7 ms·

I always thought this was somehow motivated by great divisibility, since prime factors of 360 are 2, 2, 2, 3, 3, 5. This means you can work with integers most o

I always thought this was somehow motivated by great divisibility, since prime factors of 360 are 2, 2, 2, 3, 3, 5. This means you can work with integers most of the time when dividing a circle, since all but four numbers in 1-15 are divisors.

roelschroeven 7y ago
That large number of divisors was the reason for the Babylonians to use base-60, I've always been thaught. I always assumed the the 360 degree circle was a consequence of that, but this article contradicts that. Actually I don't think the article does a great job proving its thesis ("In school we learn there are 360 degrees in a circle, but where did the 360 come from? When it is pointed out that the Babylonians counted to base-60, rather than base-10 as we do, people often ask if there is a connection. The short answer is no."). The article's conclusion is "So, although angles come from the Greeks, the 360 degrees comes from Babylonian astronomy". And it explains, more-or-less, how the Babylonians came to use 360 degrees for astronomy: because they had a habit of dividing things into 12 part, subdivided in 30. But that doesn't preclude they choose 12 and 30 (instead of, say, 13 and 28) because both are divisors of their base number 60. Wikipedia points in that direction (but admits no-one really knows): "Some ancient calendars, such as the Persian calendar, used 360 days for a year.[citation needed] The use of a calendar with 360 days may be related to the use of sexagesimal numbers." "Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system.[7][8] The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree." Another Wikipedia-quote agrees with your point of view: "Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,[note 1] making it one of only 7 numbers such that no number less than twice as much has more divisors" "
- herodotus 7y ago
  I think 30 comes from the Synodic month - the time from first crescent to first crescent of the moon, which varies between 29.18 and 29.93 days. There of 12 of these months within a year (and a few days left over).
- twodave 7y ago
  I think it more likely that both the 360-day year and the base-60 numbering system came from a common ancestor (the Babylonian's study of astronomy). Perhaps they just took the lunar year and "rounded" it to correspond more consistently with their view of the stars, which put them on the path to both things.
  - simiones 7y ago
    The (approximately) 360-day year is a property of nature (the ratio between the Earth's revolution speed and the Earth's rotation speed is approximately 360 if expressed in base 10). It is a discovered number, not invented/chosen. It is possible that the base-60 numbering comes from this basic astronomical observation, or they may be mostly unrelated.
- im3w1l 7y ago
  An arc-minute is a 60th of a degree. And an arc-second is a 60th of an arc-minute. This strongly points to a base-60 origin imo.
  - gumby 7y ago
    The minute ("small part") and second ("even smaller part") come from the era of clockmaking as they were pointless when your timekeeping resolution was crude.* We are quite lucky that hours and then minutes were divided into 60 sections rather than 10, 12, or 100. This may have come from the system you describe (arc minutes, seconds, thirds, etc) which is much older. * or not just crude but completely different; e.g. Babylonian and Roman hours varied in length each day as the time from sunrise to sunset was divided into twelve equal sections and sunset to sunrise implicitly the same. IIRC the constant-duration hour goes back only to marine navigation a few hundred years ago
    - Wowfunhappy 7y ago
      > We are quite lucky that hours and then minutes were divided into 60 sections rather than 10, 12, or 100. So let's say there's 20 hours a day, since presumably we'd still want to have two daily clock rotations. Those hours could then be divided into 100 "minutes" with 100 "seconds" each. If I'm doing my math right, this would mean: • 1 alternate-universe hour = 1.2 current-universe hours • 1 alternate-universe minute = 0.72 current-universe minutes • 1 alternate-universe second = 0.432 current-universe seconds I could very much deal with this. Current-universe seconds are a bit too long for the level of precision I want with that unit, and I don't think the < 30% change in the length of a minute or hour would matter much once I adapted. And, as a consequence, unit conversions would become so much easier! I don't think we're lucky at all. :(
      - gumby 7y ago
        Going to base 10 is a step backwards because 10 has so few factors. The meter would have been massively easier to use had it been base 12 or 60. Perhaps you can get the Mars colonists to adopt a different system. The martian day is just close enough to the terrestrial day to make adapting the terrestrial system for it quite annoying.
- toasterlovin 7y ago
  > That large number of divisors was the reason for the Babylonians to use base-60, I've always been thaught. I believe the Babylonians actually use base 12, with the number 60 merely being a convenient multiple of 12. And I think the reason their counting system is base 12 is not because of its greater divisibility, but due instead to the way they used their fingers for counting. So, in the West, we count using each of our fingers and that’s how we arrive at a base 10 counting system. But in certain parts of the world, they use one thumb to count the separate segments of the fingers on the same hand. There are three segments in each of the 4 fingers, for a total of 12 (hence the base 12). And then the five fingers of the opposite hand are used to count how many groups of 12 have been counted. So 5 fingers on the second hand multiplied by 12 finger segments on the first hand = 60 in total.
pkulak 7y ago
Yeah, I think I'm going to refuse to believe that it's just some coincidence that 360 is a highly-composite number AND a specially chosen number. Especially with how societies have made use of all the others below it throughout history (12, 24, 60, etc). Extraordinary claims require extraordinary evidence, and all.

roelschroeven 7y ago

That large number of divisors was the reason for the Babylonians to use base-60, I've always been thaught. I always assumed the the 360 degree circle was a consequence of that, but this article contradicts that. Actually I don't think the article does a great job proving its thesis ("In school we learn there are 360 degrees in a circle, but where did the 360 come from? When it is pointed out that the Babylonians counted to base-60, rather than base-10 as we do, people often ask if there is a connection. The short answer is no."). The article's conclusion is "So, although angles come from the Greeks, the 360 degrees comes from Babylonian astronomy". And it explains, more-or-less, how the Babylonians came to use 360 degrees for astronomy: because they had a habit of dividing things into 12 part, subdivided in 30. But that doesn't preclude they choose 12 and 30 (instead of, say, 13 and 28) because both are divisors of their base number 60. Wikipedia points in that direction (but admits no-one really knows): "Some ancient calendars, such as the Persian calendar, used 360 days for a year.[citation needed] The use of a calendar with 360 days may be related to the use of sexagesimal numbers." "Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system.[7][8] The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree." Another Wikipedia-quote agrees with your point of view: "Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,[note 1] making it one of only 7 numbers such that no number less than twice as much has more divisors" "

herodotus 7y ago
I think 30 comes from the Synodic month - the time from first crescent to first crescent of the moon, which varies between 29.18 and 29.93 days. There of 12 of these months within a year (and a few days left over).
twodave 7y ago
I think it more likely that both the 360-day year and the base-60 numbering system came from a common ancestor (the Babylonian's study of astronomy). Perhaps they just took the lunar year and "rounded" it to correspond more consistently with their view of the stars, which put them on the path to both things.
- simiones 7y ago
  The (approximately) 360-day year is a property of nature (the ratio between the Earth's revolution speed and the Earth's rotation speed is approximately 360 if expressed in base 10). It is a discovered number, not invented/chosen. It is possible that the base-60 numbering comes from this basic astronomical observation, or they may be mostly unrelated.
im3w1l 7y ago
An arc-minute is a 60th of a degree. And an arc-second is a 60th of an arc-minute. This strongly points to a base-60 origin imo.
- gumby 7y ago
  The minute ("small part") and second ("even smaller part") come from the era of clockmaking as they were pointless when your timekeeping resolution was crude.* We are quite lucky that hours and then minutes were divided into 60 sections rather than 10, 12, or 100. This may have come from the system you describe (arc minutes, seconds, thirds, etc) which is much older. * or not just crude but completely different; e.g. Babylonian and Roman hours varied in length each day as the time from sunrise to sunset was divided into twelve equal sections and sunset to sunrise implicitly the same. IIRC the constant-duration hour goes back only to marine navigation a few hundred years ago
  - Wowfunhappy 7y ago
    > We are quite lucky that hours and then minutes were divided into 60 sections rather than 10, 12, or 100. So let's say there's 20 hours a day, since presumably we'd still want to have two daily clock rotations. Those hours could then be divided into 100 "minutes" with 100 "seconds" each. If I'm doing my math right, this would mean: • 1 alternate-universe hour = 1.2 current-universe hours • 1 alternate-universe minute = 0.72 current-universe minutes • 1 alternate-universe second = 0.432 current-universe seconds I could very much deal with this. Current-universe seconds are a bit too long for the level of precision I want with that unit, and I don't think the < 30% change in the length of a minute or hour would matter much once I adapted. And, as a consequence, unit conversions would become so much easier! I don't think we're lucky at all. :(
    - gumby 7y ago
      Going to base 10 is a step backwards because 10 has so few factors. The meter would have been massively easier to use had it been base 12 or 60. Perhaps you can get the Mars colonists to adopt a different system. The martian day is just close enough to the terrestrial day to make adapting the terrestrial system for it quite annoying.
toasterlovin 7y ago
> That large number of divisors was the reason for the Babylonians to use base-60, I've always been thaught. I believe the Babylonians actually use base 12, with the number 60 merely being a convenient multiple of 12. And I think the reason their counting system is base 12 is not because of its greater divisibility, but due instead to the way they used their fingers for counting. So, in the West, we count using each of our fingers and that’s how we arrive at a base 10 counting system. But in certain parts of the world, they use one thumb to count the separate segments of the fingers on the same hand. There are three segments in each of the 4 fingers, for a total of 12 (hence the base 12). And then the five fingers of the opposite hand are used to count how many groups of 12 have been counted. So 5 fingers on the second hand multiplied by 12 finger segments on the first hand = 60 in total.

pkulak 7y ago

Yeah, I think I'm going to refuse to believe that it's just some coincidence that 360 is a highly-composite number AND a specially chosen number. Especially with how societies have made use of all the others below it throughout history (12, 24, 60, etc). Extraordinary claims require extraordinary evidence, and all.