How Ancient People Made Sense of Time

After reading these two articles, I started to think differently about something I normally take for granted: time. One thing that surprised me was that ancient people could use their fingers and even their finger joints to help with counting. I was also fascinated by the Babylonian base-60 system and its influence on how we measure time today—60 seconds in a minute and 60 minutes in an hour. Since 60 can be divided evenly by many numbers, it is very useful for fractions and measurement. What I found especially interesting is that we still do not know exactly why the Sumerians developed base 60 in the first place.

What surprised me even more was how different cultures developed similar ways of thinking about time, even when communication was much more limited than it is today. This immediately reminded me of traditional Chinese timekeeping. Ancient Chinese people also used sundials, and a day was divided into twelve shichen(时辰), with each one roughly equal to two modern hours. There are also the 24 solar terms, which connect the year with changes in seasons, weather, and agriculture. (https://www.travelchinaguide.com/attraction/beijing/forbidden-city/miraculous-sundials.htm) For example, Jingzhe (惊蛰), or “the awakening of insects,” describes the time when nature begins to become active again. (https://global.chinadaily.com.cn/a/202403/04/WS6222aebfa310cdd39bc8a814.html) I have always found it amazing that when this solar term arrives, you can actually start noticing small insects appearing around you. It makes me wonder how ancient people, simply by observing the Sun, stars, seasons, animals, and weather over long periods of time, were able to recognize these patterns. I find it fascinating that numbers like 12 and 24 appear in different cultures and different periods of history.

The readings also made me think about the geometry of time. I used to imagine a year mostly as a straight timeline, moving from January to December. But now I think a circle might make more sense. Seasons repeat, the 24 solar terms form a cycle, and days themselves are connected to the repeated movement of the Sun. A clock is also circular, divided into 12 sections, which creates another interesting connection between time and geometry. The Babylonian base-60 system makes this connection even stronger. A circle has 360 degrees, and angles are measured in degrees, minutes, and seconds: one degree contains 60 minutes, and one minute contains 60 seconds. I had always learned these as angle units in geometry, but I had never really stopped to think about why “minutes” and “seconds” appear in both angles and time. Now the relationship between 60 minutes in an hour, 60 seconds in a minute, and 60 minutes or seconds in angular measurement feels much more meaningful. It makes me see time, astronomy, and geometry as historically connected rather than as separate mathematical ideas.

The readings also made me curious about ancient Chinese mathematics. Babylonian mathematics was recorded in cuneiform on clay tablets, which reminded me of Chinese oracle-bone inscriptions written on animal bones and turtle shells. I did some searching after the reading and became interested in how ancient Chinese mathematics developed around decimal counting, while Babylonian mathematics used base 60 much earlier. It makes me want to learn more about the mathematical history of China and perhaps bring some of these historical and cultural connections into my future mathematics teaching.

Finally, I realized that doing calculations in base 60 would actually be quite difficult for me. If I had to multiply or divide Babylonian numbers, my instinct would be to convert everything into base 10, calculate it, and then convert it back—which was obviously not how Babylonian mathematicians worked. They had their own methods and calculation tables. Now I actually want to learn how they did multiplication and division in base 60 and experience a little bit of the joy—and probably the challenge—of doing ancient mathematics myself.

Overall, these readings made me realize that measuring time is not as “natural” or obvious as I once thought. The systems we use today carry traces of how people from different cultures observed nature, discovered patterns, and mathematically organized their world.