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Thanks for this! I loved this explanation and I had never heard that divisibility is the reason we have 24 hours in a day and 60 minutes in an hour. After readi

Thanks for this! I loved this explanation and I had never heard that divisibility is the reason we have 24 hours in a day and 60 minutes in an hour. After reading your comment, I found this article in Scientific American that gave additional detail: https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ https://www.scientificamerican.com/article/experts-time-divi...

BuildTheRobots 8y ago
I believe divisibility is also the reason we have 360-degrees in a circle.
- xamuel 8y ago
  And 12 inches in a foot, etc. Perhaps in centuries to come, the US will be vindicated for its metric system resistance :)
  - gpvos 8y ago
    It would have been nice if numbers had developed into a base-12 instead of a base-10 system. But it's even nicer that the number system (now 10-based) and the measurement system (now metric) are in sync.
    - JdeBP 8y ago
      They in fact did, many years ago. This is discussed elsewhere on this very page.
      - gpvos 8y ago
        Yeah, I was aware of that. I could have been more precise; it developed multiple times, but didn't stick around to the present.
  - 8ytecoder 8y ago
    How's that working out for inches->feet->yards->miles. Seriously, there are some good things about the imperial system but divisibility isn't exactly one. It's more relatable and human, probably yes.
    - gervase 8y ago
      Up to about a yard, divisibility for imperial distances is pretty good, but you're absolutely right that past yards, it doesn't make much sense. However, for most day-to-day, hands-on tasks (with the major exception of driving), those shorter distances are sufficient. I find this same principle is perhaps better exemplified by weights/volumes commonly used in cooking. Since many sizes (1 cup = 8 fl.oz, 1 pound = 16 oz, 1 gallon = 128 fl.oz, 1 fl.oz = 2 tablespoons, etc) are powers of 2, scaling recipes up or down on the fly is extremely easy. On the other hand, given an accurate metric scale, all recipes can be converted to weights, allowing scalar conversions. However, I suspect the proliferation of accurate scales in home kitchens is a relatively recent (nascent?) phenomena.
      - JackFr 8y ago
        >Up to about a yard, divisibility for imperial distances is pretty good, but you're absolutely right that past yards, it doesn't make much sense. Seems to work well with miles miles ft 1/10 528 1/11 480 1/12 440 1/15 352 1/16 330 1/20 264 1/22 240 1/24 220 1/30 176 1/32 165 1/40 132 miles yds 1/2 880 1/4 440 1/5 352 1/8 220 1/10 176 1/11 160 1/16 110 1/20 88
        jerf 8y ago
        One of the problems here is that given that our "home" numeric base is 2 times 5, we just aren't going to get both convenient unit conversion via moving the decimal point (or appropriate term in base of choice) and convenient divisibility. So I suppose if metric just isn't signal-y enough for you (in the general sense of "you", not JackFr), you can join the call for the world to convert to duodecimal: http://www.dozenal.org/ http://www.dozenal.org/
  - anonlastname 8y ago
    But base 10 is an archaic, arbitrary or divisibility based number system itself
    - gowld 8y ago
      Every base is base 10! Decimal is natural hands-based system. It's perhaps archaic, but neither arbitrary nor particularly divisible compared to its neighbors. (It's better than undecimal (9+2), but same as novemal (9), and worse than octal (8) or duodecimal (9+3))
  - kungtotte 8y ago
    In metric land we just tend to standardise measurements of things to fit into easily divisible numbers and keep our internally consistent system of units. E.g. IKEA cabinets are 60cm wide, and so are most appliances like fridges. Double-wide things are 120cm etc. Pre-cut lumber is sold by 120cm lengths, sheetrock is 120x240cm etc. All the easy division, plus the fancy units.
    - hedora 8y ago
      So, you’re saying that europe is about to switch away from meters to “ikeas” as the canonical unit? With brexit, it should be easy for the brits to lead the charge. I for one welcome the day when all the dimensions of all manmade objects are either products of numbers in the set {5, 3, 2, 1} or the set {1/2, 1/3, 1/5}. It will drastically simplify real world long division and factoring, and also lead to tighter packing of shipping containers. Knowing apple, they’ll screw it all up when they drop some port and shrink some device from 1/6000 to 1/6001 thick.
      - nojvek 8y ago
        Metric system is beautiful. Here’s a little poem 1 litre of water weights 1 kilogram and fills a 10cm cube to its brims. At 0 centigrade, it freezes, and at 100 it steams. Let’s try imperial units. 1 gallon of water weighs 8.34 pounds and fills 6.8in cube to its brims. At 32 farenheit it freezes and 212 it steams. Yuck!
        stephengillie 8y ago
        1 fluid ounce of water was supposed to weigh 1 ounce. But municipal differences have foiled that equivalency over time. The goal with Metric is that this won't happen - we'll see how long it takes for one group to claim their meter is 1.1 official meters.
    - chromaton 8y ago
      This has to do with Preferred numbers and ISO 2848: https://en.wikipedia.org/wiki/ISO_2848 https://en.wikipedia.org/wiki/ISO_2848
  - toss1 8y ago
    Nice thought, but not in my book! Once you need to work with real precision, the US system is even more awful. From an exactly 12" wide board, you cannot get three 4" pieces, since the saw kerf width is nonzero. It gets worse when you work with "standard" dimensions. A common 2x4 is actually only about 1.5" x 3.5" (and I don't think even the big sawmill blades take that big a kerf), and similar discrepancies all over. And converting drill bit sizes? Don't even start; it's either tables or a calculator. Whenever I get metric projects it's always such a pleasure. I wish we'd get our act together and switch...
    - InitialLastName 8y ago
      But... none of those issues have to do with imperial units. If you have a 30cm wide board, you can't get 3 10cm wide pieces either. And 2"x4" in lumber sizes refers to the size of the lumber prior to drying, treating and planing, all of which shrink the wood a bit. What is it about metric projects that makes those issues go away?
      - toss1 8y ago
        Good point - it's not so much that the issues of accounting for the kerf go away, they're just easier to deal with in decimal. I usually am using materials like structural foam, carbon fiber, or metals, just used wood as an easy example. And I'm using higher precision than most carpenters, so typically measuring with a micrometer which reads out in 0.001in (or 0.01mm) units. You can't just go from 1x12in to 3x4in pieces, you have to knock off maybe 5/64in for a kerf, which is 0.078125in so to get 3x 4in wide pieces, I'll need a board which is 12+5/32... Lots easier to work with 1.984mm so for my 3x 10cm pieces I'll need a 304 mm wide board. The bottom line is that once you get precise, the fractional regime which is indeed often easier to divide out by 1/2, 1/3, 1/4, 1/5, 1/6... etc. turns out to be no use at all because you can never actually use those nice fractions, and you're in a decimal regime with lots of fractional conversions (some micrometers even have a fractional inch readout mode, but it turns out to be not all that useful.) Once you're in decimal, it's WAAAAY easier to be in metric all the way.
  - vram22 8y ago
    I know you're joking, but I hope not, actually. Although it's fun to divide by different numbers like 2, 3, 4, 6, 12, etc., on the whole, I prefer the decimal system, because it is much easier (and hence faster) to calculate things mentally, using uniform powers of 10. As a simple example, when I need to mentally convert between millions and billions (used in the West) and lakhs and crores (used in India), it is so easy, because I convert everything to powers of 10 (e.g. million = 10^6, lakh = 10^5) and then multiply or divide as necessary, which really just amounts (pun not intended) to addition or subtraction of powers, using simple algebra. 40 million / 2 lakh = 4 * 10 * 10^6 / 2 lakh = 4 * 10^7 / 2 lakh = (4 * 10^7) / (2 * 10^5) = 2 * 10^7 / 10^5 = 2 * 10^2 = 200. https://en.wikipedia.org/wiki/Lakh https://en.wikipedia.org/wiki/Lakh https://en.wikipedia.org/wiki/Crore https://en.wikipedia.org/wiki/Crore https://en.wikipedia.org/wiki/Indian_numbering_system https://en.wikipedia.org/wiki/Indian_numbering_system I also prefer the Western numbering system (groups of 3 powers of 10) over the Indian system linked above, due to its uniformity (for the same reason as metric over Imperial).
  - stephengillie 8y ago
    USA isn't some sort of "metric-system hold-out". We sell soda in liters and wrenches in millimeters, among other things. And in the UK, cars are still rated in miles per gallon, as well as using Stones for human weight.
- dahart 8y ago
  FWIW, according to WP, "the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year." https://en.wikipedia.org/wiki/Degree_(angle) https://en.wikipedia.org/wiki/Degree_(angle) From many other sources, it's suggested that the length of the year is rounded to 360 for divisibility reasons, possibly because of the Babylonians' sexagesimal number system.
  - garmaine 8y ago
    Where do you think the sexagesimal number system came from?
    - dahart 8y ago
      I think it came from 60 being highly divisible. Why do you ask?
      - garmaine 8y ago
        There are other highly divisible numbers. 60 was probably chosen because of its approximate relationship to the length of the solar year.
        dahart 8y ago
        > There are other highly divisible numbers. 60 was probably chosen because of its approximate relationship to the length of the solar year. I had heard & read the reason was more one of counting convenience, more directly related to divisibility. What sources do you have suggesting that the length of the year is the "probable" reason? Poking around, I see several suggestions that it might be related to the number of months, which has nothing to do with the number of days. I also found this opinion, which seems to contradict the idea that the number system is related to days in the year: "Several theories have been based on astronomical events. The suggestion that 60 is the product of the number of months in the year (moons per year) with the number of planets (Mercury, Venus, Mars, Jupiter, Saturn) again seems far fetched as a reason for base 60. That the year was thought to have 360 days was suggested as a reason for the number base of 60 by the historian of mathematics Moritz Cantor. Again the idea is not that convincing since the Sumerians certainly knew that the year was longer than 360 days. Another hypothesis concerns the fact that the sun moves through its diameter 720 times during a day and, with 12 Sumerian hours in a day, one can come up with 60. [...] I [EFR] feel that all of these reasons are really not worth considering seriously." http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_numerals.html http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_nu...

BuildTheRobots 8y ago

I believe divisibility is also the reason we have 360-degrees in a circle.

xamuel 8y ago
And 12 inches in a foot, etc. Perhaps in centuries to come, the US will be vindicated for its metric system resistance :)
- gpvos 8y ago
  It would have been nice if numbers had developed into a base-12 instead of a base-10 system. But it's even nicer that the number system (now 10-based) and the measurement system (now metric) are in sync.
  - JdeBP 8y ago
    They in fact did, many years ago. This is discussed elsewhere on this very page.
    - gpvos 8y ago
      Yeah, I was aware of that. I could have been more precise; it developed multiple times, but didn't stick around to the present.
- 8ytecoder 8y ago
  How's that working out for inches->feet->yards->miles. Seriously, there are some good things about the imperial system but divisibility isn't exactly one. It's more relatable and human, probably yes.
  - gervase 8y ago
    Up to about a yard, divisibility for imperial distances is pretty good, but you're absolutely right that past yards, it doesn't make much sense. However, for most day-to-day, hands-on tasks (with the major exception of driving), those shorter distances are sufficient. I find this same principle is perhaps better exemplified by weights/volumes commonly used in cooking. Since many sizes (1 cup = 8 fl.oz, 1 pound = 16 oz, 1 gallon = 128 fl.oz, 1 fl.oz = 2 tablespoons, etc) are powers of 2, scaling recipes up or down on the fly is extremely easy. On the other hand, given an accurate metric scale, all recipes can be converted to weights, allowing scalar conversions. However, I suspect the proliferation of accurate scales in home kitchens is a relatively recent (nascent?) phenomena.
    - JackFr 8y ago
      >Up to about a yard, divisibility for imperial distances is pretty good, but you're absolutely right that past yards, it doesn't make much sense. Seems to work well with miles miles ft 1/10 528 1/11 480 1/12 440 1/15 352 1/16 330 1/20 264 1/22 240 1/24 220 1/30 176 1/32 165 1/40 132 miles yds 1/2 880 1/4 440 1/5 352 1/8 220 1/10 176 1/11 160 1/16 110 1/20 88
      - jerf 8y ago
        One of the problems here is that given that our "home" numeric base is 2 times 5, we just aren't going to get both convenient unit conversion via moving the decimal point (or appropriate term in base of choice) and convenient divisibility. So I suppose if metric just isn't signal-y enough for you (in the general sense of "you", not JackFr), you can join the call for the world to convert to duodecimal: http://www.dozenal.org/ http://www.dozenal.org/
- anonlastname 8y ago
  But base 10 is an archaic, arbitrary or divisibility based number system itself
  - gowld 8y ago
    Every base is base 10! Decimal is natural hands-based system. It's perhaps archaic, but neither arbitrary nor particularly divisible compared to its neighbors. (It's better than undecimal (9+2), but same as novemal (9), and worse than octal (8) or duodecimal (9+3))
- kungtotte 8y ago
  In metric land we just tend to standardise measurements of things to fit into easily divisible numbers and keep our internally consistent system of units. E.g. IKEA cabinets are 60cm wide, and so are most appliances like fridges. Double-wide things are 120cm etc. Pre-cut lumber is sold by 120cm lengths, sheetrock is 120x240cm etc. All the easy division, plus the fancy units.
  - hedora 8y ago
    So, you’re saying that europe is about to switch away from meters to “ikeas” as the canonical unit? With brexit, it should be easy for the brits to lead the charge. I for one welcome the day when all the dimensions of all manmade objects are either products of numbers in the set {5, 3, 2, 1} or the set {1/2, 1/3, 1/5}. It will drastically simplify real world long division and factoring, and also lead to tighter packing of shipping containers. Knowing apple, they’ll screw it all up when they drop some port and shrink some device from 1/6000 to 1/6001 thick.
    - nojvek 8y ago
      Metric system is beautiful. Here’s a little poem 1 litre of water weights 1 kilogram and fills a 10cm cube to its brims. At 0 centigrade, it freezes, and at 100 it steams. Let’s try imperial units. 1 gallon of water weighs 8.34 pounds and fills 6.8in cube to its brims. At 32 farenheit it freezes and 212 it steams. Yuck!
      - stephengillie 8y ago
        1 fluid ounce of water was supposed to weigh 1 ounce. But municipal differences have foiled that equivalency over time. The goal with Metric is that this won't happen - we'll see how long it takes for one group to claim their meter is 1.1 official meters.
  - chromaton 8y ago
    This has to do with Preferred numbers and ISO 2848: https://en.wikipedia.org/wiki/ISO_2848 https://en.wikipedia.org/wiki/ISO_2848
- toss1 8y ago
  Nice thought, but not in my book! Once you need to work with real precision, the US system is even more awful. From an exactly 12" wide board, you cannot get three 4" pieces, since the saw kerf width is nonzero. It gets worse when you work with "standard" dimensions. A common 2x4 is actually only about 1.5" x 3.5" (and I don't think even the big sawmill blades take that big a kerf), and similar discrepancies all over. And converting drill bit sizes? Don't even start; it's either tables or a calculator. Whenever I get metric projects it's always such a pleasure. I wish we'd get our act together and switch...
  - InitialLastName 8y ago
    But... none of those issues have to do with imperial units. If you have a 30cm wide board, you can't get 3 10cm wide pieces either. And 2"x4" in lumber sizes refers to the size of the lumber prior to drying, treating and planing, all of which shrink the wood a bit. What is it about metric projects that makes those issues go away?
    - toss1 8y ago
      Good point - it's not so much that the issues of accounting for the kerf go away, they're just easier to deal with in decimal. I usually am using materials like structural foam, carbon fiber, or metals, just used wood as an easy example. And I'm using higher precision than most carpenters, so typically measuring with a micrometer which reads out in 0.001in (or 0.01mm) units. You can't just go from 1x12in to 3x4in pieces, you have to knock off maybe 5/64in for a kerf, which is 0.078125in so to get 3x 4in wide pieces, I'll need a board which is 12+5/32... Lots easier to work with 1.984mm so for my 3x 10cm pieces I'll need a 304 mm wide board. The bottom line is that once you get precise, the fractional regime which is indeed often easier to divide out by 1/2, 1/3, 1/4, 1/5, 1/6... etc. turns out to be no use at all because you can never actually use those nice fractions, and you're in a decimal regime with lots of fractional conversions (some micrometers even have a fractional inch readout mode, but it turns out to be not all that useful.) Once you're in decimal, it's WAAAAY easier to be in metric all the way.
- vram22 8y ago
  I know you're joking, but I hope not, actually. Although it's fun to divide by different numbers like 2, 3, 4, 6, 12, etc., on the whole, I prefer the decimal system, because it is much easier (and hence faster) to calculate things mentally, using uniform powers of 10. As a simple example, when I need to mentally convert between millions and billions (used in the West) and lakhs and crores (used in India), it is so easy, because I convert everything to powers of 10 (e.g. million = 10^6, lakh = 10^5) and then multiply or divide as necessary, which really just amounts (pun not intended) to addition or subtraction of powers, using simple algebra. 40 million / 2 lakh = 4 * 10 * 10^6 / 2 lakh = 4 * 10^7 / 2 lakh = (4 * 10^7) / (2 * 10^5) = 2 * 10^7 / 10^5 = 2 * 10^2 = 200. https://en.wikipedia.org/wiki/Lakh https://en.wikipedia.org/wiki/Lakh https://en.wikipedia.org/wiki/Crore https://en.wikipedia.org/wiki/Crore https://en.wikipedia.org/wiki/Indian_numbering_system https://en.wikipedia.org/wiki/Indian_numbering_system I also prefer the Western numbering system (groups of 3 powers of 10) over the Indian system linked above, due to its uniformity (for the same reason as metric over Imperial).
- stephengillie 8y ago
  USA isn't some sort of "metric-system hold-out". We sell soda in liters and wrenches in millimeters, among other things. And in the UK, cars are still rated in miles per gallon, as well as using Stones for human weight.
dahart 8y ago
FWIW, according to WP, "the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year." https://en.wikipedia.org/wiki/Degree_(angle) https://en.wikipedia.org/wiki/Degree_(angle) From many other sources, it's suggested that the length of the year is rounded to 360 for divisibility reasons, possibly because of the Babylonians' sexagesimal number system.
- garmaine 8y ago
  Where do you think the sexagesimal number system came from?
  - dahart 8y ago
    I think it came from 60 being highly divisible. Why do you ask?
    - garmaine 8y ago
      There are other highly divisible numbers. 60 was probably chosen because of its approximate relationship to the length of the solar year.
      - dahart 8y ago
        > There are other highly divisible numbers. 60 was probably chosen because of its approximate relationship to the length of the solar year. I had heard & read the reason was more one of counting convenience, more directly related to divisibility. What sources do you have suggesting that the length of the year is the "probable" reason? Poking around, I see several suggestions that it might be related to the number of months, which has nothing to do with the number of days. I also found this opinion, which seems to contradict the idea that the number system is related to days in the year: "Several theories have been based on astronomical events. The suggestion that 60 is the product of the number of months in the year (moons per year) with the number of planets (Mercury, Venus, Mars, Jupiter, Saturn) again seems far fetched as a reason for base 60. That the year was thought to have 360 days was suggested as a reason for the number base of 60 by the historian of mathematics Moritz Cantor. Again the idea is not that convincing since the Sumerians certainly knew that the year was longer than 360 days. Another hypothesis concerns the fact that the sun moves through its diameter 720 times during a day and, with 12 Sumerian hours in a day, one can come up with 60. [...] I [EFR] feel that all of these reasons are really not worth considering seriously." http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_numerals.html http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_nu...