tablet from Uruk, late third or early second century BC, containing
one of the earliest known instances of the Babylonian zero; Louvre,
AO 6484 side B.
On the line
14 of the tablet we can read:
learned men of Babylon had no concept of zero around 1200 BC [as on
the tablets from Uruk]. Despite their strictly positional nature and
their sexagesimal base, learned Babylonian numerals remained decimal
and additive within each order of magnitude. This naturally created
many ambiguous expressions and was thus the source of many errors.
In any numerical system using the rule of position, there comes a
point where a special sign is needed to represent units that are
missing from the number to be represented. To overcame this
difficulty, Babylonian scribes sometimes left a blank space in the
position where there was no unit of a given order of magnitude [as
on the tablets from Suza, 1800-1700 BC].
some point, probably prior to the arrival of the Seleucid Turks in
311 BC, Babylonian astronomers and mathematicians devised a true
zero, to indicate the absence of units of a given order of
magnitude. They began to use, instead of a blank space, an actual
sign wherever there was a missing order of the powers of 60, and the
sign they used was a variant of the old ‘separator’ sign [which
was used in literary text]:
Ifrah: The universal history of numbers, Transl. from 1981
French ed., J. Wiley & Sons, New York, 1998.
zero is not an easy concept. Zero is not nothing, it is a numeral
which is essential in every positional numerical system built upon
orders of magnitude. Unfortunately, in US it remains a grueling
concept even today. You can see numbers smaller than 1 written
without zero in front of a decimal point, like zero is nothing, for
instead of 0.714
is used not only in general writings but in science and engineering
also. Nevertheless, zero is not a very modern concept: it was less
peculiar to the ancient civilizations than it is to Americans today.
If it is
true that Babylonians introduced a full-fledged zero somewhere
between the sixth and third centuries BC (read: if we don’t find
tablets between the twelfth and sixth centuries BC showing
otherwise), then Babylonians needed at least six centuries to put
the zero symbol into the empty numeral space. Thus, can we expect an
American zero in front of a decimal point before the year 2092