60 Seconds & 360 Degrees

Have you wondered why there are 60 seconds/minutes in a minute/hour? Or why we decided that a circle is exactly 360 degrees? For the curious cats, it’s likely a common musing that’s piqued your interest at one point or another — our numbering system consistently wraps around ten digits(0–9), except for a few, one-off concepts, why is this?

The short answer is because history intimately ties the proliferation of time & degrees to a period when Base-60, the sexagemisal number system, reigned supreme. The longer answer is this article — where we’ll first introduce the base numbering system, then slowly introduce the Babylonian standard that remains relevant.

What Is A Number Base System?

A base system is a fixed number of different digits, or a combination of digits, that are allowed within a specific numbering system. The universal numbering system, the one you’re most familiar with, is known as the decimal system. The prefix “dec” refers to the nine digits that make up our number system: 0 — 9. In math, instead of saying the decimal system, however, we simply refer to this numbering standard as base-10. While a bit out of scope for this piece, most math-historians theorize that the main reason many societies converged to the decimal system is that we have 10 fingers for counting. To re-state, it’s known as base-10 because the numbering system “wraps around” once the highest digit (9) has been reached.

Either way, the main point is: the decimal number system / base-10 is not the only numbering system (base) that exists. In fact, it’s quite likely that you’ve stumbled across at least one of the following common bases:

It’s this last base system, the sexagemisal base system, that’s the topic du jour. We’ll quickly explain how it works, then dive into the history of why it was established in the first place. Though we’ll review evidence, it’s accepted that no universal answer is agreed-upon, at least for now — we’re only reviewing theoriesbehind the adoption of this powerful remaining base system.

What Is The Sexagemisal (Base-60) System?

As the table above highlights, the sexagemisal system is an ancient numbering system that’s defined by its sixty different digits & is more commonly known as base-60. For reasons we’ll soon cover, the base-60 originated in ancient Sumer in the 3rd millennium BC in Mesopotamia (modern southern Iraq). Soon afterward, it was passed down to the ancient Babylonians & eventually all neighboring nations.

It’s hard to grasp now, but back then the base-60 system was a significant breakthrough in numbering; the fact that it remains relevant in modern, everyday application can’t be overlooked. As the title of the article suggests, base-60 is the numbering system used whenever people tell time or make references to the degrees of a circle.

It’s noticeably distinct in the way it “overflows” from 59 to 0, in contrast to our standard base-10 system. The following table, found in-scripted in Babylonian artifacts, indicates that the vertical wedge (V) represents 1 & the horizontal wedge (