6 ms·

Too few divisors of place values. The idea you would pick something that isn't evenly divisible by at least 3 or 4 was a mistake. This one isn't metric's fault

Too few divisors of place values. The idea you would pick something that isn't evenly divisible by at least 3 or 4 was a mistake. This one isn't metric's fault to be fair. That's just what you get for inventing numbers before inventing math. Makes me wonder what would have happened if 'French numbers' in base 12, 36 or 60 were introduced at the same time. People got used to working in octal.or hexadecimal in the past for computers, doesn't seem like it would have been as big of a change as you think.

tokai 1y ago
>evenly divisible by at least 3 or 4 Irrelevant with a decimal system.
- chungy 1y ago
  It's not irrelevant, you can choose something like 12 to make all your factors out of. It's a particular strength of working in feet and yards.
  - henrikschroder 1y ago
    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.
- IAmBroom 1y ago
  Irrelevant if you are working with computers and digital equipment. Highly relevant if you are using T-squares, compasses, and dividing calipers.
  - mfost 1y ago
    It's just a matter of working with base elements that are divisible by 3 and 4 really. So instead of buying 100cm planks, buy 120cm planks?
    - philwelch 1y ago
      And eventually you’re going to want a name for your 120cm unit. But that’s not allowed in metric because any named unit has to be base 10.
      - olddustytrail 1y ago
        It has a name. It's the plank length.
  - tempestn 1y ago
    It's pretty relevant with computers. If we were used to working in base-8 or base-16 in everyday life, numerous aspects of programming would be simplified.
- henrikschroder 1y ago
  The biggest source of communication issues around these unit systems is that in metric, you're supposed to reach for decimals when working with the units, and in imperial, you're supposed to reach for fractions when working with the units. Which is why the imperial lovers all cry out about their fractions not "working" in metric. Yes, exactly, that is the point. They don't understand that they're reaching for a tool they shouldn't be reaching for, and then they blame the unit system for it.
foobiekr 1y ago
Base 60 is genuinely the best option.
- layer8 1y ago
  That would have broken ASCII.
forty 1y ago
Don't you think base 10 was used simply because it conveniently matches the number of fingers of Humans?
- nancyminusone 1y ago
  Of course... But - look at your open hand right now. Count the number of segments on your 4 fingers - it's 12. You can even use your thumb as a pointer and count one handed.
  - tempestn 1y ago
    Or forget about the thumbs and just count fingers. 8 would be a better base than 10 for sure, and arguably better than 12. (Easier doubling and halving, easier binary conversions, but fewer integer factors and fewer digits.)
- paipa 1y ago
  Base 6 has six digits, 0 through 5. Perfect fit for the human hand, you get place value notation and counting to 35 decimal (55 seximal) for free. Base 6 would've been the real deal.
empath75 1y ago
There's two reasons to use a measurement system -- one of those is for sort of every day work -- cooking, home carpentry and the like, and in that case, having something like the imperial system is nice, because you can divide things usefully. The _other_ reason to use a measurement system is for doing _science_, and for that, having everything in base ten makes things _immensely_ easier, especially if you're working the math out by hand
- henrikschroder 1y ago
  > because you can divide things usefully. Again, this is just familiarity. You think it's super neat that you can divide a cup of whatever by 2 or 3 or 4, but if I tell you to divide it by 5, you're gonna deflect and ask me "who does that?!?" Imperial works neatly for a small domain of problems, and is useless outside that domain. Metric is less neat in that small domain, but works equally well everywhere.
  - AStonesThrow 1y ago
    Well no... Firstly, we can divide a cup by 2, 3, and 4 in the kitchen because those are common measuring-cup sizes. Nobody is prevented from using a fractional size: if I divide a cup by 5 then I have 1/5th of a cup, nothing more and nothing less. While 1/4th of a cup is 2 oz, and 1/3rd of a cup is 16 teaspoons, 1/5th of a cup doesn't divide evenly into a smaller unit and that's why "we don't do it", but there is nothing to stop the chef from using 9 teaspoons. [Or he can instinctively go up to 45mL on his graduated measuring cup, which almost always has both systems on it!] Teaspoons, tablespoons, ounces, cups, quarts and gallons are all inter-related multiples, and once you internalize it, you can convert like a boss. While I'm sure it's lovely that metric measures divide by 2 and 5, that's all they divide by, so in terms of divisors, you've lost 3, 4, 6, 8... So if it really is about dividing things usefully without resorting to fractions, then using a system that is nothing but multiples of 10 is a handicap, when we've had systems with lovely 12s and 16s with many different options for dividing them up. But the metric people can simply chop up the measures even more finely and claim victory. For example, currency: it was in multiples of 16 or 8 which allowed for limited permutations. Decimalization chopped it into pennies, and we find 100 gradations in every pound sterling. All that did is make base-10 math easier for bean counters, and confuse people on the streets with a mystifying array of coinage. [Mental math indicates that it must increase the volume of coins per average transaction, as well.] If a basic customary unit of length is an inch, many people can put two fingers together and estimate that on the human scale. But who can estimate or eyeball a millimeter? Oh, and, have you ever found a nice British recipe in metric, shopped at your American grocery store, and prepared that in your American kitchen with your Fahrenheit range? You will eventually want to tip it all in the rubbish bin. Adam Ragusea suggests as much: https://youtu.be/TE8xg3d8dBg?si=SD8wLxD6ib6InLX4 https://youtu.be/TE8xg3d8dBg?si=SD8wLxD6ib6InLX4
chthonicdaemon 1y ago
I think there is true utility in choosing a unit scheme that matches your number scheme. So we use decimal numbers, makes sense to use decimal units. It seems you're arguing that the real mistake is using decimal numbers to begin with?

tokai 1y ago

>evenly divisible by at least 3 or 4 Irrelevant with a decimal system.

chungy 1y ago
It's not irrelevant, you can choose something like 12 to make all your factors out of. It's a particular strength of working in feet and yards.
- henrikschroder 1y ago
  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.
IAmBroom 1y ago
Irrelevant if you are working with computers and digital equipment. Highly relevant if you are using T-squares, compasses, and dividing calipers.
- mfost 1y ago
  It's just a matter of working with base elements that are divisible by 3 and 4 really. So instead of buying 100cm planks, buy 120cm planks?
  - philwelch 1y ago
    And eventually you’re going to want a name for your 120cm unit. But that’s not allowed in metric because any named unit has to be base 10.
    - olddustytrail 1y ago
      It has a name. It's the plank length.
- tempestn 1y ago
  It's pretty relevant with computers. If we were used to working in base-8 or base-16 in everyday life, numerous aspects of programming would be simplified.
henrikschroder 1y ago
The biggest source of communication issues around these unit systems is that in metric, you're supposed to reach for decimals when working with the units, and in imperial, you're supposed to reach for fractions when working with the units. Which is why the imperial lovers all cry out about their fractions not "working" in metric. Yes, exactly, that is the point. They don't understand that they're reaching for a tool they shouldn't be reaching for, and then they blame the unit system for it.

foobiekr 1y ago

Base 60 is genuinely the best option.

layer8 1y ago
That would have broken ASCII.

forty 1y ago

Don't you think base 10 was used simply because it conveniently matches the number of fingers of Humans?

nancyminusone 1y ago
Of course... But - look at your open hand right now. Count the number of segments on your 4 fingers - it's 12. You can even use your thumb as a pointer and count one handed.
- tempestn 1y ago
  Or forget about the thumbs and just count fingers. 8 would be a better base than 10 for sure, and arguably better than 12. (Easier doubling and halving, easier binary conversions, but fewer integer factors and fewer digits.)
paipa 1y ago
Base 6 has six digits, 0 through 5. Perfect fit for the human hand, you get place value notation and counting to 35 decimal (55 seximal) for free. Base 6 would've been the real deal.

empath75 1y ago

There's two reasons to use a measurement system -- one of those is for sort of every day work -- cooking, home carpentry and the like, and in that case, having something like the imperial system is nice, because you can divide things usefully. The _other_ reason to use a measurement system is for doing _science_, and for that, having everything in base ten makes things _immensely_ easier, especially if you're working the math out by hand

henrikschroder 1y ago
> because you can divide things usefully. Again, this is just familiarity. You think it's super neat that you can divide a cup of whatever by 2 or 3 or 4, but if I tell you to divide it by 5, you're gonna deflect and ask me "who does that?!?" Imperial works neatly for a small domain of problems, and is useless outside that domain. Metric is less neat in that small domain, but works equally well everywhere.
- AStonesThrow 1y ago
  Well no... Firstly, we can divide a cup by 2, 3, and 4 in the kitchen because those are common measuring-cup sizes. Nobody is prevented from using a fractional size: if I divide a cup by 5 then I have 1/5th of a cup, nothing more and nothing less. While 1/4th of a cup is 2 oz, and 1/3rd of a cup is 16 teaspoons, 1/5th of a cup doesn't divide evenly into a smaller unit and that's why "we don't do it", but there is nothing to stop the chef from using 9 teaspoons. [Or he can instinctively go up to 45mL on his graduated measuring cup, which almost always has both systems on it!] Teaspoons, tablespoons, ounces, cups, quarts and gallons are all inter-related multiples, and once you internalize it, you can convert like a boss. While I'm sure it's lovely that metric measures divide by 2 and 5, that's all they divide by, so in terms of divisors, you've lost 3, 4, 6, 8... So if it really is about dividing things usefully without resorting to fractions, then using a system that is nothing but multiples of 10 is a handicap, when we've had systems with lovely 12s and 16s with many different options for dividing them up. But the metric people can simply chop up the measures even more finely and claim victory. For example, currency: it was in multiples of 16 or 8 which allowed for limited permutations. Decimalization chopped it into pennies, and we find 100 gradations in every pound sterling. All that did is make base-10 math easier for bean counters, and confuse people on the streets with a mystifying array of coinage. [Mental math indicates that it must increase the volume of coins per average transaction, as well.] If a basic customary unit of length is an inch, many people can put two fingers together and estimate that on the human scale. But who can estimate or eyeball a millimeter? Oh, and, have you ever found a nice British recipe in metric, shopped at your American grocery store, and prepared that in your American kitchen with your Fahrenheit range? You will eventually want to tip it all in the rubbish bin. Adam Ragusea suggests as much: https://youtu.be/TE8xg3d8dBg?si=SD8wLxD6ib6InLX4 https://youtu.be/TE8xg3d8dBg?si=SD8wLxD6ib6InLX4

chthonicdaemon 1y ago

I think there is true utility in choosing a unit scheme that matches your number scheme. So we use decimal numbers, makes sense to use decimal units. It seems you're arguing that the real mistake is using decimal numbers to begin with?