Demosth. de Cor. 313.

[235] Plato, Laws, 810 A (cp. the prizes for calligraphy in Teos).

[236] Athen. 453 d.

[237] Giles’ Manual of Comparative Philology, § 604.

[238] Athen. 453 c, d.

[239] A fragment of terra-cotta has been found at Athens, containing on it:

which must have belonged to some spelling-book—perhaps the brick formed part of the wall of a schoolroom.—Quoted by Girard, p. 131.

[240] Athen. 454 f.

[241] This is by no means inconceivable, when it is remembered that the Hellenes often set even the laws to music, in order to make them easier to learn and remember.

[242] Plato, Polit. 278 A, B.

[243] Ibid.

[244] Ibid. 285 C.

[245] Xen. Econ. viii. 14.

[246] See Illustr. Plate I. A.

[247] Case E 190.

[248] Plato, Protag. 325 E.

[249] Plato, Laws, 811.

[250] τὰ κεφάλαια—a phrase used in later times for “commonplaces,” “topics,” which suggests that these selections were of that sort.

[251] As the great speeches are picked out from Shakespeare for “repetition” nowadays.

[252] Plato, Laws, 802, 811.

[253] Isokrates (Paneg. 74 A). He says the object was to make the boys hate the barbarians; as, e.g., English boys might learn Henry V. in order to dislike the French!

[254] Xen. Banquet, iii. 5.

[255] Ibid.

[256] Ibid. iv. 6.

[257] Aristoph. Frogs, 1035.

[258] From the Banqueters.

[259] Straton (in Athen. 382, 383).

[260] Aristoph. Frogs, 1032.

[261] Athen. 164.

[262] Aristoph. Birds, 471; Wasps, 1446. 1401.

[263] Plato, Hipp. Maj. 286 B.

[264] Xen. Banquet, iv. 27. School friendships are also mentioned in Aristot. Eth. viii. 12; Aristoph. Clouds, 1006.

[265] Athen. 242 d.

[266] The translation is free, and I omit a good deal that is less relevant.

[267] For a picture of such a flogging see p. 599 of Bury’s Roman Empire.

[268] Plato, Laws, 809 C.

[269] The distinction between λογιστική, reckoning up and comparing numbers, chiefly in bills and the like, practical arithmetic, and ἀριθμητική, theory of numbers, is noted in Plato, Gorg. 451 B.

[270] Plato, Laws, 643 B.C.

[271] Plato, Protag. 318 D.

[272] So Theodoros in the Theaitetos.

[273] Xen. Econ. viii. 14.

[274] Xen. Mem. iv. 4. 7.

[275] Aristoph. Wasps, 656.

[276] In Diogenes Laertius, i. 2. 10.

[277] Alexis (in Athen. 117 e).

[278] An abacus of a very similar sort is still in use in China and Japan, even in banks. The “pebbles” are pushed to and fro, not in grooves, but on wires passing through the middle of them. Calculations can be made by this means with marvellous rapidity.

[279] e.g. Polit. 299 D. πεττείαν ἢ ξύμπασαν ἀριθμητικήν.

[280] Plato, Phaid. 274.

[281] Plato, Laws, 819 B.

[282] The restoration of this process rests on Athen. 671; the other two are purely conjectural.

[283] Suggests at once Hellenic, not Egyptian customs.

[284] Plato, Rep. 526 B.

[285] Plato, Laws, 747.

[286] Technically speaking, this was λύρα, the κιθάρα being a professional instrument which was not taught at school.

[287] Illustr. Plate I. B.

[288] Plato, Lusis, 209 B. On Inscriptions there are separate prizes for the two methods.

[289] Xen. Econ. ii. 13.

[290] Ibid. xvii. 7.

[291] Cp. British Museum Vase E 57, on which a man is leading a leopard by a string.

[292] Plato, Protag. 326 B.

[293] Aristoph. Clouds, 1356.

[294] Aristoph. fragment of Banqueters.

[295] Aristoph. Knights, 526.

[296] Plut. Solon, iii.

[297] Hermippos (in Athen. 619 b).

[298] Aristoph. Wasps, 959.

[299] Ibid. 989.

[300] Aristot. Pol. viii. 6. 11.

[301] For this reason it was opposed to Dorian influences by Pratinas. It was excluded from the Pythian games (Pausan. 10. vii. 5). Pratinas bids it be content to “lead drunk young men in their carousals and brawls.”

[302] Telestes, in his defence of the flute, could only retort that Athena, being condemned to eternal spinsterhood, ought not to be particular about her looks (Athen. 617).

[303] Aristot. Pol. viii. 6. 11.

[304] Athen. 184 d. Plutarch, however, says that when Alkibiades’ masters tried to make him learn the flute, he refused, declaring that it was unfit for gentlemen (Alk. ii. 5).

[305] Not a respected profession at Athens.

[306] Brit. Mus. E 495, 64, 71.

[307] Athen. 337 f.

[308] Smith’s Dictionary of Antiquities.

[309] φορβεία. It belonged to professionals.

[310] γλωσσοκομεῖον.

[311] See the “Inscription” of the Andria and other plays of Terence.

[312] See Illustr. Plate II.

[313] Athen. 20 f.

[314] Plato, Laches, 180 D.

[315] Plato, Euthud. 272 C.

[316] Ibid. 295 D.

[317] Aristoph. Knights, 987-996.

[318] Plato, Protag. 326 B.

[319] Aristot. Pol. viii. 3. 7.

[320] Ibid. viii. 3. 1.

[321] Plato, Protag. 318 B.

[322] Ibid. 311 C.

[323] Plin. Hist. Nat. 35.

[324] Stob. Floril. 98, p. 535.

[325] Plato, Laws, 769 B.

[326] See Rep. X. 596 E, 605 A, etc. In the Sophist, 235 D, 266 D, etc., Plato reserves his denunciation for φανταστική which creates illusions; he almost approves of εἰκαστική. Idealised painting is hinted at in Rep. 472 D, 484 C.

[327] Aeschylus, Agamemnon, 1329.

[328] Plato, Theait. 208 E.

[329] The modern oil process was not employed till late on in the Renaissance. Fresco was common.

[330] Aristot. Pol. viii. 3. 12.

[331] θεωρητικὸν τοῦ περὶ τὰ σώματα κάλλους.