The order of our numeral notation mirrors the order of our spoken numerals. I’m not sure if there are any languages that consistently order additive numerals from smallest to largest—“two and fifty and three hundred” instead of “three hundred and fifty two”.
>💡Flipping the local ordering of pronunciation: If we’re truly optimizing, we might as well say “twenty and hundred-three” while we’re at it. The first words “and three-” don’t tell you much until you know “three of what”? Whereas “and hundred-three” tells you the order of magnitude as soon as possible.
This suggestion is aesthetically in tension with your principle of ordering from smallest to largest. Why should we go with informativeness for multiplication and small-to-large order for addition? The larger number in a sum is more informative about the size of the value, that is probably why languages tend to pronounce additive numerals from larger to smaller.
I’m not sure if there are any languages that consistently order additive numerals from smallest to largest—“two and fifty and three hundred” instead of “three hundred and fifty two”.
I was curious about this, but the only mention I could see was classical Arabic, which is already mentioned in OP. The other flips brought up on the StackExchange question are all local ordering, where the overall structure of long numbers is still largest-to-smallest. Claude suggests Malagasy orders them backwards based on this source, but Wikipedia disagrees (see the numeral table under Vocabulary; “roapolo sy telo” = “twenty and three”), and the original source for the Malagasy claim is in French.
It’s surprising to me that the smallest->largest order would be so rare. Even if it’s less aesthetically pleasing, you’d think people’d be using it somewhere.
The order of our numeral notation mirrors the order of our spoken numerals. I’m not sure if there are any languages that consistently order additive numerals from smallest to largest—“two and fifty and three hundred” instead of “three hundred and fifty two”.
>💡Flipping the local ordering of pronunciation: If we’re truly optimizing, we might as well say “twenty and hundred-three” while we’re at it. The first words “and three-” don’t tell you much until you know “three of what”? Whereas “and hundred-three” tells you the order of magnitude as soon as possible.
This suggestion is aesthetically in tension with your principle of ordering from smallest to largest. Why should we go with informativeness for multiplication and small-to-large order for addition? The larger number in a sum is more informative about the size of the value, that is probably why languages tend to pronounce additive numerals from larger to smaller.
Interestingly, many languages actually do use the “hundred-three” order. You may be interested in this paper: https://www.nature.com/articles/s41599-023-02506-z, they have a striking geographic distribution.
this is not exactly what you’re asking for, but german swaps the ones and tens digits in spoken language
I was curious about this, but the only mention I could see was classical Arabic, which is already mentioned in OP. The other flips brought up on the StackExchange question are all local ordering, where the overall structure of long numbers is still largest-to-smallest. Claude suggests Malagasy orders them backwards based on this source, but Wikipedia disagrees (see the numeral table under Vocabulary; “roapolo sy telo” = “twenty and three”), and the original source for the Malagasy claim is in French.
It’s surprising to me that the smallest->largest order would be so rare. Even if it’s less aesthetically pleasing, you’d think people’d be using it somewhere.