# The Center of Math Blog

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## Wednesday, June 10, 2015

### Counting Systems: Ancient China

 Shards of the Shang Oracle Bones
In the 1890s, an archaeological dig in the Henan province of China unearthed a treasure trove. A set of bones carved with ancient text were dug up where the capital of the Shang Dynasty (1600 - 1046 BCE) was located. The oldest inscriptions that are recognized as Chinese were carved in about 1200 BCE on these ancient "Oracle Bones."

The Region: Chinese history is vast. There have been groups living in China for thousands of years, and we've discovered written records about the established dynasties on the Eastern side of the country dating as far back as 1200 BCE. The cultural center of China was naturally isolated, with mountains on the west and water to the east. This allowed Chinese numerals and mathematics to develop naturally, without much influence by other number systems, for centuries.

The Numerals: Of the many different variations of Chinese numerals, I've chosen to focus on the oldest known set. These numerals, like I stated at the top, come from the Oracle Bones. They use a Base-10 system, though it's not quite as developed as ours. Take a look at how the numbers are written below:

We can see that the first 10 digits are very simple. One through four, in fact, are simple tally marks. Then five through nine are more like pictograms, a little more complex and easier to identify than a group of tally marks.

The numerals have multiplicative properties. Take a look at the numeral for 100. It's a circle with an embedded triangle, and a single bar across the top. Then the numeral for 200 is the same circle with the numeral for 2 on top. This allowed the scribes to write large numbers without needing a separate numeral for each.

The largest number that archaeologists have extracted from the Oracle Bones is 30000, which was represented by the symbol for 10000 (a scorpion pictogram) combined with the symbol for 3.

The Math: Because of their additive nature, these numbers were simply combined in a list to indicate that they were being added.

 Here's how numbers are written in Latin numerals and then Ancient Chinese
Unfortunately, the Oracle Bones are the only source of information we have about the most ancient Chinese numerals. Therefore, we don't have knowledge of the limits of the Shang Dynasty's mathematics. Chinese mathematics began to flourish later, with the use of their most famous tool: the abacus.

The Problems: The system that I've featured has a few obvious problems. For one, they have no symbol for zero. This isn't so much of a problem in this system as in Babylonian numerals; the additive properties of the Chinese numerals meant there wasn't a need for placeholder zeros like in our number 108.

 Clearly!
Chinese numerals developed quickly, with every dynasty making slight changes to the system that made it more and more useful and advanced. In fact, by the year 500 CE, the Chinese had an approximation of pi accurate to 7 places. This was several hundred years before Western mathematics caught up on an approximation!

In case you missed it, I covered the Babylonian counting system two weeks ago. Stay tuned for more information on other ancient systems!
- Tori

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