The notches everyone counts differently

Claim (verbatim)

Three African bones anchor the story of the world's oldest 'mathematics': the Lebombo bone, a baboon fibula with 29 notches from Border Cave in the Lebombo mountains, around 43,000 years old; the Ishango bone from the shores of Lake Edward in the Congo, about 20,000 years old, whose columns of notches have been read as tallies, doubling, even prime numbers; and the other notched and incised pieces from Border Cave. They are cited as tally sticks, lunar counts, arithmetic. But the interpretive edifice rests on counts that the primary literature does not agree on: how many notches, in how many groups, and whether some are use-wear rather than deliberate marks, vary from analyst to analyst. As with the Palaeolithic plaques, the honest object is the instability itself. A tally you cannot count the same way twice cannot support claims about base systems or prime sequences. The missing knowledge is what, if anything, these bones recorded; the first decidable question is whether their notch-counts and groupings are stable across independent published analyses, because every arithmetical reading is downstream of that stability.

Prediction clause (verbatim)

Prediction: censusing every independently published notch-count and grouping for the Ishango, Lebombo and Border Cave incised bones, at least one of the three objects will show a maximum-to-minimum reported total-notch ratio of 1.15 or greater across independent analysts, and at least one arithmetical reading (base, doubling, or prime-sequence claim) will depend on a grouping that another published analysis does not reproduce (primary clause: an inter-analyst notch-count ratio >=1.15 on at least one object, plus one grouping-dependent arithmetic claim that fails to replicate). Disambiguation: counts must come from direct examination or published high-resolution imaging, not from secondary citation. Coverage guard: objects with only one published primary analysis are reported separately and excluded from the ratio test, so the census measures disagreement, not scarcity.

Kill-dataset (verbatim)

Kill: a census of the primary literature on the Ishango bone (de Heinzelin 1962 and later re-analyses, e.g., Pletser & Huylebrouck), the Lebombo bone (Beaumont; d'Errico's Border Cave studies), and the Border Cave incised bones - tabulate each analyst's total notch-count and grouping per object and each arithmetical reading's dependence on a specific grouping, then compute the inter-analyst count ratios and grouping-replication.

Novelty / leakage triage

anticipated in the literature — this exact test has never been run

The interpretive instability is documented at the object level - de Heinzelin's counts and groupings of the Ishango bone versus later re-readings (Pletser & Huylebrouck's base-12 'slide rule,' which depends on specific column groupings), and the Lebombo/Border Cave notch descriptions (Beaumont; d'Errico's Border Cave studies) - so it is known that counts and groupings vary and that arithmetic readings hinge on contested groupings. But the conjecture's census - every published notch-count per object, the inter-analyst max/min ratio (>=1.15 on at least one object), and an explicit grouping-dependent arithmetic claim shown to fail replication - was not located as compiled. As with the European plaques, this is census-versus-instance.

• J. de Heinzelin, 'Ishango,' Scientific American 206(6) (1962)
• V. Pletser & D. Huylebrouck, 'Does the Ishango Bone Indicate Knowledge of the Base 12? An Interpretation of a Prehistoric Discovery' (arXiv:1204.1019, 2012); and their 'The Ishango Artefact: the Missing Base 12 Link'
• F. d'Errico, L. Backwell, P. Villa et al., 'Early evidence of San material culture represented by organic artifacts from Border Cave, South Africa,' PNAS 109 (2012) - Border Cave incised bones

Predictions

No prediction registered yet.