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Except now you can't divide accurately by 5. Or 10. You're making an argument from familiarity. Yes, a 12-base system using fractions works very neatly in a sm

Except now you can't divide accurately by 5. Or 10. You're making an argument from familiarity. Yes, a 12-base system using fractions works very neatly in a small human-sized domain, but it disintegrates into complete uselessness outside that domain. That's why you get ridiculousness as things being 13/64th of an inch, or that there's 63360 inches in a mile. It's unworkable for very large distances and very small distances. With a metre and standard prefixes, you don't need any conversion factors, and you can represent any distance at any scale with a single unit. Quick, what's 11/64" + 3/8"? Quick, which weight is bigger: 0.6lbs or 10oz?

tempestn 1y ago
5 and 10 are arbitrary numbers though. Halving and doubling are really the only special operations, and base-8 or base-16 would be superior to 10 or 12 for those.
- Symbiote 1y ago
  10 is arbitrary, but it's also the base chosen for our counting system. You can use hexadecimal numbers if you wish. "He's B6 cm tall." I have found this, which seems neat: https://en.wikipedia.org/wiki/Bibi-binary https://en.wikipedia.org/wiki/Bibi-binary So he's ki-ba cm tall.
  - saalweachter 1y ago
    Ugg, that naming system is the worst I've ever seen. It's like it's asking for you to mis-hear numbers. Use a range of consonants!
  - tempestn 1y ago
    The topic of this thread is why the base 10 number system is less than optimal, and a different base would be better. Obviously having to convert to other bases when we use a base 10 system normally is inconvenient, but that's not the point.
chungy 1y ago
> That's why you get ridiculousness as things being 13/64th of an inch Such fractions are very rarely used, you're more likely to use mils (1/1000 of an inch) at that scale. > or that there's 63360 inches in a mile. Likewise, something that will probably never come up in your life. Inches/feet/yards and miles just remain separate things, never mixed. > With a metre and standard prefixes, you don't need any conversion factors, and you can represent any distance at any scale with a single unit. There's no intuition for them. Knowing what a meter is does not help with getting a feel for a kilometer. They might as well be as separate as feet and miles at that scale. > Quick, what's 11/64" + 3/8"? That one's not even hard, it's just a fraction. 35/64" > Quick, which weight is bigger: 0.6lbs or 10oz? Another arbitrary problem that will probably never come up, but to entertain you: since 0.5 lbs is 8oz, adding 1.6oz to that (another tenth of a lbs) results in 9.6oz. 10oz is bigger than 0.6 lbs. Not hard, but at least mildly harder than the first question. None of this really had to do with the convenience highlighted initially: 12 inches in a foot and 3 feet in a yard make extremely convenient divisible factors. You can trivially divide things by 2, 3, 4, and 6 and keep with whole integer values. The same definitely cannot be said of metric.
- deleted 1y ago
  [deleted]
- Symbiote 1y ago
  > Inches/feet/yards and miles just remain separate things, never mixed How tall are you, maybe 70 inches? Or 5⅚ft? 178cm or 1.78m are so obviously equivalent it doesn't matter which is used. > 12 inches in a foot and 3 feet in a yard make extremely convenient divisible factors. This requires you to start with 12 inches. If you're making a cupboard to fit in an 18¾" (476mm) space, it's no use, or is only randomly useful. If you can choose, then you can just as easily start with 36cm. For example, European kitchens are designed around a 300mm base size.
  - chungy 1y ago
    > How tall are you, maybe 70 inches? Or 5⅚ft? Are you purposely doing this? That is obviously not what I meant. Nobody says "3 miles, 500 feet", they say "3.1 miles". Effectively two systems of distance measurement: inches/feet/yards (near scale), and miles (distant scale). "5 feet 10 inches" is completely normal and fine. > This requires you to start with 12 inches. If you're making a cupboard to fit in an 18¾" (476mm) space, it's no use, or is only randomly useful. So you cut the cupboard to fit a 18¾" space, no big deal. Same as anything else, and just as random as 476mm. Typically they come in (integer!) 12-inch, 24-inch, 36-inch, or 48-inch variants.
int_19h 1y ago
Obviously, the base should be the same for units as it is for numbers in general, but there are good arguments in favor of using 12 for both. Then all your examples become as simple as division by 5 is in decimal.
philwelch 1y ago
> 63360 inches in a mile Nobody cares how many inches are in a mile. It doesn’t matter. > Quick, what's 11/64" + 3/8"? 35/64. Was that supposed to be hard? Common denominators are elementary school level arithmetic. > Quick, which weight is bigger: 0.6lbs or 10oz? 10oz. 10/16 is 5/8 which is .625. I agree that metric is easier for people who don’t have a grasp of fifth grade arithmetic.

tempestn 1y ago

5 and 10 are arbitrary numbers though. Halving and doubling are really the only special operations, and base-8 or base-16 would be superior to 10 or 12 for those.

Symbiote 1y ago
10 is arbitrary, but it's also the base chosen for our counting system. You can use hexadecimal numbers if you wish. "He's B6 cm tall." I have found this, which seems neat: https://en.wikipedia.org/wiki/Bibi-binary https://en.wikipedia.org/wiki/Bibi-binary So he's ki-ba cm tall.
- saalweachter 1y ago
  Ugg, that naming system is the worst I've ever seen. It's like it's asking for you to mis-hear numbers. Use a range of consonants!
- tempestn 1y ago
  The topic of this thread is why the base 10 number system is less than optimal, and a different base would be better. Obviously having to convert to other bases when we use a base 10 system normally is inconvenient, but that's not the point.

chungy 1y ago

> That's why you get ridiculousness as things being 13/64th of an inch Such fractions are very rarely used, you're more likely to use mils (1/1000 of an inch) at that scale. > or that there's 63360 inches in a mile. Likewise, something that will probably never come up in your life. Inches/feet/yards and miles just remain separate things, never mixed. > With a metre and standard prefixes, you don't need any conversion factors, and you can represent any distance at any scale with a single unit. There's no intuition for them. Knowing what a meter is does not help with getting a feel for a kilometer. They might as well be as separate as feet and miles at that scale. > Quick, what's 11/64" + 3/8"? That one's not even hard, it's just a fraction. 35/64" > Quick, which weight is bigger: 0.6lbs or 10oz? Another arbitrary problem that will probably never come up, but to entertain you: since 0.5 lbs is 8oz, adding 1.6oz to that (another tenth of a lbs) results in 9.6oz. 10oz is bigger than 0.6 lbs. Not hard, but at least mildly harder than the first question. None of this really had to do with the convenience highlighted initially: 12 inches in a foot and 3 feet in a yard make extremely convenient divisible factors. You can trivially divide things by 2, 3, 4, and 6 and keep with whole integer values. The same definitely cannot be said of metric.

deleted 1y ago
[deleted]
Symbiote 1y ago
> Inches/feet/yards and miles just remain separate things, never mixed How tall are you, maybe 70 inches? Or 5⅚ft? 178cm or 1.78m are so obviously equivalent it doesn't matter which is used. > 12 inches in a foot and 3 feet in a yard make extremely convenient divisible factors. This requires you to start with 12 inches. If you're making a cupboard to fit in an 18¾" (476mm) space, it's no use, or is only randomly useful. If you can choose, then you can just as easily start with 36cm. For example, European kitchens are designed around a 300mm base size.
- chungy 1y ago
  > How tall are you, maybe 70 inches? Or 5⅚ft? Are you purposely doing this? That is obviously not what I meant. Nobody says "3 miles, 500 feet", they say "3.1 miles". Effectively two systems of distance measurement: inches/feet/yards (near scale), and miles (distant scale). "5 feet 10 inches" is completely normal and fine. > This requires you to start with 12 inches. If you're making a cupboard to fit in an 18¾" (476mm) space, it's no use, or is only randomly useful. So you cut the cupboard to fit a 18¾" space, no big deal. Same as anything else, and just as random as 476mm. Typically they come in (integer!) 12-inch, 24-inch, 36-inch, or 48-inch variants.

int_19h 1y ago

Obviously, the base should be the same for units as it is for numbers in general, but there are good arguments in favor of using 12 for both. Then all your examples become as simple as division by 5 is in decimal.

philwelch 1y ago

> 63360 inches in a mile Nobody cares how many inches are in a mile. It doesn’t matter. > Quick, what's 11/64" + 3/8"? 35/64. Was that supposed to be hard? Common denominators are elementary school level arithmetic. > Quick, which weight is bigger: 0.6lbs or 10oz? 10oz. 10/16 is 5/8 which is .625. I agree that metric is easier for people who don’t have a grasp of fifth grade arithmetic.