Subject: [HM] Hittites, base 10 unit fractions
From: Milo Gardner (milo.gardner@24stex.com)
Date: Sat Jan 29 2000 - 11:00:34 EST
Denish, Kim and HM listmembers:
The study of Indian math, be it zero, infinity, and base 10 can not be
complete without the study of its diffusion, and receipt of diffusion from
nearby cultures. As another under reported subject, Hittites used base 10
unit fractions, not base 60 fractions as one would expect being closely
identified with Anatolia and Babylonian law (as Denish and others may have
assumed).
Where did Hittite unit fractions, covered by George Ifrah in his latest
book on the universal aspects of math, originate? Were Indian
mathematicians and traders first to develop unit fractions? If so, why did
Sumer and Babylon use base 60, if they too received large segments of its
early math from India?
Clearly India, by 1500 BC was closely aligned with Babylonian 'water clocks,
time keeping and other important science, yet India used base 10, without
unit fractions. The question concerning which developed what when, may be
open in minor respects. However, after 1500 BC Indian mathematicians did
use base 10 unit fractions, as aside subject, for puzzle and game solving,
much as we do today in the USA and Europe. Could have Indians used unit
fractions earlier, and provided them to the Hittites (and Minoans)?
Stated another way, very early, if not throughout its history, Hittites
used base 10 unit fractions, vividly looking like Egyptian fractions. The
same can be said of Minoans. The Mediterranean trading region, often
dominated by Egypt required the use of base 10 unit fractions, and not
base 10 from India, correct?
Why then have historians stressed the Babylonian law side of Hittites, a
cultural fact that was not true in several important mathematical respects?
Could be that an open discussion of diffussion, taking into account India,
zero, base 10 or base 60 infinite numeration systems is very difficult
to pin down, time and place wise, with India being its originator?
However, the finite side of base 10 unit fractions is rather easy to pin
down. However, rather than stressing the objective side of ancient
mathematical documents, as the RMP, EMLR, Moscow P, Hibeh P. and closely
aligned Hittite and Minoan base 10 unit fractions, discussions often
ranging into fuzzy myths. Is myth being used as a strawman to confuse the
scientific aspects of vivid cultural diffusions, placing Babylonians and/or
Indians into a higher role in developing Western mathematics than the two
cultures actually produced?
Again, the under reporting of the Indian Valley may one day show the date(s)
that base 10 unit fractions first appeared there. Until that data appears,
and confirms predating of Egyptian trade and intellectual use of unit
fractions, the hard facts of several Egyptian texts should be considered a
primary subject soft study (and not reduced to a scrap heal - as Otto
Neugebauer discusses as a sign of intellectual decline - Exact Sciences of
Antiquity.
Finally, Hittites and Minoans used base 10 unit fractions, probably stated
only in an infinite series context. However, in these two cases, one day
the finite series of Egyptian hieratic numeration may one day be found,
totally changing the view of the role of Egyptian math in the regions.
Regards,
Milo Gardner
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