Early Counting Methods

The Mechanism of Counting

Before numbers were written, humans needed to count things like cattle or days. They used One-to-One Mapping:

1. Physical Objects: Using a pebble or a stick for each cow.
2. Sounds/Names: Assigning a sound (like ‘a’, ‘b’, ‘c’) to each object.
3. Written Symbols: Making scratches or marks.

Tally Marks

One of the oldest methods is making notches on bones.

• Ishango Bone: 20,000–35,000 years old (Democratic Republic of Congo).
• Lebombo Bone: ~44,000 years old (South Africa) with 29 notches.

Counting in Twos (Gumulgal System)

The Gumulgal people of Australia used a system based on just two numbers:

1. urapon (1)
2. ukasar (2)

Larger numbers were built by combining these:

• 3 = ukasar-urapon (2 + 1)
• 4 = ukasar-ukasar (2 + 2)
• 5 = ukasar-ukasar-urapon (2 + 2 + 1)

This is an early example of an additive system using a small “base” (grouping size).