Sand Songs: The Formal Languages of Warlpiri Iconography

algebra we learn ed . The visual algebraic components of Warlpiri iconography are obvious. We have a finite set of symbols and the symbols may becombined to make more complex struc tu res accord ing to a finite set of ru les. Compare this to the formation of equations in college algebra where the letters x and y, the in tegers 2 and 3, and the symbols =, + : , and " combine to make the complex notion of a qu adra tic function: y = x" 2 + 3x. Beyond what we see in the iconography is its power to model the real world of the Warlpiri. The iconographic designs are, to a large extent, models of the Dreaming, the fundamental reality of the Warlpiri. The Warlpiri iconographic system can, in this way, be seen as a mathematical mod el of aspects of rea lity parallel in form and function to the mathe matical mod els of trajectories we study in college algebra. The Warlpiri recognize the components and rules of their iconography and they recognize its modeling functions. What they d on't seem to have is a "theory of iconography" that abstracts general patterns from the sand scenes, yawalyu, and guru wari. Here we may question whether or not the iconography is mathematics. Perhaps we are safer to say, as Marcia Ascher has suggested, that the Warlpi ri iconography be called "mathematical ideas" rather tha n ma thematics." I prefer to leave the question open at this time. Obv ious ly, that we can model the iconography with mathematics does not imply that the iconography is mathemat ics, but neither does it imply that it isn't. The quandary may be resolved by researchers working in the field of ethnomathematics. Ethn omathematics includes "all practices of a mathematical na ture, such as sorting, classifying, counting, and measuring, wh ich are performed in different cultural settings, through the use of practices acquired, developed , and transmitted through generations."16 The Austrian mathema tician Roland Fischer provides a way of viewing mathematics that is helpful in understanding "ethnornathematics." Fischer writes, Mathematics provides a means for individ uals to exp lain and control complexsituations of the natural and of the