150 Transactions. 



Akt. XV. — Maori Numeration : Some Account of the Single, 

 Binary, and Semi - vigesimal Systems of Numeratio7i 

 formerly employed by the Maori. 



By Elsdon Best. 



[Read before the Anckland Institute, 3rd October, 1906.] 

 Maori numeration is a subject which appears to have- 

 received little attention from writers who have dealt witii 

 the customs of the Native race, and of what has been placed 

 on record a certain proportion thereof is certainly erroneous 

 and misleading. The following notes, albeit somewhat brief 

 and incomplete, will serve to give the reader some idea of 

 the system of numeration which obtained among the Tuhoe 

 Tribe of Maoris prior to the arrival of Europeans in New 

 Zealand. 



There were, in former times, two different methods of 

 numeration in use among the Maori people, single and binary. 

 Some profess to see in the dual system a primitive method of 

 enumeration which obtained in times long past, before the 

 arrival of the race in Polynesia. From information obtained 

 in this district of Tuhoeland, it would appear that the binary 

 system was used in counting game, &c. : that is to say, such 

 items were counted, or tallied, in pairs — hence the term used 

 (topti) in this method is equivalent to our word " brace." 



The systems of numeration of primitive peoples are often 

 quoted by anthropologists as a sign of the grade of culture to 

 which such peoples have attained. Thus we read of tribes of 

 so low a culture as to have no system of counting beyond five, 

 or even three. It will be seen that the Maori, a barbarous 

 people, had evolved, or borrowed, a very good system of 

 numeration, and doubtless quite elaborate enough for their 

 purposes. Some writers have stated that the Natives of New 

 Zealand did not count above one hundred, any number above 

 that not being counted with precision, but simply styled as 

 " numberless," or "a great many," " a multitude." It does 

 not, however, appear to have been so, although it is probable 

 that the statement given would be correct if applied to thou- 

 sands instead of hundreds. Albeit the term mano has been 

 used to define " a thousand " in modern times — i.e., since Euro- 

 pean settlement in these isles — yet it is not clear that it was so 

 used in ancient times. I am inclined to think that the word 

 7na7io may have been originally used as the term tini is at 

 the present time — viz., to imply a great number, a multitude. 

 The Ngati-Kahungunu Tribe have an expression — niano tini 

 ngeangea — which is used to denote a great number. It ap- 



