When a chief is getting ready to pay in the door tax of two dollars a door, he does not count the doors and then multiply the number by two: he simply lays down two dollars for each door and pays in the lot, generally without knowing the sum total of the dollars. If a chief were told to pay in the tax for half his doors only, he would not know how to carry out the instruction. Subtraction is accomplished only in the most concrete manner, E.G. if a man wished to take away eight from twenty-five, he would count out twenty-five of the objects in question, or of bits of leaf or stick, then push away eight and count up the remainder. A dodge sometimes adopted, especially by the Kenyah, for counting the persons present, is to take a fern-leaf with many fronds, tear off a half of each frond, handing each piece to one of the men, until every man present affirms that he has a piece, and then to count the number of torn fronds remaining on the stalk.
It will thus be seen that the arithmetical operations of the Kayans are of an extremely concrete character; those of the other tribes are similar (with the exception again of the Punans, who do not count beyond three); though many of the Klemantans get confused over simple counting and reckoning, which the Kayans accomplish successfully.
Tama Bulan, the Kenyah chief whom we have had occasion to mention in several connections, obtained and learnt the use of an abacus from a Chinaman, and used it effectively. This deficiency in arithmetic is, however, no evidence of innate intellectual inferiority, and there seems to be no good reason to doubt that most of the people could be taught to use figures as readily as the average European; those children who have entered the schools seem to pick up arithmetic with normal rapidity.
The Sea Dayaks sometimes deposit sums of money with the Government officers, and they know accurately the number of dollars paid in; but when they withdraw the deposit, they generally expect to receive the identical dollars paid in by them.
Measurement
The Kayans use two principal standards of length, namely, the BUKA and the BUHAK. The former is the length of the span from finger-tip to tip of outstretched arms; the latter is the length of the span from tip of the thumb to tip of the first finger of the same hand. In buying a pig, for example, the price is determined by the number of BUHAK required to encircle its body just behind the forelegs. The half BUKA is also in general use, especially in measuring rattans cut for sale, the required length of which is two and a half BUKA. In order to express the half, they have adopted the Malay word STINGAH, having no word of their own.
Distances between villages are always expressed in terms of the average time taken by a boat in ascending the stream from one to the other. Distances by land are expressed still more vaguely; for example, the distance between the heads of two streams might be expressed by saying that, if you bathe in one, your hair would still be wet when you reach the other (which means about one hour); or a longer distance, by saying that if you started at the usual time from one of the places you would reach the other when the sun is as high as the hawk (which means a journey from sunrise to about 10 A.M.), or when the sun is overhead (I.E. noon), or when it is declining (about 3 P.M.), or when the sun is put out (sunset), or when it is dark.
In order to describe the size of a solid object such as a fish, a Kayan would compare its thickness with that of some part of his body, the forearm, the calf of the leg, the thigh, or head, or the waist. In describing the thickness of the subcutaneous fat of a pig, he would mention one, two, three, or even four fingers.
Cosmological and Geographical Notions
The more intelligent Kayans can give a fairly good general description of the geographical features and relations of the district in which they live. In order to do this a Kayan will map out the principal features on a smooth surface by placing pieces of stick to represent the rivers and their tributaries, and pieces of leaf to represent the hills and mountains; he will pay special attention to the relations of the sources of the various streams. In this way a Kayan chief of the Baram would construct a tolerably accurate map of the whole Baram district, putting in Bruni and USUN APO and the heads of the Rejang, Batang Kayan, Tutong, and Balait rivers. He knows that all the rivers run to the sea, though few Kayans have seen the sea or, indeed, been outside the basin of their own river. To have been to another river, or to have seen the sea, is a just ground of pride. He does not know that Borneo is an island, though he knows that the white men and the Chinese come from over the sea; he will confidently assert that the sea is many times larger than the Baram river, even ten times as large. They seem to regard the sea as a big river of which their main river is a tributary.