Base 60
(Before Research)
(1) Think for yourself why 60 might be a convenient, significant or especially useful number to use as the base for a number notational system. What is special about the number 60? How is it different from 10?
As other people have mentioned, 60 gives us good ratios, for example, we can divide in quarters, thirds, halves, fifths without fractions. 10 does not give a numerical representation of those ratios in a nice way.
(2) Then think for yourself how we still use 60s in our own
daily lives, in Canada, and across cultures if you have knowledge of
other systems (like the Chinese zodiac and time-telling system, for
example.) Why is 60 significant in so many situations involving time
and/or space?
We see base 60 in time, in the way we count our minutes. So in the time when we were looking at the sun-dial, I imagine it would've have been useful to give labels to the shape that they are seeing, without having to figure out fractions in a rigorous manner. We see it in space as well, where talk of a full revolution in 360 degrees. I think it makes sense because we can inherently understand something about ratios, and by using base-60, its easier to express.
Research phase:
(3) Finally, do a bit of research via the internet and/or the library to find out what others have learned about the significance of 60 in Babylonian numeration systems, in our contemporary world, and possibly across cultures.
So I find after research that a lot of our intuitions are right, and that it has been useful as it is easy to work with ratios. However, there seem to be some divergence in terms of its origins, with some claiming that it arised naturally out of its usefulness, and that it has to do with the weight system that they used in the past. Others have attributed astronomical knowledge during that time as to the reason why we started using the sexagesimal system.
In terms of other cultures, I found that the Chinese calendar has its cycle repeat every 60 time units, as the smaller cycles that make it up are 10 and 12 time units long. I also found that the time units could be interchangeable between each units of time as we think of today, with some adjustments.
Sources:
https://mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_numerals/
https://en.wikipedia.org/wiki/Sexagesimal
https://www.travelchinaguide.com/intro/focus/stems.htm
Jason, you explained very clearly why base 60 is mathematically convenient, and I liked how you connected it to sundials and angles—it shows you are thinking about practical applications. Your research phase also adds depth, especially by pointing out different theories about the origins of base 60 and linking it to the Chinese calendar. One suggestion would be to elaborate a bit more on how Babylonians themselves used this system (for astronomy, weights, or trade), so your historical connection is stronger.
ReplyDelete