history of mathematics - National STEM Centre

Figure 1.3a
Figure 1.3b
8
The Babylonians
From the epilogue to the Code of Hammurabi
I
Let the wronged man who has a case go before my statue called 'King of
Justice' and read out my inscribed stele and hear my valuable words. Let
my stele reveal to him the case, so that he will discover his rights appease
his heart.
Evolution of counting and writing
A group of Old Sumerian clay tablets may be some of the world's earliest forms of
written communication, for they probably pre-date Egyptian hieroglyphic writing.
The tablets, each about the size of the palm of a hand, were found in Uruk, southern
Mesopotamia, and date from about 3200 BC. The Sumerians used a round stylus to
make the circular and D-shaped impressions that you can make out on these tablets,
and a pointed stylus to incise the pictures. A tablet and styluses are shown in
Figure 1.3.
What might these signs have represented? What were the tablets used for? How did
writing come into being? The answers to these questions can be traced back to
earlier developments of counting and using symbols.
Throughout most of human history people have lived without writing; yet images,
symbols and other devices were used to transmit thought long before people could
write. During the Upper Palaeolithic era (the Old Stone Age), about 30 000 to
12 000 years ago, incised bones may have been used to keep track of lunar time.
If so, these pieces of bone represent the earliest known system of counting, or
'reckoning'. Most such developments, however, ended with the decline of
Palaeolithic cultures by the end of the last ice age, about 10 000 BC.
Throughout the Near East, small clay or (less often) stone tokens of varying shapes,
which date back to the eighth millennium BC, have surfaced in archaeological
excavations.
Figure 1.4 shows these small - 3 mm to 2 cm - symbolic tokens which may
represent counters in an archaic recording system. It is believed that some of these
tokens represented a measure of some commodity.
1 10 60 600 3600 36000
Figure 1.4
Figure 1.5 shows other tokens which might have represented commodities.
The tokens would have been used for stock-taking, or for keeping records of
transactions, or for bartering, or conceivably for tabulating the number of animals in
a flock or the produce from the harvest.
This token system remained in place from the eighth to the third millennium BC.