7. Conclusion
We are faced with the need to upgrade our estimation of the
cultural advancement of paleolithic people. To the great arts
of the Gravettian period, including the fabulous paintings of
Lascaux and the Venus figurines, we must now add an advanced
musical arithmetic previously ascribed to Pythagoras. This
supports the suggestion of McClain that advanced arithmetic
preceded writing, and demands a rethinking of prehistoric
mathematics and music. It would seem useful to proceed with
measurements of the other figurines and artifacts of paleolithic
times, in the style of Alexander Marshak, in search of further
clues to the quadrivial pursuits of prehistory.
Acknowledgments
We are grateful to our colleagues of the Lindisfarne Association
for the collegial sharing of ideas over the years.