NATURE 



145 



THURSDAY, JUNE 18, 1896. 



THE EVOLUTION OF COUNTING. 

 The Nuinhcr Concept : i/s Origin and Dez'elopment. By 

 Levi Leonard Conant, Ph.D. 8vo. Pp. 218. (New 

 York and London: Macmillan and Co., 1896.) 



PROF. CONANT has produced a book which sup- 

 plies a gap in scientific hterature, and on it he has 

 expended great diligence in collecting the materials, and 

 circumspection in dealing with them. The problems of 

 the origin and development of the number concept are 

 important alike to the anthropologist and the psychol- 

 ogist, and all attempts to connect these two branches of 

 science are most welcome ; for the scope of the book, 

 therefore, and for its execution. Dr. Conant is to be 

 congratulated. 



In a itv! instances, languages have Ijeen found to be 

 absolutely destitute of pure numeral words ; the Chiquitos 

 of Bolivia, for example, expressed their idea for one by 

 efama — " alone " — they had no real numerals. A few other 

 South American languages are almost equally destitute 

 of numeral words, but some indirect expression shows a 

 conception of the difference between i and 2, or, at least, 

 between i and many. 



There is a surprising paucity of numeral words among 

 the native races of South America, Australia, New 

 C'juinea, and among the Pigmy peoples. Many of these 

 have only two numerals. It is probably true that no 

 .\ustralian language contains a pure, simple numeral for 

 4 : a few tribes have a numeral for 3. The same obtains 

 for the Papuan as opposed to the Melanesian tribes of 

 British New Guinea, whereas the numerals of the latter 

 iS. H. Ray, Trans. Internal. Congr. Orientalists, 

 London, 1892-93, p. 770) have decided affinities with 

 those of the Melanesian archipelagoes. It is also 

 characteristic of the Australians and the Papuans (as 

 here restricted) to count by pairs ; but this is not a 

 Melanesian custom, though it is employed in Polynesia. 

 The Mincopies (Andaman Islands) and the Veddas have 

 numerals for only i, 2, beyond which they say "and one 

 more, and one more," &c. ; for the Bushmen, 3 means 

 simply many. The Pigmies of Central Africa, accord- 

 ing to -Stanley, have separate numerals up to 5, but the 

 words for i {ttjju) and 6 {ijju) are so closely akin, that 

 it suggests that 6 was to them a new i. These Pigmy 

 people are considerably in advance of the others just 

 referred to, so far as their system of numeration is 

 concerned. 



The author carefully points out that it is not a general 

 law that those races which are lowest in the scale of 

 civilisation have the feeblest number sense or the least 

 possible power of grasping the abstract idea of number. 

 If the life of any tribe is such as to induce trade and 

 barter, a considerable quickness in reckoning will be 

 developed among them. In giving i, 2, 3, 5, 10, or any 

 other small number as a system limit, it must not be 

 overlooked that this limit mentioned is in all cases the 

 limit of the spoken numerals at the savage's command. 

 The actual ability to count is almost always, if not 

 always, somewhat greater than their vocabularies would 

 indicate. By means of their fingers, toes, or other parts 

 NO. 1390, VOL. 54J 



of their body, or by the aid of sticks and other objects, 

 the savages with even the lowest number concept can 

 indicate higher numbers than their spoken numbers. 

 Most proceed with more or less readiness as far as their 

 fingers will carry them, and this litnit is frequently 

 extended to 20. 



The primitive savage counts on his fingers until he has 

 reached the end of one, or more probably of both, hands. 

 Then if he wishes to proceed further some mark is made, 

 a pebble is laid aside, a knot tied, &c., to signify that all 

 the counters at his disposal have been used. Then the 

 count begins anew, the terms already used are again 

 resorted to, and the name by which the first halting-place 

 was designated is repeated with each new numeral ; 

 hence thirteen, fourteen., &c. In Teutonic languages the 

 smaller number is prefixed to the base, e.g., fiinf und 

 zwanzig; but the direct method {twenty-five) is far more 

 common, though both are found in all parts of the 

 world. 



The formation of numeral words by subtraction, 

 though it seems decidedly odd to us, is of common 

 occurrence. In Latin, 19 is undeviginti (i from 20) ; the 

 Bellacoola, of British Columbia, say for 19 "one man 

 less I," as in their numeral scale 20 is "one man," 

 for them 15 is "one foot," and 16 "one man less 4." 

 Many tribes seem to regard 9 as " almost 10," and to 

 give it a name which conveys this thought. 



The following Zuni scale is interesting : — 



1, " taken to start with." 



2, "put down together with." 



3, " the equally dividing finger." 



4, " all the fingers but one done with." 



5, " the notched off." 



6, "another brought to add to the done with." 



7, "two brought to and held up with the rest." 



8, "three brought to and held up with the rest. 



9, "all but all are held up with the rest." 



10, "all the fingers." 



1 1, "all the fingers and another over above held." 

 20, "two times all the fingers." 



100, " the fingers all the fingers. 



1000, "the fingers all the fingers times all the fingers." 

 While the savage almost always counts on his fingers, 

 it does not seem at all certain that these words would 

 necessarily be of finger formation. The numerals for 

 I and 2 would be formed long before the need would 

 be felt for terms to describe any higher number. 

 Universal as finger counting has been, finger origin for 

 numeral words has by no means been universal. In 

 nearly all languages the origin of the words for i, 2, 3, 

 and 4 are so entirely unknown that speculation respecting 

 them is almost useless. 



The first real difficulty which the savage experi- 

 ences in counting, the difficulty which comes when 

 he attempts to pass beyond 2, and to count 3, 4, 

 and 5, is of course slight. Beyond 5, primitive man 

 often proceeds with the greatest difficulty. Whenever 

 the fingers and hands are used at all, it would seem 

 natural to expect for 5 some general expression signifying 

 hand, for 10 both hands, and for 20 man. ■ Such is the 

 ordinary method of progression, but some people express 

 10 by man, perhaps because they do not use the toes in 

 counting ; thus the Api word for 200 is " 10 times the 

 whole man taken 2 times." 



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