It is impossible to study the decorations on these South American clubs without becoming convinced that their makers shared the same ideas as the ancient Mexicans. They offer, indeed, a whole set of variations on the native theme and idea of Heaven and Earth. Two instances (fig. 5_a_, pl. IX, and 6_a_, pl. XI) in which the union of two figures produces a third, or a single one produces two, elucidate the meaning sometimes expressed by the designs. In the round or spiral forms, which are most frequently accompanied by a zigzag border, I am inclined to see a presentation of air and water, corresponding to the Mexican symbols of the Above.
As lack of space forbids my making here a more extended comparison of the native symbols, I shall but point out how the tau, in juxtaposition and contraposition painted in two colors, produces fig. 40, no. 3. The picture from the Codex Mendoza of a native tlachtli, the form of which is represented by two taus in contraposition, is partly painted black. The same division of a single tau into two parts, colored differently, transforms no. 3 into no. 4 and shows that a single tau could have been employed cursively to symbolize union. 2 and 7 are but variants of 3 and 4. If, instead of angles, curved lines be given to the taus, the first half of fig. 5 is the result. When spaces between the incurving hooks and the border are filled out with color, the familiar design on the second half of 5 results. With exception of the latter, the South American clubs exhibit each of the above forms, as well as no. 8. It will be shown later that these also occur in ancient Peru.
The foregoing examples of the employment of taus in upright and reversed positions is, however, by no means exhaustive. Fig. 41 teaches that the familiar checker-board or tartan design, symbolically employed in ancient Mexico, was the simple result of taus in contraposition, the square spaces thus found being alternately filled with black and brown or gray. The symbolism of this design only becomes evident when all the combinations in which it occurs have been carefully studied. It is represented in the Codices in the doorways and arches of certain sacred edifices which are shown to be estufas or temaz-calli by further illustrations which I could not reproduce here, but which exhibit even the steam escaping from the building and other unmistakable features.