Base 60 Traces Back to Mesopotamian Civilization
I found an interesting bit of trivia, so let’s take a look at “number bases.”
Things like “binary” or “decimal” or “hexadecimal.”
First, let me explain simply
what a number base
actually is.
Put simply,
it’s a way of expressing
how many units it takes before a digit rolls over.
Decimal is what we normally use day to day,
0 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 →
and after that the digit rolls over to become 10.
In binary,
0 → 1 →
after that it doesn’t become 2 — the digit rolls over to become 10.
In hexadecimal,
0 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 → A → B → C → D → E → F →
and after that the digit rolls over to become 10.
By the way, binary is what’s commonly recognized as “digital,”
and it’s used to send data as either 0 or 1.
Why sending data that way is convenient is a topic for another time.
Now,
here I want to talk about
“base 60”
This term isn’t one you hear often compared to the examples above,
but everyone encounters it all the time.
That’s time.
1 minute = 60 seconds, 1 hour = 60 minutes.
That’s this.
Base 60 traces all the way back to
Mesopotamian civilization
Ancient Mesopotamia held that “one year is 360 days.”
This came from astronomical observation by the astronomers of the time,
but it’s slightly off from the roughly 365.24 days we recognize today.
Given the precision available at the time, that’s unavoidable.
From that “one year = 360 days,” the idea of a full circle being 360 degrees took hold,
and from that, a month was set at 30 days and a year at 12 months.
The prevailing theory is that 60 was adopted as the official number base because it’s
the least common multiple of those two numbers (30 and 12).
When people think of Mesopotamian civilization,
cuneiform
is the iconic symbol,
and characters representing 0 through 59 have in fact been found.
Now,
it later became clear that the basis itself — “one year = 360 days” — was wrong.
Whether anyone ever asked “so what do we do now?” isn’t known,
but think it through and 60
- is also the least common multiple of 10, the base commonly used for counting, and 12, as in “one year = 12 months”
- makes geometric calculations easy if you set a full circle at 360 degrees
so it was probably convenient enough that it simply stuck around.
Since time itself was originally defined based on angles,
it has kept base 60 in step with that.
Dig a little and all sorts of things come into view.
So, that was today’s bit of trivia.
Originally published in Japanese at https://clazytech.com/2012/12/73/. Translated with LLM assistance and reviewed before publication.