INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 



91 



■ ■ ■ ■ 



numerals in the inscriptions, or otherwise he will quickly find himself 

 involved in a tangle from which there seems to be no egress. Proba- 

 bly more errors in reading the inscriptions have been made 

 through the incorrect identification of these numerals than " 



through any other one cause, and the student is urged ■ ■ 

 to be continually on his guard if he would avoid making ■ ■ ■ 

 tliis capital blunder. 



Although the early Spanish authorities make no mention 

 of the fact that the Maya expressed their numbers by bars 

 and dots, native testimony is not lacking on this point. 

 Doctor Brinton (1882 b: p. 48) gives this extract, accom- 

 panied by the drawing shown in figure 44, from a native 

 writer of the eighteenth century who clearly describes this 

 system of writing numbers : 



They [our ancestors] used [for numerals in their calendars] dots and 

 lines [i. e., bars] back of them; one dot for one year, two dots for two 

 years, three dots for three years, four dots for four, and so on; in ad- 

 dition to these they used a Une; one line meant five years, two lines 

 meant ten years; if one line and above it one dot, six years; if two 

 dots above the line, seven years; if three dots above, eight years; if 

 four dots above the line, nine; a dot above two Lines, eleven; if two 

 dots, twelve; if three dots, thirteen. 



This description is so clear, and the values therein as- 

 signed to the several combinations of bars and dots have 

 been verified so extensively throughout both the inscrip- 

 tions and the codices, that we are justified in identifying 

 the bar and dot as the signs for five and one, respectively, wherever 

 they occur, whether they are found by themselves or in varying 

 combinations. 



In the codices, as mil appear in Chapter VI, the bar and dot 

 numerals were painted in two colors, black and red. These colors 

 were used to distinguish one set of numerals from another, each of 

 which has a different use. In such cases, however, bars of one color 

 are never used with dots of the other color, each number being either 

 all red or all black (see p. 93, footnote 1, for the single exception to 

 this rule). 



By the development of a special character to represent the number 

 5 the Maya had far surpassed the Aztec in the science of mathematics; 

 indeed, the latter seem to have had but one numerical sign, the dot, 

 and they were obliged to resort to the clumsy makeshift of repeating 

 this in order to represent all numbers above 1. It is clearly seen 

 that such a system of notation has very definite limitations, which 

 must have seriously retarded mathematical progress among the Aztec. 



In the Maya system of numeration, which was vigesimal, there was 

 no need for a special character to represent the number 20,^ because 



Fig. 44. Nor- 

 mal forms 

 ofnumerals 

 1 to 13, in- 

 clusive, in 

 the Books 

 of Cliilan 

 Balam. 



1 Care should be taken to distinguish the number or figm-e 20 from any period which contained 20 periods 

 of the order next below it; otherwise the uinal, katun, and cycle glj'phs could all be construed as signs 

 for 20, since each of these periods contains 20 units of the period next lower. 



