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  • The Long Count

    In a refreshingly straightforward essay James Rauff, a professor of mathematics, considers North American rock art tallies from a mathematical point of view. [1] “Tallies represent a count of something, ” he says, and recognizes, “the ambiguity between artistic choice and tally.”  And notes, “As we study the tallies on rock art, a particularly difficult question arises: How is one to distinguish a tally from a design.”

    Rauff’s thoughts and sketches provoked me to think more carefully about series of marks, lines, dots, strokes, and figures as possible sequences and patterns that may be instances of tallies. The question is not so simple. I may be seeing linear, or what I perceive as logical progressions, as universal counting. A mistake to do so. I conclude there is no pure tally given the marks’ (and the makers’) own internal and obscure meanings. There may be an accounting of objects or a marking of time intervals, but the visual configuration of a petroglyph on stone is always an image with various signs and/or symbolic elements. [2]    

    As I identify possible tally marks, I see the complexity of notations merging as symbols or figures. Yes, the visual sense of counting in the sense of mathematics lends a density to inherent meaning. Further, I think of the possible use sequential marks as a form of re-counting, as memory-making, as a mnemonic. This remembering manifests as re-collection and storytelling, bridging realms.

    Rauff elegantly sums up his position, “Ultimately, the bulk of the interpretations of tally marks are pure speculation. My favorite interpretation is that of George Bull Tail. He is quoted as saying that the tally marks were made 'by the Little People to keep track of numbers or something' ".

    Photos possible Tallies:  Rock Art Tally Marks

    [1] James V. Rauff. "Rock Art Tallies: Mathematics on Stone in Western North America." Journal of Humanistic Mathematics 3, no. 2 (2013): 76-87. Bull Tail quote p.85. Available as a PDF at
    [2] The complexities of notation, or schemata, and pictures as images are well elucidated by art historian and theorist James Elkins in his numerous books and papers.
    Further reading. William Breen Murray, "Numerical representations in North American rock art," in Native American mathematics (1986), 45-70. Michael P Closs, ed., University of Texas Press.