The Chinese abacus is called “suanpan”, which means “calculating deck”. It is made of columns of beads on bamboo rods, separated with a beam into upper deck and lower deck. Each bead on upper deck counts as five and the bead on lower deck counts as one. The first column on the right represent one place, to the left are the tens, hundred, thousand place, and so on. It appeared in China about two thousand years ago and has been used in trade, business and accounting until they were replaced by calculators and computers. As a little kid, I used to add up the time table (1×1 + 1×2 + 2×2 …….. + 9×9) using abacus for math practice. If everything goes right, the end result should be 1155 as shown in the picture below.
Some may wonder why you need that many beads for calculations. In fact, recent abacus using plastic beads only have one row of beads in the upper deck and four rows in the lower deck to reduce the cost.
Then why does the traditional Chinese abacus contain extra beads that are not used? The answer is that the traditional abacus are used for both decimal and hexadecimal calculations. When all the beads in the suanpan are used, each column can be used to represent numbers between 0 and 15. Traditional Chinese weighing units is a hexadecimal system. One jin (斤) equals sixteen liang (兩). This system was started after the first emperor, Qin Shi Huang, unified China in 221 BC. The hexadecimal system made it easier for regular folks to divide one jin to its base unit one liang using a balance which is cheaper and easier to get than a scale. Let’s say that you have one jin of some material and you need an accurate measure of one liang, but you only have a balance at home. You can evenly divide one jin into two 8 liang; then you use the balance to evenly divide 8 liang into two 4 liang; repeat this twice, you will have one liang with reasonable accuracy.
This system is particularly important when expansive materials are measured (e.g., medicine, gems, spices, etc.). In 1959, the Chinese government switched to a one jin (500 g) equals to 10 liang system. This greatly improved the trade system and allowed the Chinese economy to take full advantage of modern science and technology. However, recognizing the importance of traditional Chinese medicine and the common practice used for thousands of years across the country, hexadecimal measurement system for traditional Chinese medicine remained until 1979.
We use decimal system because we have ten fingers. Hexadecimal system was developed over two thousand years ago because of the need of measurement system. The traditional Chinese abacus can handle both systems with two extra rows of beads. What a clever design! Today, hexadecimal system is widely used in mathematics and computer because it is a human friendly representation of binary-coded values in computing and digital electronics (https://en.wikipedia.org/wiki/Hexadecimal) – similar reason why hexadecimal measurement system was created two thousand years ago.
Counting and measurement systems have always been closely linked. In the old days, you need both to solve daily challenges. A famous general, Han Xin (ca 231 – 196 BC), once saw two men tried to divide 10 litre cooking oil into two 5 litres at a market. In addition to a 10 litre pail, they had a 7 litre pot and a 3 litre bottle. It only took him a moment to solve the problem as shown in the following table:
|Pail (10 litre)||Pot (7 litre)||Bottle (3 litre)|
|Fill bottle from pot||3||4||3|
|Empty bottle into pail||6||4||0|
|Fill bottle from pot||6||1||3|
|Empty bottle into pail||9||1||0|
|Pour 1 litre oil from pot into bottle||9||0||1|
|Fill pot from pail||2||7||1|
|Fill bottle from pot||2||5||3|
|Empty bottle into pail||5||5||0|
Of course you can start with filling the bottle first. Why don’t you try this with your family or friends over dinner? It’s fun!
Over the long history of civilization, we humans have developed many systems to measure, assess, and inform. Beads are used in many cultures for counting and knowledge transfer. Monks use beads to count the number of chants. North America native communities use story beads to pass knowledge and history from generation to generation.
In designing a credible and relevant environmental monitoring, evaluation and reporting system for Alberta, we need to think about how to make the system easily understandable; how to get more people to access, and how we can help people to participate in the system. When information is based on complex calculations of huge amounts of data, how do we explain the process so that both academia and general public can understand? When a huge amount of data is disseminated, what tools should we provide (e.g., data visualization) so that people can extract useful information? When we establish standards and protocols, what level of detail should be considered so that necessary flexibility is available while maintaining data consistency and comparability? To do so, we need to work respectfully with our partners and stakeholders. From time to time, we may find ourselves seeking guidance from traditional wisdom and gaining inspirations from those ancient beads. In the treasure of our common knowledge, every bead counts.