Number (linguistics)

“ We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought. ”

“ Sanskrit has twenty-seven, while Japanese possesses twenty-four, and the Chinese a number almost equally great. Very many languages, as might be expected, contain special numeral expressions, such as the German dutzend and the French dizaine; but these, like the English dozen and score, are not to be regarded as numerals proper.
The formation of numeral words shows at a glance the general method in which any number scale has been built up. The primitive savage counts on his fingers until he has reached the end of one, or more probably of both, hands. ”

“ But races as fond of metaphor and of linguistic embellishment as are those of the East, or as are our American Indians even, might readily resort to some other source than that furnished by the members of the human body, when in want of a term with which to describe the 5, 10, or any other number of the numeral scale they were unconsciously forming. ”

“ We experienced some little trouble in mastering the French numerals, until I tried a new scheme, and called out, "From the right, number, in French!" Then my merry convalescents began shouting gleefully, "Oon," "Doo," "Troy," "Catta," "Sink," etc.; but the French numerals stuck in their heads. Never did any one, I imagine, have such a set of jolly, cheery boys in blue as pupils, and the strong remnant of the child left in many of them made them the more attractive. ”

“ It often happens that the composition of numeral words is less easily understood, and the original meanings more difficult to recover, than in the examples already given. But in searching for number systems which show in the formation of their words the influence of finger counting, it is not unusual to find those in which the derivation from native words signifying finger, hand, toe, foot, and man, is just as frankly obvious as in the case of the Zuñi, the Arawak, the Eskimo, or the Montagnais scale. ”

“ If a savage expresses the number 3 by the combination 2-1, it will at once be suspected that his numerals will, by the time he reaches 10 or 20, become so complex and confused that numbers as high as these will be expressed by finger pantomime rather than by words. Such is often the case; and the comment is frequently made by explorers that the tribes they have visited have no words for numbers higher than 3, 4, 5, 10, or 20, but that counting is carried beyond that point by the aid of fingers or other objects. ”

“ It is quite a mistake to suppose that savages have no sense of number, because the simple-minded European traveller, compiling a short vocabulary in the usual way, can get no equivalent for our numerals, say from 5 to 10. The fact is that the numerical interest has taken a different turn, incorporating itself with other interests of a more concrete kind in linguistic forms to which our own type of language affords no key at all. ”

“ If there are two numbers, they are neither of them properly described in this definition, or in any of the preceding ones. There is a gross misconception, in taking each or either of them to be an alternate representation of two incompatible ideas. And this sort of error is far from being confined to the present subject; it runs through a vast number of the various definitions contained in our grammars. (18.) "Number is the inflection of a noun, to indicate one object or more than one. Or, Number is the expression of unity or of more than unity."--Hiley's Gram., p. ”

“ In counting from 70 to 100, or in using any number which lies between those limits, no Frenchman is conscious of employing a method of numeration less simple or less convenient in any particular, than when he is at work with the strictly decimal portions of his scale. He passes from the one style of counting to the other, and from the second back to the first again, entirely unconscious of any break or change; entirely unconscious, in fact, that he is using any particular system, except that which the daily habit of years has made a part himself. ”

“ But among races whose intelligence is of a low order, or—if it be permissible to express it in this way—among races whose number sense is feeble, progression from one number to the next is not always in accordance with any well-defined law. After one or two distinct numerals the count may, as in the case of the Veddas and the Andamans, proceed by finger pantomime and by the repetition of the same word. Occasionally the same word is used for two successive numbers, some gesture undoubtedly serving to distinguish the one from the other in the savage's mind. ”

“ OBS. 18.—Since nouns and adjectives are different parts of speech, the suggestion, that, "Numeral adjectives are also names, or nouns," is, upon the very face of it, a flat absurdity; and the notion that "the name of a number" above unity, conveys only and always the idea of unity, like an ordinary "singular noun," is an other. A number in arithmetic is most commonly an adjective in grammar; and it is always, in form, an expression that tells how many, or—"denotes how many things are spoken of."—Chase, p. 11. But the name of a number is also a number, whenever it is not made plural in form. ”

“ THE HINDU-ARABIC NUMERALS CHAPTER I EARLY IDEAS OF THEIR ORIGIN
It has long been recognized that the common numerals used in daily life are of comparatively recent origin. The number of systems of notation employed before the Christian era was about the same as the number of written languages, and in some cases a single language had several systems. ”

“ Almost all civilized languages, however, except the Teutonic, and practically all uncivilized languages, begin their direct numeral combinations as soon as they have passed their number base, whatever that may be. To give an illustration, selected quite at random from among the barbarous tribes of Africa, the Ki-Swahili numeral scale runs as follows:53
The words for 11, 12, and 13, are seen at a glance to signify ten-and-one, ten-and-two, ten-and-three, and the count proceeds, as might be inferred, in a similar manner as far as the number system extends. ”

“ The combinations of these characters, intended to express all the radical words in any language, are to be arranged in numerical order, from unity to 10,000, which number he thinks sufficient to express all words in general use; and to each number is to be annexed the word in any language, as for example English, of which it is a symbol, thus forming a numerical vocabulary. The same words are also to be arranged in another vocabulary in the alphabetical order of the language they belong to; thus each serves for a key to the other. ”

“ If the grammatical structure of the earlier languages of the world's history is examined, the student is struck with the prevalence of the dual number in them—something which tends to disappear as language undergoes extended development. ”

“ I've analyzed both my home phone number and my office phone number in this fashion, figuring out what their components connote singly and as gestalts. And I can see why these fortuitous combinings command attention, why these numbers leap out of the directory pages right at you. Privately I call such a number a common denominator with a way of accreting its numerator.
I hope you're not laughing at me.
After all, when you remember what number is, what's happening follows naturally. Number's a language we use to blaze our way through the wood of reality. ”

“ Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited ”

“ Examples of this poverty of number knowledge are found among the forest tribes of Brazil, the native races of Australia and elsewhere, and they are considered in some detail in the next chapter. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words. The Chiquitos of Bolivia had no real numerals whatever,1 but expressed their idea for “one” by the word etama, meaning alone. ”

“ The fingers are, however, often employed in counting numbers far above the first decade. After giving the Il-Oigob numerals up to 60, Müller adds:8 “Above 60 all numbers, indicated by the proper figure pantomime, are expressed by means of the word ipi.” We know, moreover, that many of the American Indian tribes count one ten after another on their fingers; so that, whatever number they are endeavouring to indicate, we need feel no surprise if the savage continues to use his fingers throughout the entire extent of his counts. ”

“ One noteworthy and interesting fact relating to numeral nomenclature is the variation in form which words of this class undergo when applied to different classes of objects. To one accustomed as we are to absolute and unvarying forms for numerals, this seems at first a novel and almost unaccountable linguistic freak. But it is not uncommon among uncivilized races, and is extensively employed by so highly enlightened a people, even, as the Japanese. This variation in form is in no way analogous to that produced by inflectional changes, such as occur in Hebrew, Greek, Latin, etc. ”

“ The systems adopted for numeration and for notation do not always agree with one another; nor do they always correspond with the idea which the numbers subjectively present. This latter presentation may, in the absence of any accepted term, be called number-ideation; this word covering not only the perception or recognition of particular numbers, but also the formation of a number-concept.
13. Notation of Numbers.—The system which is now almost universally in use amongst civilized nations for representing cardinal numbers is the Hindu, sometimes incorrectly called the Arabic, system. ”

“ Words now have an added significance; for this purpose they have become and from this time they will be NUMBERS, as well as WORDS.
Always keep in mind that SOUND determines the number value of the word regardless of how it is spelled.
Forming Larger Number Words
In order to form words for larger numbers first become familiar with the figure value of the one hundred code words. These will often combine to form the larger number pictures. For example:
A combination picture of Nero and Papa would represent 2499. ”

“ The acquisition of a scale for which we had no other means of expression than that just described would be a matter of the extremest difficulty, and could never, save in the most exceptional circumstances, progress beyond the attainment of a limit of a few hundred. If the various numbers in question were designated by words instead of by symbols, the difficulty of the task would be still further increased. Hence, the establishment of some number as a base is not only a matter of the very highest convenience, but of absolute necessity, if any save the first few numbers are ever to be used. ”

“ He resolves, indeed, that no one of the four words used, "is in construction with" any of the rest; for he thinks, "The meaning is, 'The number two taken twice is equal to four.'" Here, then, is a fourth opinion in relation to the subject of the verb: it must be "number" understood. Again, it is conceded by the same hand, that, "When numerals denoting more than one, are used as adjectives, with a substantive expressed or understood, they must have a plural construction." Now who can show that this is not the case in general with the numerals of multiplication? ”

“ How they indicated any number greater than one is a point still requiring investigation. In all other known instances we find actual number systems, or what may for the sake of uniformity be dignified by that name. In many cases, however, the numerals existing are so few, and the ability to count is so limited, that the term number system is really an entire misnomer.
Among the rudest tribes, those whose mode of living approaches most nearly to utter savagery, we find a certain uniformity of method. The entire number system may consist of but two words, one and many ”

“ Among almost all savage races one form or another of palpable arithmetic is found, such as counting by seeds, pebbles, shells, notches, or knots; and the derivation of number words from these sources can constitute no ground for surprise. The Marquesan word for 4 is pona, knot, from the practice of tying breadfruit in knots of 4. The Maori 10 is tekau, bunch, or parcel, from the counting of yams and fish by parcels of 10.154 The Javanese call 25, lawe, a thread, or string ”

“ And it is, perhaps, still more surprising to find that a similar origin can be traced even in the numerals, which involved the very triumph of abstraction; for, in using a numeral, “we strip things of all their sensible properties, [133] and consider them as merely relations of number, as members of a series, as perfectly general relations of place.” And yet abstract as they are, and, absolutely as we might suppose them to be removed from concrete objects of sense, it is a matter of certainty that their genesis can be traced. ”