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Mathematics Goes to the Movies
by Burkard Polster and Marty Ross
Clan of the Cave Bear (1986)
Ayla (Nicole Eggert) is a Cro-Magnon child who has been taken into a Neanderthal
clan. She is watching Creb (James Remar), the Mog-ur (leader and wise man) of
the Clan, as he ponders some stones. Ayla asks him to teach her (the communication
is by isolated words and hand gestures, with the meaning indicated in subtitles).
CREB: (He points at three stones and then pulls Ayla’s left ear). Doh… (He pulls Ayla’s right ear)…Makra…(He touches Ayla’s nose)…Chia. The Clan knows this much. (Creb then lays out five stones and places his hand to match the fingers with the stones). Shah…They don’t understand this. Only Mog-ur counts this far.
AYLA: (Ayla matches her fingers with the stones). Shah!
(Creb puts down five more stones. Ayla smiles, and grabs five stones in each hand). Makra-Shah!
(She grabs more stones to make two more groups of five. She touches each pile, and shows the fingers of each hand twice).
CREB (astounded): Don’t show this to the Clan. Only you and I will know.
59:30 Ayla has been punished by the tribe, sent away for one “turning of the moon”. While she is away, Ayla and Creb both keep track of the time past by making notches on a stick. Creb simply makes the notches, while Ayla matches them with her fingers to group them in fives.
The movie is based on the book The Clan of the Cave Bear by Jean Auel (Hodder and Staughton, London, 1980).
Both scenes are largely faithful to the book. In the book Creb can, with difficulty, count to twenty, and Ayla immediately grasps the full force of the idea, using the hands of as many people as needed to keep counting. In the book, Creb does not seem to be sufficiently comfortable with counting to keep track of the days in a lunar cycle, though he is aware of the concept, and he knows Ayla can do it.
The story is set around 30000 years ago, shortly before the Neanderthals died out. There is a fascinating debate over the numerical abilities of both Cro-Magnons and Neanderthals. The evidence of counting ability is largely in the form of tally sticks - bones with etched marks - but the age of and the function of such sticks is contentious. It does seem that Cro-Magnons at least had some sense of one-to-one correspondence, and it seems likely that some of the earliest sticks were used to keep track of lunar cycles. Less clear is early evidence of the arithmetic grouping abilities displayed by Creb (in the book) and Ayla. It is also seems that the use of numerals, and probably number names, only began thousands of years later. For an excellent survey, see Chapter 2 of The Mathematical Brain by Brian Butterworth (Macmillan, 1999), and the references sited there.