Some Early Number Systems
I. Use of Some Body Parts Such as Fingers
A few number systems in some
parts of the world originated without any arithmetic base. One such system is
the body-part counting system which makes use of further body parts to extend
the system beyond the ten fingers.
Counting typically begins by
touching (and usually bending) the fingers of one hand, moves up the arm to the
shoulders and neck, and in some systems, to other parts of the upper body or
the head. A central point serves as the half-way point. Once this is reached,
the counter continues, touching and bending the corresponding points on the
other side until the fingers are reached.
II. Tally Marks on Surfaces
Tally marks on bones and other surfaces are ancient artifacts with
notches carved into them dating back over 20,000 years ago. Examples like the Ishango
bone and the wolf bone are considered ancient evidence of
early mathematical counting perhaps used for record keeping of quantities or to
track lunar eclipses and so on.
Oldest Bone Markings
a. Ishango bone: This bone was discovered 20,000 to 35,000
years ago in the Republic of Cango. It features three columns of notches.
b. Lebombo bone: This is 44,000 years old baboon leg bone
from South Africa bearing 29 distinct notches. (The oldest maths artifact).
c. Wolf bone found in Czechoslovakia: This is
30,000 years old bone, which has 57 tally marks arranged in groups of 5 and 2
left over.
III. Counting in Twos
In Australia, a group of indigenous people, known as Gumulgal, used
the words urapon (for 1) and ukasar (for 2), and so on to
represent numbers.
1 = urapon
2 = ukasar
3 = ukasar-urapon
4 = ukasar-ukasar
5 = ukasar-ukasar-urapon
6 = ukasar-ukasar-ukasar, and so on.
Similar number systems had evolved in South America and South Africa,
without any influence from each other. Counting of numbers in a certain group
size and using it to represent numbers is an important idea in the development
of number systems.
Counting in Fives
Most humans can easily see up to 5 objects in a single glance, leading
to use of tally marks as a symbol for groups of five.
Even though this is easier to use, the tally system representing large
numbers can be an overwhelming process.
You can study the some other popular number systems from the following
linkes.
Some Early Number Systems