This immediately brought to mind the immortal words of Terry Pratchett/Neil Gaiman in "Good Omens", pertaining old british money:
> It helps to understand the antique finances of the Witchfinder Army if you know the original British monetary system: Two farthings = One Ha'penny. Two ha'pennies = One Penny. Three pennies = A Thrupenny Bit. Two Thrupences = A Sixpence. Two Sixpences = One Shilling, or Bob. Two Bob = A Florin. One Florin and One Sixpence = Half a Crown. Four Half Crowns = Ten Bob Note. Two Ten Bob Notes = One Pound (or 240 pennies). One Pound and One Shilling = One Guinea.
The British resisted decimalized currency for a long time because they thought it was too complicated.
An amusing thing about that joke is that the florin (2 shilling coin, 1/10 pound) was introduced as a half-hearted move towards decimalisation in the 1800s, and after proper decimalisation in 1970 the florin continued to be used as the 10p coin (still 1/10 pound). It was finally abolished in about 1990 when they made the coin smaller and less expensive to manufacture. https://en.wikipedia.org/wiki/Florin_(British_coin)
(The Imperial system was another half-hearted move towards decimalisation: the biggest changes were to define the gallon as the volume of 10 lb water, and change the number of fl.oz in a pint from 16 to 20 so that a fl.oz weighs exactly an ounce - https://en.wikipedia.org/wiki/Imperial_units)
That doesn't sound right, since in the system we still use in America a pint is 16 oz and a fluid ounce of water still weighs (very close to) one ounce.
That’s because American customary units predate the British Imperial units reform of 1825 - Americans still use the Queen Anne wine gallon for liquid volume and the Winchester bushel for dry volume. (The Imperial gallon more closely matches the earlier ale gallon.)
It’s common for people to refer to all British units as “Imperial” but that name doesn’t apply to the pre-1825 units used in the US. Some of the confusion is that the Imperial reform only made significant changes to volume measures: the yard and avoirdupois weights remained basically the same.
My parent was claiming that the 1825 reform is what made the Imperial fluid ounce weigh one ounce, though, but the pre-1825 units as used in the US also have that property.
No, an ounce avoirdupois is 454g / 16 == 28.4g but a Queen Anne wine fluid ounce is 231 x 2.54^3 / (16 x 8) == 29.6g which is a difference of about 4%. The imperial fluid ounce is exact, because the weight and volume units were designed to work the same way as the metric system. The older units had no such connection.
There is a mnemonic rhyme for the imperial system: “a pint of water weighs a pound and a quarter”. This is exactly precise, due to the way the imperial gallon was defined.
There is a mnemonic rhyme for US customary units: “a pint is a pound the world around”. This is wrong because the first part has a measurement error of 4%, and the second part is wrong because the error is 25% outside the USA.
Since water is not a fixed density you can't have an exact conversion unless you specify a lot of other things. For example, a US fluid ounce of water at 212F weighs almost exactly one US ounce ;)
Yes, I did not specify which standard temperature and pressure were required for the correspondence to work, because I thought that was an obvious requirement when defining units in the metric style. In fact stp differs between the metric system and the imperial system. There was no stp for the Queen Anne wine gallon because there was no intention to link units of volume and weight.
The Wikipedia article I linked above says, “The 1824 Act defined as the volume of a gallon to be that of 10 pounds (4.54 kg) of distilled water weighed in air with brass weights with the barometer standing at 30 inches of mercury (102 kPa) at a temperature of 62 °F (17 °C).”
As far as I know, that a fluid ounce of water weighs an ounce at the boiling point is a complete coincidence, but it does illustrate that joining weight and volume this way is tricky business.
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.
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.
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".)
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.
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.
> 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.
> 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.
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).
> 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.
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.
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.
> It helps to understand the antique finances of the Witchfinder Army if you know the original British monetary system: Two farthings = One Ha'penny. Two ha'pennies = One Penny. Three pennies = A Thrupenny Bit. Two Thrupences = A Sixpence. Two Sixpences = One Shilling, or Bob. Two Bob = A Florin. One Florin and One Sixpence = Half a Crown. Four Half Crowns = Ten Bob Note. Two Ten Bob Notes = One Pound (or 240 pennies). One Pound and One Shilling = One Guinea. The British resisted decimalized currency for a long time because they thought it was too complicated.