Speculative Phase:
Base 60 has some obvious advantages as opposed to base 10. For one, its factors are comprised of: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, which includes the first 6 countable numbers, and the wondrous digit 10 itself; meaning that base 60 has the convenience of being easily divided into halves, thirds, quarters, fifths, and sixths, and is the smallest possible number that can do so! So, in a time where mathematics was most societally necessary for various types of bookkeeping, it makes sense that the base number is one that can be broken into so many sections. Another convenience to base 60 has to do with our basic anatomy as well- humans have 2 hands, and 2 feet (adding to 4 main limbs); 5 fingers per hand and 5 toes per foot (adding to 10 appendages per group, or a collective 20); and, each finger is subdivided into 3 sections (for 1 hand, 4 fingers x 3 groups = 12 subsections, plus the thumb- which makes 15 subsections; and 2 hands make 30). So right off the bat, the numbers 1, 2, 3, 4, 5, 10, 12, 15, 20, and 30 appear, making tallying an effective and tangible process. 60 offers a tremendous amount of flexibility when it comes to counting and grouping, which I think could have familial significance in terms of sharing and dividing basic needs, and societal significance in regards to distributing resources.
In order to understand how base 60 truly permeates our lives, we need to identify its relevance, and its various factors. To list a few examples, an hour has 60 minutes, a minute has 60 seconds, a year has roughly 360 days or 12 months, a month has about 30 days, and a day has roughly 2 sets of 12 hours; however, there is also the imperial measure of feet which has 12 inches, grocery items bought per dozen (aka per 12), 5 days in a defined work week… and so forth. But the true convenience of base 60 is in regards to its measure of time, and that's what has stayed relatively consistent across multiple cultures across the globe. For instance, there are 12 animal signs in the chinese Zodiac, which corresponds to a 12 year cycle; the islamic calendar has 12 months, following a lunar cycle; and our Western calendar consists of 12 months, relating to a solar cycle, drawing attention to the use of astronomy in mathematics. Perhaps the synthesis of our anatomy in combination with astronomical based mathematics is what led to the use of Base 60 in the first place.
Research Phase:
There are multiple theories why base 60 was chosen, over any other number there is out there. According to ThoughtCo., 60 is the most appropriate choice for a base, because it “has more divisors than any other smaller positive integer”, which means it’s very convenient for carrying out calculations (1). In addition, base 60 seems to have arisen when 2 different cultures, one using base 5 for 5 fingers, and the other using base 12 for 12 finger subsections, fused their mathematical processes which resulted in base 60 (from 5 x 12). In regards to why a year has roughly 12 months or 360 days, it seems that this resulted from the use of both a solar and lunar calendar (3). The time it takes for the Earth to orbit the sun is about 360 days, and the Moon cycle is roughly 30 days, so by dividing the Solar cycle by the Lunar cycle, we result in having 12 months. The point at which I was confused though, is at the designation of a day having 2 sets of 12 hours- certainly, growing up in an area outside of the equatorial regions means that during different parts of the year, the days and nights vary in length to each other. Some research confirmed this confusion, because I read that “In the Egyptian system, the length of the day-time and night-time hours were unequal and varied with the seasons” (2). However, it seems that the Babylonian tendency to base 60 heavily influenced their division of time, and our today.
Lovely! And you're right about hours having different lengths (in non-equatorial regions at least) in different seasons. We'll talk more about that today.
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