Convenience Does Not Explain the Use of the Mayan Duodecimal Number System
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The invention or selection of a duodecimal numbering system is difficult to reconcile with the fact that primitive peoples count on ten fingers. The word "digit" which means either finger or number indicates the origin of counting. At about 3000 B.C. the Sumerians possessed a sexegisimal system that formed the basis of our time-keeping notation. W e use 60 seconds, 6 0 minutes, a 12-hour day or night on our clocks, a 12month year, and 360" in a circle. It is claimed that the advantage of a 6 or 12 based counting system over the natural decimal system is the convenience of having more divisors (1, p. 16 ; 2, p. 7 9 ) . Only 2 or 5 divide into 1 0 whereas four numbers are factors for 12. The argument of convenience for merchants or astrologers cannot be supported if we refer to another civilization using duodecimal notation. The Mayan Indians had a simple number system based on dots and bars denoting one(s ) and f ive(s) , but they also employed duodecimal symbols which were complicated glyphs carved onto stone monuments. Each of 12 glyphs depicted a carved head associated with an invariant ornament that identified the intended number ( 3 , 4 ) . A fist or hand above a head represented "2", a comblike ornament stood for the numeral "5". while freckled or spotted cheeks on a profile was the symbol for "9". A skull face or jawbone stood for "10". By adding a jawbone to the face glyphs of the numbers between three and nine, the symbols for 1 3 to 1 9 were produced. h c e glyphs for 1 1 and 12 existed; a glyph for 1 3 may also have been used in addition to the compound symbol for 10 + 3 ( 3 , pp. 189-190). This labor-intensive method of creating number symbols, plus the artistic demands placed on stone masons, makes any claim of convenience for the Mayan duodecimal glyphs untenable. Since both Sumerian and Mayan civilizations also had available the simple and natural decimal system, the existence and use of the duodecimal system is inexplicable except in terms of magical, religious, or aesthetic imperatives. If the duodecimal notation served a ritual purpose, some unknown psychological factor in ancient man made the selection against the more "normal" decimal system.