PSYCHOLOGY 273 



The conclusiveness of this experiment is not unassailable, 

 but it is anyhow remarkable that the Australian aborigine, 

 according to travellers' accounts, cannot even count up to four. 



The reason why primitive races have not learnt to count is 

 explained by Kohler 1 on the grounds that there was no necessity 

 for it, since man only learns to count when he begins to acquire 

 property (?). 



If the question is raised when man first began to count, the 

 answer can only be based on conjecture. 



Probably the numerous notches filed in a reindeer's horn 

 may be regarded as the earliest effort to register a tally of the 

 animals killed by the reindeer hunter. It is generally supposed 

 that numbers were reckoned on the fingers first of one hand, 

 then of the other, and finally on the toes, as is done to-day by 

 savages. 



Tylor believes that counting with the fingers in particular 

 positions has led to the development of written symbols. The 

 Roman V may represent a reduced diagram of the hand with 

 the five fingers spread out, and the X may be simply derived 

 from the combination of two Vs. Lubbock thinks that our 

 early forefathers could not have counted beyond ten, although 

 still there are savages who go no further than four. Whether 

 counting on the fingers originated in prehistoric times spon- 

 taneously in different races (Bastian's " folk-thought "), or was 

 spread by direct transmission from one race to another, is a 

 very difficult problem to decide. If one assumes the unity 

 of the human race (and it cannot well be otherwise), one inclines 

 rather to the likelihood of independent discovery. 



While it appears probable that many animals besides man 

 can count, yet the power of reckoning, or thinking, in numbers 

 is confined to man alone, for no animal is so constituted as to 

 be able by an independent psychical process to add up, mul- 

 tiply or divide figures. 



Calculating horses, dogs and parrots are carefully trained by 

 means of their good memory to perform with certain signs 

 which are given to them. Even the intelligent Berlin horse 

 Hans is no exception to this. Reckoning is an art acquired 

 by man after he has emerged from his primitive state. 

 1 Kohler, Zur Urgeschichte der Eke, Stuttgart, 1897, p. 5. 



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