Yesterday, a friend of mine who is studying Middle Eastern Studies showed me her phone. I immediately noticed that she had changed the language to Arabic, and for some reason, my eyes went to the digital clock. It said “١٧:١١”, and I asked her what time it was. She responded that it’s eleven past seventeen. I thought about it for a minute and exclaimed, “Hang on! You read Arabian text right to left. Why are numbers read left to right?” She didn’t have an answer, and we ended up both being quite puzzled by this. So I did some digging.
Arabian and Mashriki Numerals
It turns out the numerals on her phone were the “Mashriki” numerals:[1]
٩ , ٨ , ٧ , ٦ , ٥ , ٤ , ٣ , ٢ , ١ , ٠
which are also called the Eastern Arabic numerals, as opposed to the more familiar Western Arabic numerals:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
(In fact, in Arabian the numbers are read out loud from left to right, so that the left most number is spoken out first. E.g. the “nine hundred twenty four” in 924).
The Arabic numerals were introduced to Europe by Fibonacci in the 10th century, but the numerals seem to be decended from Brahmi which is from India:
And it just happens that the Brahmi script is typically written left to right![2] So it doesn’t seem unreasonable that the Arabian numerals not only inharieted the system but also the direction it is read.
But the Wrong Way Is the Right Way!
But the arabians should have changed it to fit their scripture rules!
The way we read numbers in nearly all languages is with the most significant digit at the beginning (when reading left to right). That means a number like \(924 = 9\cdot 100 + 2\cdot 10 + 4\cdot 1\) is written with the most significant digit as the first digit the eye sees. This is also how it’s spoken: “nine hundred twenty-four”. So it’s written as spoken, and it gives the most important information first. Perfect, right?
The problem lies in the fact that you really have to read the entire number before you can even know which order of magnitude the first digit has.
The algorithm is to first scan the number and count the number of digits, then go back and read out the number with the proper orders of magnitude. This is quite a wasteful algorithm for such a simple task.
If we reverse the order of the magnitudes, so that the number 924 from before now becomes 429 in the new system, and we would read it as \(4\cdot 1 + 2\cdot 10 + 9\cdot 100".
Here the algorithm is simple, since we know that the first digit is always the ones place. The second digit is always the tenths place. And so on. So we need only do one scan of the number, whereas before we needed two.
It’s quite a simple change.
Side note: Using this system p-adic number representations would also be much nicer to read and write!
Counter arguments
“But it makes no difference because I see the entirety of the number at once!"
This is a fair claim for small integers like 924. But try to read out the following number:
2398472723748634690
It actually takes quite a while. In fact, this task is so difficult for us humans, that we had to introduce commas in our numbers to aid us in keeping track of which order of magnitude we’re at:
2,398,472,723,748,634,690.
And it gets even worse when you have to learn binary because even rather small numbers can have quite long binary representations. For example, 26.523 in binary is 110011110011011.
“I only care about the approximate size."
You still need to count all the digits before you can attach an order of magnitude to the first digit to get an approximation. So the work load is the same.
However, in this case, scientific notation comes and saves us. It’s a different solution to this exact problem!
Sources:
[1] https://en.wikipedia.org/wiki/Arabic_numerals
[2] https://en.wikipedia.org/wiki/Brahmi_script#Characteristics