Because numbers written in the given number system don’t necessarily match up with the words in the given language. Take the number 475, for example. In English that reads as ‘four hundred seventy five’. When you look at the number, the symbols correspond to the words. You have 4 (four, in position of hundreds), 7 (seven, in position of tens), and 5 (five).
Now consider a language which uses a different base, base 12 for example. The same number might be read as ‘three gross three dozen seven’. But when you look at the number, there is no symbol representing three, and no symbol representing seven in the position of units. The number is hard to parse and read out, and it is also hard to write when going by the words.
Although thirteen to nineteen show a clear connection to the older style of saying the ones place before the tens place (“four and twenty blackbirds baked into a pie…”). Spanish has special words for eleven (once—pronounced ohn-say) to fifteen (quince) before moving to a standard form for sixteen (dieciséis—ten and six) through nineteen diecinueve—ten and nine).
Not really. French is effectively base-10, but with some vestigial names. English is basically the same -- we say eleven instead of ten-one. The only real difference is that we say eighty instead of quatre-vingt. But neither system maintains any semblance of base-20 beyond that.
A more familiar sense of disorientation of language mismatch would be when metric users encounter imperial units and their arbitrary bases.
You can get a very close analog by comparing English numbers (base 1,000) to Chinese numbers (base 10,000). The terminology coincides (with a couple asterisks) for numbers below 10,000, but above 10,000 it's essentially impossible to do mental conversion of numbers even though all the digits are the same.
Trying to operate simultaneously in a base 20 system and a base 10 system would be much worse than that, since all the digits would be different between representations.
I thought nonante (and septante, octante) were only used in Zwitserland and Belgium?
(If true, it would be a bit like saying in some dialects colour is written as color, while the latter is only(?) used in the States?)
So do the Danish, however the Danish language only counts the 10s in base-20. The 100s, the 1000s, the decimals and so on are still in base-10. So what ends up happening is that the numbers 40-90 are simply numbers with weird names and a perfect mapping to base 10. I don’t know how French count, but perhaps it is similar. This does not appear to be the case with Inuit counting.
You could certainly write numbers above 9 as their base-10 representation. For example, 12. That number can be represented in both Kaktovik numerals and arabic. But you end up with an extra digit in arabic numerals, because you're supposed to carry the 1 once you reach 10.
Instead, we represent hexadecimal (base-16) in programming as 0-9 AND a-f, for example, A is 10, B is 11, C is the same as saying 12.
If you have multiple digits, like A4C in hex, it gets more complicated to figure out what number you're talking about in base-10. A is 10, 4 is 4, C is 12. To convert base-10 number you need to do this equation: (10 * 16 * 16) + (4 * 16) + (12) = 2636
It explains the problem: they are not a good way to express a base-20 numbering system used in the language.
(Now, you could easily augment or modify them to do that—and the creators [0] of this system initially tried that but were unsatisfied—the common way of expressing base-16 using arabic numerals plus the first six letters of the alphabet as added numerals is an example, but if you aren't using a language whose existing writing system conventionally users Arabic numerals, why would you?)
I guess I was confused about that. I didn't think that a numbering system was considered part of a language. I always thought that a numbering system was more of an ADAPTER pattern (like Hexadecimal, binary, and octal are all "addons" to the English language).
The way that a language constructs number words can have an implied base; English has an implied based 10 in most of the language (though 0-19 uses a different structure that could imply base 20 if it continued.) Most germanic and romance languages I think do something similar, though, e.g. French (FR-fr, but not some other dialects) breaks back into an implicit base-20 at 60-99.
Having numerals that map well to words reduces friction for practical arithmetic.
It used to be common to count by scores (twenties) in English, though this has mostly disappeared other than for poetical/literary usage (e.g., "Four score and seven years ago").
Dozens (twelves) were also quite common, and are still in everyday use for certain commodities (eggs, donuts, etc.).
> It used to be common to count by scores (twenties) in English, though this has mostly disappeared
Counting by scores isn't enough to be base 20. The special quantities designated by the system are still 10, 100, and 1000, an obvious sign that the numbers are conceived of in base 10. If the system pivoted around 20, 400, and 8000 (as the dozen/gross system you mention does), then you could (and should) call it a base 20 system.
Dozens even go out to another level of base 12, now that I think about it. A gross (144) is twelve dozen, so you could have something like 6 gross, 5 dozen, and 3.
The long (=great) hundred is 120, while the long thousand is 1200. It seems pretty understanding, so I wonder if anyone ever needed to use a long hundred thousand and worked out what that was supposed to be.
I am curious as to why Arabic numerals (or any number system, for that matter) are inadequate for a language.