Ishango

Further studies of crania from ancient Northern Africa: An analysis of crania from First Dynasty Egyptian tombs, using multiple discriminant functions

“…Hiernaux's perspectives are relevant to the creators of ancient Nile Valley culture, which is an integral part of, and originated in a larger African context (Frankfort, 1950;Childe, 1953;de Heinzelin, 1962;Arkell and Ucko, 1965;Fairman, 1965;Clark, 1970;Shaw, 1976;Vercoutter, 1978;Aldred, 1978;Hassan, 1988), and is not simply a part of, or a corridor to or from the "Mediterranean world"-a cultural construct with limited explanatory power today, as noted by Herzfeld (1984), and almost certainly less in the early Holocene. "Mediterranean," connoting a "race," "one interbreeding population," at the craniometric level, is questionable as defining the "Middle East" during the Bronze Age (Finkel, 1974(Finkel, ,1978, invalid as a term linking geography to a uniform external phenotype (see Snowden, 1970;MacGaffey, 1966;Keita, 1990), inaccurate as a metric taxon for many groups previously assigned to it (Rightmire, 1975a,b), and problematic as a bony craniofacial morphotype denoting a "race" or mendelian population because of its varied soft-part trait associations and wide geographical distribution (see "Hamitic" in Coon et al, 1950;Gabel, 1966;MacGaffey, 1966;Hiernaux, 1975;Rightmire, 1975a).…”

The Pattern of Prime Numbers

“…To put prime numbers into context, let's begin by saying anecdotally, as late as 20,000 years ago humans marked the bone of Ishango with 19, 17, 13, 11 [4] and 2300 years ago Euclid proved that there are infinitely many prime numbers (e.g. Williamson, 1782) [5].…”

On mathematics in the history of Sub-Saharan Africa

“…The bone has what appear to be tallying marks on it, notches carved in groups. Its discoverer, De Heinzelin, interpreted the patterns of notches as an "arithmetical game of some sort, devised by a people who had a number system based on 10 as well as a knowledge of duplication and of prime numbers" [145,110]. Marshack [200], however, explained the bone as an early lunar phase count.…”