Which direction do numbers go?
Feels like a weird thing to not have known, but now I know: the symbols we refer to in the West as “Arabic numerals,” aka regular ol’ numbers, while indeed (“Western”) Arabic, are not the (“Eastern”) symbols used in conjunction with the actual Arabic alphabet.
While learning to count in Arabic, it occurred to me that English having acquired the (Western) Arabic numerals from a language written right-to-left, the way we write numbers in left-to-right English is arguably backwards in relation to the rest of written language. This probably would not have occurred to me had I not just taken a class on digital logic, where the basic material often involves converting between decimal and binary (or hexadecimal if you’re fancy). The understanding required to do that, which generally goes unspoken even though everyone who has mastered counting does know on some level know it, is that a “number” is a collection of symbols representing multiplications of each power of whatever base you happen to be counting in, going up from the right to the left, starting with the base to the power of 0. So the number 6358, in our base-10 system, is implicitly understood as (6 × 103) + ( 3 × 102) + (5 × 101) + (8 × 100), or if you prefer, (6 × 1000) + (3 × 100) + (5 × 10) + (8 × 1).
When you’re reading a number in English, your eyeball hits the most significant digit, i.e. the one on the left which is multiplied by the largest power, first; but you don’t actually know what that digit means until your eyeball hits the least significant digit, i.e. the one on the right. The fact that the number 6358 starts with a 6 means nothing about its magnitude until I know that there are four digits making up the number. In regular life nobody could possibly care about or even notice this discrepancy with how the rest of the language works. But if you wanted to convert numbers between different bases, the first thing you might do is write out all of the powers of the base you have, from 0 up to the highest power needed to give you the number you want– and the only reasonable way to do that is starting at the right and working to the left, since that’s the order in which the final number is going to be written. Similarly, any basic arithmetic operations have to proceed in a right-to-left fashion, since you need to add/multiply/whatever the digits in the smaller positions in order to bring any carries forward to the larger.
Numbers, then, are written in reverse from the rest of the English language in terms of the direction in which you need to work through them. The names we give to numbers fixes the “don’t know what the first digit means until your eye hits the last one” problem, if that could be called a problem; in general the most significant digit is stated first, using a word that tells you how many digits there are going to be in the number before you actually know all of them. The word “twenty nine” tells you from the first word that there are only two digits. In contrast, the Arabic words for numbers reads them out right to left, giving them in order of least to most significant; so 29, or ٢٩, is read “tis’a wa-’ishrun”; first there’s a 9, tis’a, and then a 20, ‘ishrun. You don’t know the order of magnitude of the number until it’s finished being stated, but proceeds in what seems to be a more logical and extensible fashion, from smallest to largest.
So for instance this page states that “numerals in Arabic are written from left to right, while letters are written from right to left.” Unless it’s perhaps referring to usual stroke order, in which case I have no idea, this seems to me to be incorrect or at least Anglocentric. An Anglophone would consider the “direction” a number goes to be from most to least significant digit, but there is no reason that insist that’s the case, and several good reasons to say it’s not and the real “direction” of a number is from least to most significant digit. In which case numerals in Arabic are written right to left, just like they secretly are in English.
Today’s journey through the Hajar mountains, from Sohar to Nizwa by way of Ibri:
