The recent post that cited 0-4 counting as base 4
may have meant base 5, as Egyptians from the Lower
Kingdom may have practiced, as Greek may have
been told by oral histories.
Consideration of the foundations of Greek base 10
as fact that the Upper and Lower Kingdoms of Egypt
also used a form of base 2, called Horus-Eye
should also be mentioned in ways that our kids
might enjoy studying.
As related to New World numerations points, Incan
mathematicians used base 10, reported by George G.
Joseph, Crest of the Peacock, as a mental abacus.
Even more interesting, to myself, is that Mayan
base 20 was seen as a combination of base 4, counting
0-3, and base 5, counting 0-4, as George Sanchez
reported in Arithmetic in Maya, that later Aztecs
debased to 1-20 counting.
As additional proof that Mesoamerican 0-19 counting
was founded on a merging of bases 4, 5 (maybe as
another mental abacus), nearby Californian groups
used bases 4, 5, 8, 10, 12, 16, 20 and combinations
thereof (as reported by A.L. Kroeber, Handbook of
the Indians of California.). Reading Kroeber provides
a sense that each tribe tended to structure its own
number based (possibly based on their own tribal
cosmology), much as Aztecs were sunworshippers and
Mayans, and earlier Olmecs plausibly considered sidereal
time as very different from solar time.
Yes, our K-6 students should be exposed to a wide
array of numeration systems, based on a world-wide
view of number such that a strong foundation is
provided for the later use of our modern positional
base 10 system, and the use of algorithms.
Regards to all,
Milo Gardner