7 ms·

That's exactly the kind of thinking that I'm alluding to. Okay, if base 12 is so great, why are gallons not divisible by 12? Why is our currency not divisible b

by nayuki 3y ago

That's exactly the kind of thinking that I'm alluding to. Okay, if base 12 is so great, why are gallons not divisible by 12? Why is our currency not divisible by 12? Why is a mile 1760 yards - what if you wanted to parcel a square mile into thirds on each side? Why is an inch partitioned into binary fractions? Why are pounds not divisible by 12? The imperial customs (it's hard to even call it a system) have no internal consistency. To add to the observation about lack of internal consistency: Metalworkers use decimal inches. Woodworkers use feet, inches, and binary fractions. Surveyors use decimal feet. Some people use decimal miles. You could argue that each of the aforementioned systems make sense on its own, but none of them interoperate. Seriously - you'll be baffled if you pick up a decimal foot measuring tape in real life (they exist). Metric doesn't have this problem because if someone is doing detailed work in millimetres, someone is planning a house's rooms in metres, and someone is organizing a town's land in kilometres, they can all work with each other by simply moving the decimal place and changing the prefix. Another problem is that you're presupposing that the products you interact with are designed in a whole number of feet, and then you subdivide from there. I don't see this as true at all; things come in all sizes like 2'5", how are you going to divide that into thirds?

kemotep 3y ago
Unlike metric, all the different imperial measurements are just combinations of different kinds of initially unrelated measurement systems. So a gallon has absolutely nothing to do with foot, miles are a completely different measurement system than feet, pounds and so on. Needing to know the weight of a cubic hectare of water and then how many gallons that is, is not a common issue. Metric does give you a system that can quickly calculate these things comparatively.
philwelch 3y ago
> The imperial customs (it's hard to even call it a system) have no internal consistency. "Internal consistency" doesn't matter. Virtually nobody ever has to convert miles to yards; the use cases for measuring a distance in miles and the use cases for measuring a distance in yards almost never overlap. For the rare cases where they do, the units do have an integer conversion. For the use cases that do commonly overlap, e.g. inches and feet, you get a useful-for-that-specific-domain conversion factor of 12. Some domains use decimal miles or decimal inches and that's totally fine; sounds to me like they didn't need the metric system after all. But if you're going to be so insistent on "internal consistency", riddle me this: why do we measure time in hours, days, weeks, months, and years rather than in decaseconds, hectoseconds, kiloseconds, megaseconds, etc.? > if someone is doing detailed work in millimetres, someone is planning a house's rooms in metres, and someone is organizing a town's land in kilometres, they can all work with each other These people never work with each other. This is a fantasy.
- thfuran 3y ago
  >why do we measure time in hours, days, weeks, months, and years rather than in decaseconds, hectoseconds, kiloseconds, megaseconds, etc.? Because it would be astronomically expensive to slow earth's rotation enough for a day to be 100 ksec.
  - nayuki 3y ago
    There's no theoretical problem if we define 86400 seconds = 1000000 newseconds. One big practical problem is that because SI is a coherent system, the second is embedded in many units. For example, 1 N = 1 kg m/s^2. 1 J = 1 N m. 1 V = 1 J/C. 1 Pa = 1 N/m^2. And so on and so forth. So all of those units will have to be replaced with units derived from the newsecond. This is kind of like how SI has the unit tesla but the CGS electromagnetic unit is gauss. A long-term problem is that no matter what, the length of the day on Earth will drift from scientifically accurate atomic time. Sometime in the near future, a day will be 86401 seconds. Then 86402, and so on. So the old second or the new second will not solve this problem.
    - philwelch 3y ago
      > A long-term problem is that no matter what, the length of the day on Earth will drift from scientifically accurate atomic time. Sometime in the near future, a day will be 86401 seconds. Then 86402, and so on. So the old second or the new second will not solve this problem. How long term is this problem? For instance, we habitually insert "leap seconds" in order to keep things lined up, but if we didn't insert leap seconds, we might accumulate an error of maybe half an hour between the solar meridian and "noon" in the next 500 years, which is less error than we introduce by putting Madrid and Belgrade in the same time zone. And in 500 years, most of humanity will not even be living on the Earth anyway.
- nayuki 3y ago
  > "Internal consistency" doesn't matter. The lack of an opinionated stance on internal consistency is exactly how we arrive at traditional measures and also the US Customary set of units. It's far easier politically to be accommodating and allow more units than to put down your foot and say no, this is redundant, this cannot be used. > Virtually nobody ever has to convert miles to yards That's mostly true because it seems yards are only used to measure football fields and fabric. Everything else is measured in feet, from personal heights to furniture to rooms to house yards to building structures (the Empire State Building is 1454 feet tall). But my point still stands. You think you don't have to convert between miles and feet? Okay: https://www.researchgate.net/figure/a-Typical-multi-lane-highway-California-USA-b-5-lane-highway-in-the-simulator_fig1_333658431 https://www.researchgate.net/figure/a-Typical-multi-lane-hig... . There's a highway exit coming up in 800 feet and another in 1/2 mile. How many times longer does it take to reach the second exit compared to the first exit? You have no clue. In metric it's 250 m and 800 m, and it obviously takes about 3 times longer to reach the second exit. > These people never work with each other. This is a fantasy. Tell me you haven't worked in engineering without telling me you haven't worked in engineering. If you eyeball everything and use intuition, I can see why you don't care about units, conversions, and calculations. If you actually need to plan and analyze things carefully before you order materials and cut things, you'll quickly see that having a plethora of units adds complexity and chances for error without adding any functionality that a pure system has (whether you're using millimetres or only decimal inches).

by nayuki 3y ago

kemotep 3y ago

Unlike metric, all the different imperial measurements are just combinations of different kinds of initially unrelated measurement systems. So a gallon has absolutely nothing to do with foot, miles are a completely different measurement system than feet, pounds and so on. Needing to know the weight of a cubic hectare of water and then how many gallons that is, is not a common issue. Metric does give you a system that can quickly calculate these things comparatively.

philwelch 3y ago

> The imperial customs (it's hard to even call it a system) have no internal consistency. "Internal consistency" doesn't matter. Virtually nobody ever has to convert miles to yards; the use cases for measuring a distance in miles and the use cases for measuring a distance in yards almost never overlap. For the rare cases where they do, the units do have an integer conversion. For the use cases that do commonly overlap, e.g. inches and feet, you get a useful-for-that-specific-domain conversion factor of 12. Some domains use decimal miles or decimal inches and that's totally fine; sounds to me like they didn't need the metric system after all. But if you're going to be so insistent on "internal consistency", riddle me this: why do we measure time in hours, days, weeks, months, and years rather than in decaseconds, hectoseconds, kiloseconds, megaseconds, etc.? > if someone is doing detailed work in millimetres, someone is planning a house's rooms in metres, and someone is organizing a town's land in kilometres, they can all work with each other These people never work with each other. This is a fantasy.

thfuran 3y ago
>why do we measure time in hours, days, weeks, months, and years rather than in decaseconds, hectoseconds, kiloseconds, megaseconds, etc.? Because it would be astronomically expensive to slow earth's rotation enough for a day to be 100 ksec.
- nayuki 3y ago
  There's no theoretical problem if we define 86400 seconds = 1000000 newseconds. One big practical problem is that because SI is a coherent system, the second is embedded in many units. For example, 1 N = 1 kg m/s^2. 1 J = 1 N m. 1 V = 1 J/C. 1 Pa = 1 N/m^2. And so on and so forth. So all of those units will have to be replaced with units derived from the newsecond. This is kind of like how SI has the unit tesla but the CGS electromagnetic unit is gauss. A long-term problem is that no matter what, the length of the day on Earth will drift from scientifically accurate atomic time. Sometime in the near future, a day will be 86401 seconds. Then 86402, and so on. So the old second or the new second will not solve this problem.
  - philwelch 3y ago
    > A long-term problem is that no matter what, the length of the day on Earth will drift from scientifically accurate atomic time. Sometime in the near future, a day will be 86401 seconds. Then 86402, and so on. So the old second or the new second will not solve this problem. How long term is this problem? For instance, we habitually insert "leap seconds" in order to keep things lined up, but if we didn't insert leap seconds, we might accumulate an error of maybe half an hour between the solar meridian and "noon" in the next 500 years, which is less error than we introduce by putting Madrid and Belgrade in the same time zone. And in 500 years, most of humanity will not even be living on the Earth anyway.
nayuki 3y ago
> "Internal consistency" doesn't matter. The lack of an opinionated stance on internal consistency is exactly how we arrive at traditional measures and also the US Customary set of units. It's far easier politically to be accommodating and allow more units than to put down your foot and say no, this is redundant, this cannot be used. > Virtually nobody ever has to convert miles to yards That's mostly true because it seems yards are only used to measure football fields and fabric. Everything else is measured in feet, from personal heights to furniture to rooms to house yards to building structures (the Empire State Building is 1454 feet tall). But my point still stands. You think you don't have to convert between miles and feet? Okay: https://www.researchgate.net/figure/a-Typical-multi-lane-highway-California-USA-b-5-lane-highway-in-the-simulator_fig1_333658431 https://www.researchgate.net/figure/a-Typical-multi-lane-hig... . There's a highway exit coming up in 800 feet and another in 1/2 mile. How many times longer does it take to reach the second exit compared to the first exit? You have no clue. In metric it's 250 m and 800 m, and it obviously takes about 3 times longer to reach the second exit. > These people never work with each other. This is a fantasy. Tell me you haven't worked in engineering without telling me you haven't worked in engineering. If you eyeball everything and use intuition, I can see why you don't care about units, conversions, and calculations. If you actually need to plan and analyze things carefully before you order materials and cut things, you'll quickly see that having a plethora of units adds complexity and chances for error without adding any functionality that a pure system has (whether you're using millimetres or only decimal inches).