Whenever I think about a year, I visualize a giant oval track, summer sits at the top, winter is down at the bottom, and I'm just jogging around the loop as the months pass. An hour looks like a round pie cut into slices, while a month feels like a straight row of calendar blocks.
What’s crazy is how much we treat our time system as if it's just basic common sense. In school, we use decimal (base-10) math for almost everything - money, science, counting on our ten fingers. But the second we glance at a clock, our brains instantly flip to base-12 and base-60 without breaking a sweat. Reading these articles made me realize that my mental geometry of time isn't natural at all, it's just a set of habits passed down from civilizations thousands of years ago.
Comparing the two articles turned up some pretty clear contradictions in how experts explain where these numbers came from.
- Who actually counted finger joints?
- Scientific American credits the Egyptians with using finger joints to count to 12 (three joints on four fingers, using the thumb as a pointer), which is why they split the day into 12 daylight hours.
- MacTutor article, on the other hand, uses that exact same finger-joint trick, counting 12 joints on one hand while keeping track with 5 fingers on the other hand (12 x 5 = 60), to explain how the Sumerians and Babylonians came up with base-60.
- Math neatness vs. human messiness
- Scientific American claims base-60 took off because 60 is super convenient for fractions, since it divides evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.
- MacTutor calls this fraction argument "too scholarly a reason". The author points out that ancient societies didn't sit down in a committee to pick a neat math base. Instead, MacTutor argues base-60 came from messy, real-world stuff, like physical finger counting or two different ancient tribes merging together (like a base-12 group trading with a base-5 group).
Reading through the history of time measurement completely changed how I look at my watch:
- Hours used to stretch and shrink with the seasons: For most of human history, an hour wasn't a fixed 60-minute block. Early Egyptian sundials just split whatever daylight existed into 12 parts. That meant summer hours were way longer than winter hours. A Greek astronomer named Hipparchus suggested equal-length hours, but people ignored him and kept using seasonal hours until mechanical clocks showed up in Europe in the 1300s.
- Minutes and seconds were astronomy math, not clock units: Terms like "minute" and "second" come from Claudius Ptolemy subdividing degrees of latitude and longitude in his astronomy book Almagest (partes minutae primae and partes minutae secundae). Nobody even had minute hands on regular clocks until the late 1500s!
- Some minutes have 61 seconds: Today, time isn't measured by Earth's rotation anymore; it's defined by atomic vibrations of cesium atoms. Because Earth's spin speeds up and slows down slightly, scientists have to throw in "leap seconds" about eight times a decade, meaning roughly eight minutes every ten years actually last 61 seconds.
It's wild to realize that whenever I set an alarm or check my phone, I'm using a mix of ancient Egyptian star-gazing, Babylonian base-60 math, medieval mechanical clockmaking, and modern atomic physics. We treat time like an unchangeable law of nature, but it's really just a 4,000-year-old group project.
I liked your example of the San-Gaku boards. It’s interesting to see math being shared in a community like that, because it gives such a different picture of math from the one we usually see in textbooks and classrooms.
ReplyDelete(Hmmm, Malihe, I didn’t notice the reference to San-Gaku boards here!) But what an interesting reflection on our bizarre notions of time! Parminder, I am really enjoying your well-written posts, full of curiosity and fascinating connections and observations!
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