‘One’s none,Two’s some,Three’s a many,Four’s a penny,Five’s a little hundred.’
‘One’s none,Two’s some,Three’s a many,Four’s a penny,Five’s a little hundred.’
‘One’s none,Two’s some,Three’s a many,Four’s a penny,Five’s a little hundred.’
‘One’s none,
Two’s some,
Three’s a many,
Four’s a penny,
Five’s a little hundred.’
To notice this state of things among savages and children raises interesting points as to the early history of grammar.W.von Humboldt suggested the analogy between the savage notion of 3 as ‘many’ and the grammatical use of 3 to form a kind of superlative, in forms of which ‘trismegistus,’ ‘ter felix,’ ‘thrice blest,’ are familiar instances. The relation of single, dual, and plural is well shown pictorially in the Egyptian hieroglyphics, where the picture of an object, a horse for instance, is marked by a single line | if but one is meant, by two lines | | if two are meant, by three lines | | | if three or an indefinite plural number are meant. The scheme of grammatical number in some of the most ancient and important languages of the world is laid down on the same savage principle. Egyptian, Arabic, Hebrew, Sanskrit, Greek, Gothic, are examples of languages using singular, dual, and plural number; but the tendency of higher intellectual culture has been to discard the plan as inconvenient and unprofitable, and only to distinguish singular and plural. No doubt the dual held its place by inheritance from an early period of culture, and Dr. D. Wilson seems justified in his opinion that it ‘preserves to us the memorial of that stage of thought when all beyond two was an idea of indefinite number.’[335]
When two races at different levels of culture come into contact, the ruder people adopt new art and knowledge, but at the same time their own special culture usually comes to a standstill, and even falls off. It is thus with the art of counting. We may be able to prove that the lower race had actually been making great and independent progress in it, but when the higher race comes with a convenient and unlimited means of not only naming all imaginable numbers, but of writing them down and reckoning with them by means of a few simple figures, what likelihood is there that the barbarian’s clumsy methods should be farther worked out? As to the ways in which the numerals of thesuperior race are grafted on the language of the inferior, Captain Grant describes the native slaves of Equatorial Africa occupying their lounging hours in learning the numerals of their Arab masters.[336]Father Dobrizhoffer’s account of the arithmetical relations between the native Brazilians and the Jesuits is a good description of the intellectual contact between savages and missionaries. The Guaranis, it appears, counted up to 4 with their native numerals, and when they got beyond, they would say ‘innumerable.’ ‘But as counting is both of manifold use in common life, and in the confessional absolutely indispensable in making a complete confession, the Indians were daily taught at the public catechising in the church to count in Spanish. On Sundays the whole people used to count with a loud voice in Spanish, from 1 to 1,000.’ The missionary, it is true, did not find the natives use the numbers thus learnt very accurately—‘We were washing at a blackamoor,’ he says.[337]If, however, we examine the modern vocabularies of savage or low barbarian tribes, they will be found to afford interesting evidence how really effective the influence of higher on lower civilization has been in this matter. So far as the ruder system is complete and moderately convenient, it may stand, but where it ceases or grows cumbrous, and sometimes at a lower limit than this, we can see the cleverer foreigner taking it into his own hands, supplementing or supplanting the scanty numerals of the lower race by his own. The higher race, though advanced enough to act thus on the lower, need not be itself at an extremely high level. Markham observes that the Jivaras of the Marañon, with native numerals up to 5, adopt for higher numbers those of the Quichua, the language of the Peruvian Incas.[338]The cases of the indigenes of India are instructive. The Khonds reckon 1 and 2 in native words, and then take to borrowedHindi numerals. The Oraon tribes, while belonging to a race of the Dravidian stock, and having had a series of native numerals accordingly, appear to have given up their use beyond 4, or sometimes even 2, and adopted Hindi numerals in their place.[339]The South American Conibos were observed to count 1 and 2 with their own words, and then to borrow Spanish numerals, much as a Brazilian dialect of the Tupi family is noticed in the last century as having lost the native 5, and settled down into using the old native numerals up to 3, and then continuing in Portuguese.[340]In Melanesia, the Annatom language can only count in its own numerals to 5, and then borrows Englishsiks,seven,eet,nain, &c. In some Polynesian islands, though the native numerals are extensive enough, the confusion arising from reckoning by pairs and fours as well as units, has induced the natives to escape from perplexity by adoptinghuneriandtausani.[341]And though the Esquimaux counting by hands, feet, and whole men, is capable of expressing high numbers, it becomes practically clumsy even when it gets among the scores, and the Greenlander has done well to adoptuntrîteandtusintefrom his Danish teachers. Similarity of numerals in two languages is a point to which philologists attach great and deserved importance in the question whether they are to be considered as sprung from a common stock. But it is clear that so far as one race may have borrowed numerals from another, this evidence breaks down. The fact that this borrowing extends as low as 3, and may even go still lower for all we know, is a reason for using the argument from connected numerals cautiously, as tending rather to prove intercourse than kinship.
At the other end of the scale of civilization, the adoptionof numerals from nation to nation still presents interesting philological points. Our own language gives curious instances, assecondandmillion. The manner in which English, in common with German, Dutch, Danish, and even Russian, has adopted Mediæval Latindozena(fromduodecim) shows how convenient an arrangement it was found to buy and sell by thedozen, and how necessary it was to have a special word for it. But the borrowing process has gone farther than this. If it were asked how many sets of numerals are now in use among English-speaking people in England, the probable reply would be one set, the regularone,two,three, &c. There exist, however, two borrowed sets as well. One is the well-known dicing-set,ace,deuce,tray,cater,cinque,size; thussize-aceis ‘6 and one,’cinquesorsinks, ‘double five.’ These came to us from France, and correspond with the common French numerals, exceptace, which is Latinas, a word of great philological interest, meaning ‘one.’ The other borrowed set is to be found in the Slang Dictionary. It appears that the English street-folk have adopted as a means of secret communication a set of Italian numerals from the organ-grinders and image-sellers, or by other ways through which Italian or Lingua Franca is brought into the low neighbourhoods of London. In so doing, they have performed a philological operation not only curious, but instructive. By copying such expressions as, Italiandue soldi,tre soldi, as equivalent to ‘twopence,’ ‘threepence,’ the wordsalteebecame a recognized slang term for ‘penny,’ and pence are reckoned as follows:—
Oney saltee... 1d.uno soldo.Dooe saltee... 2d.due soldi.Tray saltee... 3d.tre soldi.Quarterer saltee... 4d.quattro soldi.Chinker saltee... 5d.cinque soldi.Say saltee... 6d.sei soldi.Say oney saltee or setter saltee... 7d.sette soldi.Say dooe saltee or otter saltee... 8d.otto soldi.Say tray saltee or nobba saltee... 9d.nove soldi.Say quarterer saltee or dacha saltee... 10d.dieci soldi.Say chinker saltee or dacha oney saltee... 11d.undici soldi.Oney beong... 1s.A beong say saltee... 1s.6d.Dooe beong say saltee or madza caroon... 2s.6d.(half crown, mezza corona.)[342]
Oney saltee... 1d.uno soldo.Dooe saltee... 2d.due soldi.Tray saltee... 3d.tre soldi.Quarterer saltee... 4d.quattro soldi.Chinker saltee... 5d.cinque soldi.Say saltee... 6d.sei soldi.Say oney saltee or setter saltee... 7d.sette soldi.Say dooe saltee or otter saltee... 8d.otto soldi.Say tray saltee or nobba saltee... 9d.nove soldi.Say quarterer saltee or dacha saltee... 10d.dieci soldi.Say chinker saltee or dacha oney saltee... 11d.undici soldi.Oney beong... 1s.A beong say saltee... 1s.6d.Dooe beong say saltee or madza caroon... 2s.6d.(half crown, mezza corona.)[342]
Oney saltee... 1d.uno soldo.Dooe saltee... 2d.due soldi.Tray saltee... 3d.tre soldi.Quarterer saltee... 4d.quattro soldi.Chinker saltee... 5d.cinque soldi.Say saltee... 6d.sei soldi.Say oney saltee or setter saltee... 7d.sette soldi.Say dooe saltee or otter saltee... 8d.otto soldi.Say tray saltee or nobba saltee... 9d.nove soldi.Say quarterer saltee or dacha saltee... 10d.dieci soldi.Say chinker saltee or dacha oney saltee... 11d.undici soldi.Oney beong... 1s.A beong say saltee... 1s.6d.Dooe beong say saltee or madza caroon... 2s.6d.(half crown, mezza corona.)[342]
Oney saltee... 1d.uno soldo.
Dooe saltee... 2d.due soldi.
Tray saltee... 3d.tre soldi.
Quarterer saltee... 4d.quattro soldi.
Chinker saltee... 5d.cinque soldi.
Say saltee... 6d.sei soldi.
Say oney saltee or setter saltee... 7d.sette soldi.
Say dooe saltee or otter saltee... 8d.otto soldi.
Say tray saltee or nobba saltee... 9d.nove soldi.
Say quarterer saltee or dacha saltee... 10d.dieci soldi.
Say chinker saltee or dacha oney saltee... 11d.undici soldi.
Oney beong... 1s.
A beong say saltee... 1s.6d.
Dooe beong say saltee or madza caroon... 2s.6d.(half crown, mezza corona.)[342]
One of these series simply adopts Italian numerals decimally. But the other, when it has reached 6, having had enough of novelty, makes 7 by ‘six-one,’ and so continues. It is for no abstract reason that 6 is thus made the turning-point, but simply because the costermonger is adding pence up to the silver sixpence, and then adding pence again up to the shilling. Thus our duodecimal coinage has led to the practice of counting by sixes, and produced a philological curiosity, a real senary notation.
On evidence such as has been brought forward in this essay, the apparent relations of savage to civilized culture, as regards the Art of Counting, may now be briefly stated in conclusion. The principal methods to which the development of the higher arithmetic are due, lie outside the problem. They are mostly ingenious plans of expressing numerical relation by written symbols. Among them are the Semitic scheme, and the Greek derived from it, of using the alphabet as a series of numerical symbols, a plan not quite discarded by ourselves, at least for ordinals, as in schedulesA, B, &c.; the use of initials of numeral words as figures for the numbers themselves, as in GreekΠandΔfor 5 and 10, RomanCandMfor 100 and 1,000; the device of expressing fractions, shown in a rudimentary stage in Greekγ’,δ’, for 1/3, 1/4, γδ for 3/4; the introduction of the cipher or zero, by means of which the Arabic or Indian numerals have their value according to their position in a decimal order corresponding to the succession of the rows of the abacus; and lastly, the modern notation of decimal fractions by carrying down below the unit the proportionalorder which for ages had been in use above it. The ancient Egyptian and the still-used Roman and Chinese numeration are indeed founded on savage picture-writing,[343]while the abacus and the swan-pan, the one still a valuable school-instrument, and the other in full practical use, have their germ in the savage counting by groups of objects, as when South Sea Islanders count with coco-nut stalks, putting a little one aside every time they come to 10, and a large one when they come to 100, or when African negroes reckon with pebbles or nuts, and every time they come to 5 put them aside in a little heap.[344]
We are here especially concerned with gesture-counting on the fingers, as an absolutely savage art still in use among children and peasants, and with the system of numeral words, as known to all mankind, appearing scantily among the lowest tribes, and reaching within savage limits to developments which the highest civilization has only improved in detail. These two methods of computation by gesture and word tell the story of primitive arithmetic in a way that can be hardly perverted or misunderstood. We see the savage who can only count to 2 or 3 or 4 in words, but can go farther in dumb show. He has words for hands and fingers, feet and toes, and the idea strikes him that the words which describe the gesture will serve also to express its meaning, and they become his numerals accordingly. This did not happen only once, it happened among different races in distant regions, for such terms as ‘hand’ for 5, ‘hand-one’ for 6, ‘hands’ for 10, ‘two on the foot’ for 12, ‘hands and feet’ or ‘man’ for 20, ‘two men’ for 40, &c., show such uniformity as is due to common principle, but also such variety as is due to independent working-out. These are ‘pointer-facts’ which have their place and explanation in a development-theory of culture, while a degeneration-theory totally fails to take them in. They are distinct records of development, and of independent development,among savage tribes to whom some writers on civilization have rashly denied the very faculty of self-improvement. The original meaning of a great part of the stock of numerals of the lower races, especially of those from 1 to 4, not suited to be named as hand-numerals, is obscure. They may have been named from comparison with objects, in a way which is shown actually to happen in such forms as ‘together’ for 2, ‘throw’ for 3, ‘knot’ for 4; but any concrete meaning we may guess them to have once had seems now by modification and mutilation to have passed out of knowledge.
Remembering how ordinary words change and lose their traces of original meaning in the course of ages, and that in numerals such breaking down of meaning is actually desirable, to make them fit for pure arithmetical symbols, we cannot wonder that so large a proportion of existing numerals should have no discernible etymology. This is especially true of the 1, 2, 3, 4, among low and high races alike, the earliest to be made, and therefore the earliest to lose their primary significance. Beyond these low numbers the languages of the higher and lower races show a remarkable difference. The hand-and-foot numerals, so prevalent and unmistakable in savage tongues like Esquimaux and Zulu, are scarcely if at all traceable in the great languages of civilization, such as Sanskrit and Greek, Hebrew and Arabic. This state of things is quite conformable to the development-theory of language. We may argue that it was in comparatively recent times that savages arrived at the invention of hand-numerals, and that therefore the etymology of such numerals remains obvious. But it by no means follows from the non-appearance of such primitive forms in cultured Asia and Europe, that they did not exist there in remote ages; they may since have been rolled and battered like pebbles by the stream of time, till their original shapes can no longer be made out. Lastly, among savage and civilized races alike, the general framework of numeration stands throughout the world as anabiding monument of primæval culture. This framework, the all but universal scheme of reckoning by fives, tens, and twenties, shows that the childish and savage practice of counting on fingers and toes lies at the foundation of our arithmetical science. Ten seems the most convenient arithmetical basis offered by systems founded on hand-counting, but twelve would have been better, and duodecimal arithmetic is in fact a protest against the less convenient decimal arithmetic in ordinary use. The case is the not uncommon one of high civilization bearing evident traces of the rudeness of its origin in ancient barbaric life.