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It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long. 1 x 2 x 3 x 4 That way you could ha

It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long. 1 x 2 x 3 x 4 That way you could have half days, quarter days, or third of days. An hour is divided into 60 minutes: 3 x 4 x 5 The word "second" means a "second division by 3 x 4 x 5"

simulate 8y ago
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...
krylon 8y ago
I guess it was useful for other people, too! Thank you so much for that explanation!
killjoywashere 8y ago
It's not just the divisibility of the day, it's the divisibility of the compass that ties into it. There are all sorts of shortcuts in the math.
jessriedel 8y ago
> That way you could have half days, quarter days, or third of days. The day needs to be divided into eighths in order to justify the factor of 2. Otherwise, the factor of 4 is able to handle both quarters and halves.
_bxg1 8y ago
Yeah, at first this seems like a shocking coincidence, until you realize that days are divided up into completely man-made units, not in any fundamentally natural way. If someone discovered something similar about the number of days in an Earth-year, that would be different.
- mbfg 8y ago
  It's quite surprising that in 2018, February still has 28 days. You'd think we'd bump it to 30, and pull two other 31's in a day.
jlebar 8y ago
This article (from downthread) suggests that 60 comes from the Sumerians, who had a base-60 number system, and 24 comes from the Egyptians, who had a base-12 number system. Although it agrees that 12 and 60 are conveniently divisible in the way you describe, I'm not finding any evidence to connect this specifically to sailors, or even to people dividing up shifts. Rather it seems likely that the civilization's numeric base was chosen first, and then it was applied to timekeeping. https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ https://www.scientificamerican.com/article/experts-time-divi...
- d0lph 8y ago
  Like natural selection at a cultural level.
  - andai 8y ago
    [ triggered ]
  - subcosmos 8y ago
    This is just theoretical appropriation!
- kungtotte 8y ago
  Shipboard life was one of the first large scale applications of precise timekeeping. You need it for navigation and for organising shifts and jobs (though I think navigation is the major player here). For most people at that time there was no need for even hourly timekeeping, much less minutes or seconds. You woke up in the morning and ate your breakfast, milking the cows took however long it took, then you gathered the eggs from the hens, probably around that time you had lunch, then depending on the season you'd do whatever was needed in the fields until the sun started setting and then you ate supper. But with navigation you had to know how far to sail in any given direction to not get knocked off your course. I'm certain that the use of 60 and 12 base systems came from the Sumerians and Egyptians, but their application for timekeeping is probably influenced heavily by sailors.
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nonbel 8y ago
>"It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long." Is there a source for specifically "sailors"? Also: 1 x 2 x 3 x 4 x 5 = 120 120 hrs would be even more divisible (including by 5 and 10). So really they should have used 120 hrs per day consisting of 12 minutes each instead of 24 hours of 60 minutes each.
- ChuckMcM 8y ago
  Back when I discovered how flexible the number 12 was this was something I thought would be awesome. (120 "hour" days). So much better than the metric proposal for 10 "hour" days (so called "decimal time").
  - droidist2 8y ago
    120 hour days would be pretty cool, then you could say things like "Oh my god, it's almost 90."
- simonh 8y ago
  But then you can't count to 120 on one hand, whereas you can count to 12 by pointing to the joints of your fingers with your thumb. Also since you have four fingers and three joints on each finger it makes it easy to count in groups of those numbers, by counting up or across the fingers.
Someone 8y ago
”It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long.” To be able do divide a day into halves, thirds and quarts you only need 12 parts in a day, not 24. Also, according to Wikipedia, the 24 hour clock started with the Egyptians dividing the night into 12 parts around 2800 B.C. (https://en.m.wikipedia.org/wiki/Hour#History https://en.m.wikipedia.org/wiki/Hour#History). That “12” may have come from the ability to split it into halves, thirds and quarts, but I couldn’t find evidence for that.
- gowld 8y ago
  Wikipedia's source says that the "12" hours was simply derived from the 36 (12*3) already in use in the annum calendar (36 10-day weeks in a year). https://books.google.com.hk/books?id=xKKPUpDOTKAC&printsec=frontcover#v=snippet&q=civil%20calendar%20night&f=false https://books.google.com.hk/books?id=xKKPUpDOTKAC&printsec=f... It's a bit strange to argue which use-case came first, as there are many use-cases of varying important to varying people, that all have the same natural solution.
Balgair 8y ago
Numbers like 24, 60, and 360 are 'highly composite numbers'. Here is a GREAT video on these 'anti-prime' numbers :https://www.youtube.com/watch?v=2JM2oImb9Qg https://www.youtube.com/watch?v=2JM2oImb9Qg These anti-prime numbers were studied first by Ramanujan (of course) and conditions are that: 1) The prime factors must be consecutive (2^n X 3^m not 2^n X 5^m) 2) The powers of the prime factors must be deceasing as the prime number increases (2^4 X 3^3 not 2^1 X 3^5) 3) The numbers end with the the highest prime to the highest prime (2^4 X 3^1 not 2^3 X 3^2). Except for the numbers 2 and 4. More here: https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Highly_composite_number
- vram22 8y ago
  >These anti-prime numbers were studied first by Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
  - Balgair 8y ago
    Ramanujan was easily one of the greatest mathematicians in history. Full Stop. Entirely self-taught, his insights were incredibly novel and have helped human advancement immeasurably. Incredible stories about this great person abound. Sadly, he died at 32 from a curable disease, though misdiagnosed. He was deeply religious, a devout Hindu and vegetarian. His legacy is truly astonishing despite his few years. What he could have accomplished, had he lived, is a tragedy of the first order to mathematics and the human quest for truth. Here is a good biography if you are interested: https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/1476763496 https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/14...
    - vram22 8y ago
      >Here is a good biography if you are interested: https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/14.. https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/14.... Thanks, will check it.
    - 8y ago
hedora 8y ago
Also, there were exactly 30 days in a month and 360 days in a year until more precise accounting screwed up the math.
vram22 8y ago
Wow, that's interesting, thanks for sharing. I've always wondered why date, time and even other units of measure were not calibrated in the decimal system from the beginning. I had read about the controversy when Britain adopted the metric system, that may have been when I started thinking about this.
- TremendousJudge 8y ago
  They actually tried to introduce decimal time[1], as well as a decimal week[2]. They didn't stick though. If you are interested on the topic of the history of the metric system, check out The Measure of All Things[3], an absolutely fantastic read [1] https://en.wikipedia.org/wiki/Decimal_time https://en.wikipedia.org/wiki/Decimal_time [2] https://en.wikipedia.org/wiki/French_Republican_Calendar https://en.wikipedia.org/wiki/French_Republican_Calendar [3] https://www.amazon.com/Measure-All-Things-Seven-Year-Transformed/dp/0743216768 https://www.amazon.com/Measure-All-Things-Seven-Year-Transfo...
  - vram22 8y ago
    Thanks, sounds good, will check those out.
deleted 8y ago
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simulate 8y ago

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...

krylon 8y ago

I guess it was useful for other people, too! Thank you so much for that explanation!

killjoywashere 8y ago

It's not just the divisibility of the day, it's the divisibility of the compass that ties into it. There are all sorts of shortcuts in the math.

jessriedel 8y ago

> That way you could have half days, quarter days, or third of days. The day needs to be divided into eighths in order to justify the factor of 2. Otherwise, the factor of 4 is able to handle both quarters and halves.

_bxg1 8y ago

Yeah, at first this seems like a shocking coincidence, until you realize that days are divided up into completely man-made units, not in any fundamentally natural way. If someone discovered something similar about the number of days in an Earth-year, that would be different.

mbfg 8y ago
It's quite surprising that in 2018, February still has 28 days. You'd think we'd bump it to 30, and pull two other 31's in a day.

jlebar 8y ago

This article (from downthread) suggests that 60 comes from the Sumerians, who had a base-60 number system, and 24 comes from the Egyptians, who had a base-12 number system. Although it agrees that 12 and 60 are conveniently divisible in the way you describe, I'm not finding any evidence to connect this specifically to sailors, or even to people dividing up shifts. Rather it seems likely that the civilization's numeric base was chosen first, and then it was applied to timekeeping. https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ https://www.scientificamerican.com/article/experts-time-divi...

d0lph 8y ago
Like natural selection at a cultural level.
- andai 8y ago
  [ triggered ]
- subcosmos 8y ago
  This is just theoretical appropriation!
kungtotte 8y ago
Shipboard life was one of the first large scale applications of precise timekeeping. You need it for navigation and for organising shifts and jobs (though I think navigation is the major player here). For most people at that time there was no need for even hourly timekeeping, much less minutes or seconds. You woke up in the morning and ate your breakfast, milking the cows took however long it took, then you gathered the eggs from the hens, probably around that time you had lunch, then depending on the season you'd do whatever was needed in the fields until the sun started setting and then you ate supper. But with navigation you had to know how far to sail in any given direction to not get knocked off your course. I'm certain that the use of 60 and 12 base systems came from the Sumerians and Egyptians, but their application for timekeeping is probably influenced heavily by sailors.

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nonbel 8y ago

>"It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long." Is there a source for specifically "sailors"? Also: 1 x 2 x 3 x 4 x 5 = 120 120 hrs would be even more divisible (including by 5 and 10). So really they should have used 120 hrs per day consisting of 12 minutes each instead of 24 hours of 60 minutes each.

ChuckMcM 8y ago
Back when I discovered how flexible the number 12 was this was something I thought would be awesome. (120 "hour" days). So much better than the metric proposal for 10 "hour" days (so called "decimal time").
- droidist2 8y ago
  120 hour days would be pretty cool, then you could say things like "Oh my god, it's almost 90."
simonh 8y ago
But then you can't count to 120 on one hand, whereas you can count to 12 by pointing to the joints of your fingers with your thumb. Also since you have four fingers and three joints on each finger it makes it easy to count in groups of those numbers, by counting up or across the fingers.

Someone 8y ago

”It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long.” To be able do divide a day into halves, thirds and quarts you only need 12 parts in a day, not 24. Also, according to Wikipedia, the 24 hour clock started with the Egyptians dividing the night into 12 parts around 2800 B.C. (https://en.m.wikipedia.org/wiki/Hour#History https://en.m.wikipedia.org/wiki/Hour#History). That “12” may have come from the ability to split it into halves, thirds and quarts, but I couldn’t find evidence for that.

gowld 8y ago
Wikipedia's source says that the "12" hours was simply derived from the 36 (12*3) already in use in the annum calendar (36 10-day weeks in a year). https://books.google.com.hk/books?id=xKKPUpDOTKAC&printsec=frontcover#v=snippet&q=civil%20calendar%20night&f=false https://books.google.com.hk/books?id=xKKPUpDOTKAC&printsec=f... It's a bit strange to argue which use-case came first, as there are many use-cases of varying important to varying people, that all have the same natural solution.

Balgair 8y ago

Numbers like 24, 60, and 360 are 'highly composite numbers'. Here is a GREAT video on these 'anti-prime' numbers :https://www.youtube.com/watch?v=2JM2oImb9Qg https://www.youtube.com/watch?v=2JM2oImb9Qg These anti-prime numbers were studied first by Ramanujan (of course) and conditions are that: 1) The prime factors must be consecutive (2^n X 3^m not 2^n X 5^m) 2) The powers of the prime factors must be deceasing as the prime number increases (2^4 X 3^3 not 2^1 X 3^5) 3) The numbers end with the the highest prime to the highest prime (2^4 X 3^1 not 2^3 X 3^2). Except for the numbers 2 and 4. More here: https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Highly_composite_number

vram22 8y ago
>These anti-prime numbers were studied first by Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
- Balgair 8y ago
  Ramanujan was easily one of the greatest mathematicians in history. Full Stop. Entirely self-taught, his insights were incredibly novel and have helped human advancement immeasurably. Incredible stories about this great person abound. Sadly, he died at 32 from a curable disease, though misdiagnosed. He was deeply religious, a devout Hindu and vegetarian. His legacy is truly astonishing despite his few years. What he could have accomplished, had he lived, is a tragedy of the first order to mathematics and the human quest for truth. Here is a good biography if you are interested: https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/1476763496 https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/14...
  - vram22 8y ago
    >Here is a good biography if you are interested: https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/14.. https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/14.... Thanks, will check it.
  - 8y ago

hedora 8y ago

Also, there were exactly 30 days in a month and 360 days in a year until more precise accounting screwed up the math.

vram22 8y ago

Wow, that's interesting, thanks for sharing. I've always wondered why date, time and even other units of measure were not calibrated in the decimal system from the beginning. I had read about the controversy when Britain adopted the metric system, that may have been when I started thinking about this.

TremendousJudge 8y ago
They actually tried to introduce decimal time[1], as well as a decimal week[2]. They didn't stick though. If you are interested on the topic of the history of the metric system, check out The Measure of All Things[3], an absolutely fantastic read [1] https://en.wikipedia.org/wiki/Decimal_time https://en.wikipedia.org/wiki/Decimal_time [2] https://en.wikipedia.org/wiki/French_Republican_Calendar https://en.wikipedia.org/wiki/French_Republican_Calendar [3] https://www.amazon.com/Measure-All-Things-Seven-Year-Transformed/dp/0743216768 https://www.amazon.com/Measure-All-Things-Seven-Year-Transfo...
- vram22 8y ago
  Thanks, sounds good, will check those out.

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