252 THE POPULAR SCIENCE MONTHLY, 



ANIMAL ARITHMETIC. 



By Madame CLIiMENCE EOYER. 



ALL degrees of arithmetical aptitude may be found among 

 tlie human races, from the genius of a Newton and a La- 

 place to an absolute inability to conceive the abstract notion of 

 number aside from concrete facts furnished by direct perception. 

 The savage is not deficient in the perception of the multiple. He 

 never confounds one tree with two, or two with three, or four ; 

 and is well aware of the difference between two, three, or ten men, 

 when he is going out to fight them. The thing that he can not 

 do is to abstract the idea of a number from the things to which it 

 is attached, and generalize it, without reference to the concrete 

 objects with which he has seen it associated. He may compre- 

 hend two, because it is associated with his two hands and his two 

 feet ; three, by the aid of the triads with which he is acquainted, 

 and of the triangle with which those objects may be arranged ; 

 four, from the four limbs of animals and the four corners of a 

 square. But his ability to form such conceptions is very lim- 

 ited. The first steps in learning in this direction, in savages and 

 children, are to distinguish the abstract notions of unity and 

 plurality, and in plurality, of two and three from larger plurali- 

 ties. The difficulty in the way of their reaching a concept of 

 abstract numbers is their inability to form a mental representa- 

 tion : four trees not being identical in the savage's thought with 

 four stones, he can not imagine that there is anything common 

 between them. Nevertheless, he can distinguish clearly enough 

 between four trees and three others, and the two groups will 

 leave quite different impressions in his mind. Four trees in a 

 row will also make a different impression from four trees in a 

 square. He is most struck with differences of distribution in 

 space, and derives from them his notions of differences in plu- 

 rality. While he is a poor arithmetician he is a good geome- 

 trician. 



It is by the exercise of this faculty that he finds his way so 

 readily where he has once gone. He recognizes a wood he has 

 been in by the relative distances apart of the trees, their heights, 

 sizes, the inclination of their trunks to one another, the profile of 

 their masses, and their kinds. He learns the landscape by the 

 relief and accidents of the ground, the wave-lines of the horizon, 

 and a thousand details which he fixes upon his memory by a sin- 

 gle keen observation so clearly as to give imagination no chance 

 to play tricks with him. He estimates distances by the weaken- 

 ing of tones and the convergence of the lines and planes of the 



