5 ms·

Divisible by both 2 and 3, which decimal, well 10s, isn't. Archaic in today's deals of prices ending in 99 pence or cents, it made a lot of sense to have thing

Divisible by both 2 and 3, which decimal, well 10s, isn't. Archaic in today's deals of prices ending in 99 pence or cents, it made a lot of sense to have things easily divisible by both 2s and 3s, and fractions of such.

dylan604 6y ago
Again, someone saying math by 10s is hard. Explain to me how moving the decimal point is hard. No dividing required. 1km = 1000m = 100000cm 1m = 5280ft = 63360in Yup, math by 10s is definitely harder
- gwd 6y ago
  > 1km = 1000m = 100000cm > 1m = 5280ft = 63360in How many times have you ever needed to know how many centimeters in a kilometer? Is that something you do a lot? On the other hand, suppose you have 1x1 km of land three children, and you want to divide the inheritance equally. What do you do? Give two of them 1km x 333.33m of land, and the oldest one 1km x 333.34m? If you were using miles and you had 1 x 1 mile of land, you could give each one exactly 1m x 1760ft of land.
  - iso947 6y ago
    So what if I have 100 acres of land and want to split it in three?
    - gwd 6y ago
      You give each one 33 1/3 acres. Just it's easy to make 1/3 mile by breaking it down to 1760 feet, it's easy to make 1/3 acre by breaking 660ft x 66ft down to 220ft x 66ft ([EDIT] or 660ft x 22ft, if you want to keep it 1 furrow long for easier plowing). And if you needed to, you could break one of the feet down into 1/3 foot (4 inches). That's a key factor in all these "archaic" measurement systems.
  - squiggleblaz 6y ago
    > On the other hand, suppose you have 1x1 km of land three children, and you want to divide the inheritance equally. What do you do? Give two of them 1km x 333.33m of land, and the oldest one 1km x 333.34m? This is a silly example. You're going to give them all about a third of the land. But the precise measures are going to depend on the land. Perhaps one of them got the steep hill and a bit more to compensate. Or the creek serves as a division between child 2 and child 3 but that just so happens to mean that child 3 gets a wee bit more than half the remainder. In any case, you aren't going to give them 1 km x 333.33 m unless the law of your state really stangely provides a maximum precision of 10 cm. The system is infinitely divisible and the survey happens once with a fair degree of precision. There are good arguments for the convenience of non-metric systems. This one is just a terrible one.
    - gwd 6y ago
      > In any case, you aren't going to give them 1 km x 333.33 m unless the law of your state really stangely provides a maximum precision of 10 cm. Nit: That's 1cm precision, which I chose because that's about where it should be clear to everyone that it really doesn't matter. A slightly unreasonable person might be miffed about 1m; a very unreasonable person might be miffed about 10cm; but if you're miffed about your older brother getting 1cm more than you, I think you're going into mental illness territory.
      - Symbiote 6y ago
        Therefore your example doesn't support your argument. A division to 333.3+333.3+333.4 works to the satisfaction of all parties involved. You can also write 333⅓m, no-one prevents you from using fractions with the metric system. You have the same assumption implicit in your square mile of land, as you assume everyone is satisfied with measuring to the nearest inch (or half-foot, or whatever is realistic with the measuring device).
        gwd 6y ago
        > You can also write 333⅓m, no-one prevents you from using fractions with the metric system. ...except that nobody does. And that would pretty much void the entire point of the metric system, which is to "make the math easier" by making everything a power of 10. > A division to 333.3+333.3+333.4 works to the satisfaction of all parties involved. Sure, you can, but it's less satisfying. Remember how we got here in the discussion: A: "Miles are easier because you can divide by 3 evenly." B: "How is the math easier? <Does math converting km to cm, miles to inches>" Me: "How often do you convert miles to inches or km to cm, compared to how often do people have to divide distances by 3?" I'm not saying that I think we should all stick with / switch back to using furlongs. On the whole I think having a simple universal system like the metric system is better. But there is a trade-off involved.
  - throw0101a 6y ago
    > Give two of them 1km x 333.33m of land, and the oldest one 1km x 333.34m? If your children are going to fight over 1cm of land, I think you've got bigger personal problems than mathematical division.
- paulmooreparks 6y ago
  He's not saying math is hard in base 10. Moving the decimal is easy in any base. The problem is the base itself. Items were, and often still are, sold by the dozen precisely because 12 is evenly divisible by 2 and 3. One may split a dozen into 6 of 2, 4 of 3, 3 of 4, or 2 of 6. Quantities of 10, however, may be split into 5 of 2 or 2 of 5. Not as many options for subdivision. Had we evolved 6 fingers on each hand, this wouldn't be an issue. Likewise, the original article is about harmonising the length of a mile with the sides of an acre, again for convenient subdivision.
- squiggleblaz 6y ago
  I think you misread the parent comment. Dividing by 10s is easy, but useless. If you have a kilo of rice, you can easily divide it into two or even three equal subdivisions, without scales or with primitive scales, if you trust the participants. And then you can divide the shilling that you paid for it into three. The advantages of the old systems exist but they have largely been superseded by modern technology and small currency subdivisions. (Remember that a new penny is worth a lot less than an old penny was, even though a new penny is nominally worth a bit under "tuppence ha'penny".) Not advocating the old system. I'm 100% metric.
- dalbasal 6y ago
  I read your first comment, and didn't understand who you were referring to. Now I get it. It's actually real interesting. It's not that base 10 "math" is harder. It's specific "math" of everyday life and commerce that was easier using those systems. You could pay using fewer coins, for example. You buy butter in in ppunds, half pounds, etc.. These corresponded to money denominations.
JdeBP 6y ago
You clearly haven't worked out how many shillings there are to a pound, or to a crown for that matter, from M. Pratchett's explanation. The whole foundation of this "10 isn't divisible by 3" and "it only has prime factors 2 and 5" argument is fundamentally flawed, undermined by the fact that (as the headlined article quite clearly pointed out) several old units used vigesimal, which also is only evenly divisible by two prime factors: 2 and 5. Indeed, reading the headlined article reveals the important point that there are eight furlongs to a mile, which is only evenly divisible by one prime factor, putting the lie even more to the "it's because they're also divisible by 3" arguments. There's a multiple of 4 in the headlined article. And other units elsewhere were subdivided into 16ths. Some were sometimes subdivided into 14ths, for reasons that this article touches upon but doesn't actually go into in enough depth: namely that standards in different places were so out of synch in Mediaeval Europe that multiplying by 16 in one town sometimes gave the same length/weight/whatever as multiplying by 14 in another town, and people formalized that to try to make things work. The idea that the pre-cursors to the metric system were some wonderfully Babylonian system composed purely of 12s and 60s is nonsense.
- zhte415 6y ago
  There are eight furlongs to a mile because a horse has four feet. I thought this was obvious.

dylan604 6y ago

Again, someone saying math by 10s is hard. Explain to me how moving the decimal point is hard. No dividing required. 1km = 1000m = 100000cm 1m = 5280ft = 63360in Yup, math by 10s is definitely harder

gwd 6y ago
> 1km = 1000m = 100000cm > 1m = 5280ft = 63360in How many times have you ever needed to know how many centimeters in a kilometer? Is that something you do a lot? On the other hand, suppose you have 1x1 km of land three children, and you want to divide the inheritance equally. What do you do? Give two of them 1km x 333.33m of land, and the oldest one 1km x 333.34m? If you were using miles and you had 1 x 1 mile of land, you could give each one exactly 1m x 1760ft of land.
- iso947 6y ago
  So what if I have 100 acres of land and want to split it in three?
  - gwd 6y ago
    You give each one 33 1/3 acres. Just it's easy to make 1/3 mile by breaking it down to 1760 feet, it's easy to make 1/3 acre by breaking 660ft x 66ft down to 220ft x 66ft ([EDIT] or 660ft x 22ft, if you want to keep it 1 furrow long for easier plowing). And if you needed to, you could break one of the feet down into 1/3 foot (4 inches). That's a key factor in all these "archaic" measurement systems.
- squiggleblaz 6y ago
  > On the other hand, suppose you have 1x1 km of land three children, and you want to divide the inheritance equally. What do you do? Give two of them 1km x 333.33m of land, and the oldest one 1km x 333.34m? This is a silly example. You're going to give them all about a third of the land. But the precise measures are going to depend on the land. Perhaps one of them got the steep hill and a bit more to compensate. Or the creek serves as a division between child 2 and child 3 but that just so happens to mean that child 3 gets a wee bit more than half the remainder. In any case, you aren't going to give them 1 km x 333.33 m unless the law of your state really stangely provides a maximum precision of 10 cm. The system is infinitely divisible and the survey happens once with a fair degree of precision. There are good arguments for the convenience of non-metric systems. This one is just a terrible one.
  - gwd 6y ago
    > In any case, you aren't going to give them 1 km x 333.33 m unless the law of your state really stangely provides a maximum precision of 10 cm. Nit: That's 1cm precision, which I chose because that's about where it should be clear to everyone that it really doesn't matter. A slightly unreasonable person might be miffed about 1m; a very unreasonable person might be miffed about 10cm; but if you're miffed about your older brother getting 1cm more than you, I think you're going into mental illness territory.
    - Symbiote 6y ago
      Therefore your example doesn't support your argument. A division to 333.3+333.3+333.4 works to the satisfaction of all parties involved. You can also write 333⅓m, no-one prevents you from using fractions with the metric system. You have the same assumption implicit in your square mile of land, as you assume everyone is satisfied with measuring to the nearest inch (or half-foot, or whatever is realistic with the measuring device).
      - gwd 6y ago
        > You can also write 333⅓m, no-one prevents you from using fractions with the metric system. ...except that nobody does. And that would pretty much void the entire point of the metric system, which is to "make the math easier" by making everything a power of 10. > A division to 333.3+333.3+333.4 works to the satisfaction of all parties involved. Sure, you can, but it's less satisfying. Remember how we got here in the discussion: A: "Miles are easier because you can divide by 3 evenly." B: "How is the math easier? <Does math converting km to cm, miles to inches>" Me: "How often do you convert miles to inches or km to cm, compared to how often do people have to divide distances by 3?" I'm not saying that I think we should all stick with / switch back to using furlongs. On the whole I think having a simple universal system like the metric system is better. But there is a trade-off involved.
- throw0101a 6y ago
  > Give two of them 1km x 333.33m of land, and the oldest one 1km x 333.34m? If your children are going to fight over 1cm of land, I think you've got bigger personal problems than mathematical division.
paulmooreparks 6y ago
He's not saying math is hard in base 10. Moving the decimal is easy in any base. The problem is the base itself. Items were, and often still are, sold by the dozen precisely because 12 is evenly divisible by 2 and 3. One may split a dozen into 6 of 2, 4 of 3, 3 of 4, or 2 of 6. Quantities of 10, however, may be split into 5 of 2 or 2 of 5. Not as many options for subdivision. Had we evolved 6 fingers on each hand, this wouldn't be an issue. Likewise, the original article is about harmonising the length of a mile with the sides of an acre, again for convenient subdivision.
squiggleblaz 6y ago
I think you misread the parent comment. Dividing by 10s is easy, but useless. If you have a kilo of rice, you can easily divide it into two or even three equal subdivisions, without scales or with primitive scales, if you trust the participants. And then you can divide the shilling that you paid for it into three. The advantages of the old systems exist but they have largely been superseded by modern technology and small currency subdivisions. (Remember that a new penny is worth a lot less than an old penny was, even though a new penny is nominally worth a bit under "tuppence ha'penny".) Not advocating the old system. I'm 100% metric.
dalbasal 6y ago
I read your first comment, and didn't understand who you were referring to. Now I get it. It's actually real interesting. It's not that base 10 "math" is harder. It's specific "math" of everyday life and commerce that was easier using those systems. You could pay using fewer coins, for example. You buy butter in in ppunds, half pounds, etc.. These corresponded to money denominations.

JdeBP 6y ago

You clearly haven't worked out how many shillings there are to a pound, or to a crown for that matter, from M. Pratchett's explanation. The whole foundation of this "10 isn't divisible by 3" and "it only has prime factors 2 and 5" argument is fundamentally flawed, undermined by the fact that (as the headlined article quite clearly pointed out) several old units used vigesimal, which also is only evenly divisible by two prime factors: 2 and 5. Indeed, reading the headlined article reveals the important point that there are eight furlongs to a mile, which is only evenly divisible by one prime factor, putting the lie even more to the "it's because they're also divisible by 3" arguments. There's a multiple of 4 in the headlined article. And other units elsewhere were subdivided into 16ths. Some were sometimes subdivided into 14ths, for reasons that this article touches upon but doesn't actually go into in enough depth: namely that standards in different places were so out of synch in Mediaeval Europe that multiplying by 16 in one town sometimes gave the same length/weight/whatever as multiplying by 14 in another town, and people formalized that to try to make things work. The idea that the pre-cursors to the metric system were some wonderfully Babylonian system composed purely of 12s and 60s is nonsense.

zhte415 6y ago
There are eight furlongs to a mile because a horse has four feet. I thought this was obvious.