Aboriginal Number Systems & Counting
Discover how Aboriginal and Torres Strait Islander peoples developed sophisticated counting systems over tens of thousands of years, and compare them with the number system we use today.
Acknowledgement: Aboriginal and Torres Strait Islander peoples are the Traditional Custodians of the lands on which we learn. Their cultures are the oldest continuous cultures on Earth, stretching back more than 65,000 years. We pay our respects to Elders past, present and emerging, and acknowledge that sovereignty was never ceded.
Counting That Goes Back Thousands of Years
You might think that all number systems work the same way. In school, we use a base-10 system (also called decimal), which means we group numbers in tens: 1, 2, 3... 10, 11, 12... 100, and so on. But this is just one way of counting!
Aboriginal and Torres Strait Islander peoples developed many different ways to count and keep track of quantities. With over 250 distinct language groups across Australia, there are many different number systems, each designed for the needs of that community.
These systems are not simpler than ours. They are different, and they were perfectly suited to the purposes of the people who used them. Some are incredibly clever!
Different Ways to Group Numbers
Base-10 (Our System)
We group things in tens. After 9, we start a new group of ten. We have 10 different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Base-5 Systems (Hand Counting)
Several Aboriginal language groups use a base-5 system, grouping numbers in fives, which matches the five fingers on one hand. For example, the number we call "7" would be described as "one hand and two" (5 + 2).
Base-2 Systems (Pair Counting)
Some Aboriginal languages, such as those in parts of the Western Desert, use a base-2 (binary) system, counting in pairs. This is remarkably similar to the binary system that modern computers use!
Body-Tally Counting Systems
One of the most sophisticated counting methods used across many parts of Australia is the body-tally system. Instead of just using fingers, people count by touching or pointing to different parts of the body in a set order. This allows counting well beyond 10!
A common body-tally system starts at the little finger on one hand, moves up the arm to the shoulder, across the head, and then down the other arm. This can reach numbers of 25 to 33 or more, depending on the system.
Example Body-Tally Sequence
Torres Strait Islander Trade Counting
Torres Strait Islander peoples are renowned seafarers and traders. They travelled between islands and to Papua New Guinea and the Australian mainland, trading goods like shells, food, tools and ochre.
To keep track of goods being traded, Torres Strait Islander peoples developed counting systems that could handle large numbers accurately. The Meriam Mir language (from the Eastern Islands) has a well-documented number system that counts well beyond 100.
Why Did Trading Need Counting?
- ● Keeping track of how many items were exchanged
- ● Ensuring fair trades between groups
- ● Recording how many days until the next trading voyage
- ● Counting catches of fish, turtle and dugong to share with the community
Try It: Counting in a Different Base
Let's try counting in base-5, just like many Aboriginal number systems. In base-5, we only use the digits 0, 1, 2, 3 and 4. When we reach 5, we start a new group.
Base-10 vs Base-5 Comparison
| Our Number (Base-10) | Base-5 (Hand Groups) |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 10 (one hand, zero fingers) |
| 6 | 11 (one hand, one finger) |
| 7 | 12 (one hand, two fingers) |
| 10 | 20 (two hands) |
| 13 | 23 (two hands, three fingers) |
| 25 | 100 (one group of five-fives!) |
Think about it: In base-5, the number "100" means 25 in our system. That's because 1 group of 5x5 = 25!
Key Vocabulary
Base (Number System)
The number of digits used before starting a new group. Our system is base-10 (10 digits: 0-9).
Body-Tally System
A method of counting by pointing to different body parts in a set order, allowing counts beyond 10.
Binary (Base-2)
A number system that uses only two digits (0 and 1) or groups things in pairs. Used by some Aboriginal groups and modern computers.
Language Group
A community of Aboriginal or Torres Strait Islander peoples who share a common language. There are over 250 across Australia.
Worked Examples
In a base-5 system, how would you say the number 8?
Step 1: How many complete groups of 5 fit into 8? Answer: 1 group of 5 (that's 5).
Step 2: How many are left over? 8 - 5 = 3.
Answer: "One hand and three" or 13 in base-5.
Using a body-tally system, what body part represents the number 8?
Step 1: Start at the little finger (1) and count up: little finger (1), ring finger (2), middle finger (3), index finger (4), thumb (5), wrist (6), forearm (7), inside elbow (8).
Answer: The number 8 is the inside of the elbow.
In a base-2 (pair) system, how would you express the number 5?
Step 1: How many complete pairs in 5? Answer: 2 pairs (that's 4).
Step 2: How many left over? 5 - 4 = 1.
Answer: "Two pairs and one" or tara-tara-ninta.
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Our everyday number system is called base-10. What does "base-10" mean?
Question 2
In a base-5 counting system, how would you express the number 7?
Question 3
What is a body-tally counting system?
Question 4
Why did Torres Strait Islander peoples need reliable counting systems?
Question 5
Some Aboriginal languages use a base-2 counting system. Which modern technology also uses base-2?
Key Concepts Summary
- ● Aboriginal and Torres Strait Islander peoples developed many different counting systems over tens of thousands of years.
- ● These include base-5 (hand counting), base-2 (pair counting), and body-tally systems.
- ● Body-tally counting can reach 25 or more by using body parts in a fixed order.
- ● These systems are not simpler than base-10. They are different and sophisticated, designed for specific purposes.
- ● Different number bases (2, 5, 10) each have advantages. Our base-10 system is just one of many ways to count.