Fig. 47. Sign for 0 in the inscriptions.
Fig. 48. Figure showing possible derivation of the sign for 0 in the inscriptions: a, Outline of the days of the tonalamatl as represented graphically in the Codex Tro-Cortesiano; b, half of same outline, which is also sign for 0 shown in fig. [47].
Both normal forms and head variants for zero, as indeed for all the numbers, have been found in the inscriptions. The normal forms for zero are shown in figure [47]. They are common and are unmistakable. An interesting origin for this sign has been suggested by Mr. A. P. Maudslay. On pages 75 and 76 of the Codex Tro-Cortesiano[[64]] the 260 days of a tonalamatl are graphically represented as forming the outline shown in figure [48], a. Half of this (see fig. [48], b) is the sign which stands for zero (compare with fig. [47]). The train of association by which half of the graphic representation of a tonalamatl could come to stand for zero is not clear. Perhaps a of figure [48] may have signified that a complete tonalamatl had passed with no additional days. From this the sign may have come to represent the idea of completeness as apart from the tonalamatl, and finally the general idea of completeness
applicable to any period; for no period could be exactly complete without a fractional remainder unless all the lower periods were wanting; that is, represented by zero. Whether this explains the connection between the outline of the tonalamatl and the zero sign, or whether indeed there be any connection between the two, is of course a matter of conjecture.
There is still one more normal form for zero not included in the examples given above, which must be described. This form (fig. [49]), which occurs throughout the inscriptions and in the Dresden Codex,[[65]] is chiefly interesting because of its highly specialized function. Indeed, it was used for one purpose only, namely, to express the first, or zero, position in each of the 19 divisions of the haab, or year, and for no other. In other words, it denotes the positions 0 Pop, 0 Uo, 0 Zip, etc., which, as we have seen (pp. [47], [48]), corresponded with our first days of the months. The forms shown in figure [49], a-e, are from the inscriptions and those in f-h from the Dresden Codex. They are all similar. The general outline of the sign has suggested the name "the spectacle" glyph. Its essential characteristic seems to be the division into two roughly circular parts, one above the other, best seen in the Dresden Codex forms (fig. [49], f-h) and a roughly circular infix in each. The lower infix is quite regular in all of the forms, being a circle or ring. The upper infix, however, varies considerably. In figure [49], a, b, this ring has degenerated into a loop. In c and d of the same figure it has become elaborated into a head. A simpler form is that in f and g. Although comparatively rare, this glyph is so unusual in form that it can be readily recognized. Moreover, if the student will bear in mind the two following points concerning its use, he will never fail to identify it in the inscriptions: The "spectacle" sign (1) can be attached only to the glyphs for the 19 divisions of the haab, or year, that is, the 18 uinals and the xma kaba kin; in other words, it is found only with the glyphs shown in figures [19] and [20], the signs for the months in the inscriptions and codices, respectively.