Entry ( Sep 21) ----- Base 60

 

Thousands of years ago, the Babylonians used a number system based on 60. One of the reasons to use 60-based number system is because of its convenience. From 1 to 100, 60 is the only number has factors including 1, 2, 3, 4 and 5. That means if an ancient people has 60 fish, he could equally distribute these fish to 2, 3, 4, or 5 person, and if he has 2 times 60 fish, he still could evenly divide fish into 2, 3, 4, or 5 parts. With this property of 60, they divided many things including the time, the year, and the circle. 

Especially in the astronomy measurement, (yes, ancient people like to watch the sky, me too), people often need to divide angles. If they use Base-10, it would be difficult to divide an angle into 3 parts equally.  

In human history, there existed the base-8, base-12, base-16 and base-20 number systems. In China, people are still using the idiom "Half catty eight taels" to describe two things which have no difference to each other. It proves that Chinese people ever used base-16 number systems in the past. 

Nowadays, the base-10 number system is mostly used  in our daily life. Comparing with the base-60, the base-10 needs less symbols to represent digits, and can be easily learned. However, when we tell time and measure angles, the sexagesimal plays an irreplaceable role. Even today, in Chinese traditional calendar, they still use traditional way to  count year based on the sexagesimal. 

The base-60 number system embodies the ancient people's wisdom. Through writing this blog, I have an opportunity to learn and show my appreciation to those great endeavor.   

Below is the link of the reference article:" Why is a minute divided into 60 seconds, and hour into 60 minutes, yet there are only 24 hours in a day?"

https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/#:~:text=The%20Babylonians%20made%20astronomical%20calculations,the%20first%20six%20counting%20numbers

Course Note:

Our detailed look at the history of mathematics will start in an area known as Mesopotamia (meso: 'between', potamia: 'rivers' -- between the Tigris and Euphrates Rivers), in what are now the countries of Iraq, Syria, parts of Turkey and Kuwait. The area is sometimes called the 'fertile crescent' because the river systems flowing down to the Persian Gulf made agriculture and cities viable.

In accounts of mathematics history, the mathematics of Mesopotamia circa 3100 BCE - 300 BCE is usually called Babylonian mathematics. But if you look more carefully at the history of Mesopotamia in this period, there were several different peoples and nations that governed this region, including the Sumerians, Akkadians, Assyrians and Babylonians. 

For our purposes, we will use the term 'Babylonian mathematics' to refer to the fairly unified mathematics traditions over this 3,000 year period (starting approximately 5,000 years ago). 

Babylonian writing was done with a wedge-shaped reed stylus in wet clay tablets the size of a person's palm, and then dried in the sun or in a kiln. Their ingenious writing system was known as cuneiform: 'wedge-shaped', and it was possible to write words, numbers and other symbols with just these wedge-shaped forms. Because these baked clay tablets are very durable, we have many of them in museum collections to this day -- and quite a few of these seem to be teaching tablets for scribes learning mathematics to take government jobs in the Mesopotamian cities!

Here is an example of one of the existing mathematical clay tablets from ancient Mesopotamia. Your job is to figure out what is written here, and how the writing system for this mathematical tablet works!