3 ms·

This got me thinking if in general (outside computing) it was a good choice having numbers represented the way they are. What if we had 1234 read as "four thous

This got me thinking if in general (outside computing) it was a good choice having numbers represented the way they are. What if we had 1234 read as "four thousand, three hundred and twenty one"? Or even more different than how we pronounce it today - in order to read the number left-to-right to spell it "one and twenty and three hundred and four thousand"! This way the last digit lingering in your mind would be the one representing the most significant part of the given number (unlike the current practice of hearing first then tuning off for the less interesting smaller parts). Would it have been practical?

jerf 12y ago
If you take into account the fact that you can obtain the order-of-magnitude for most "human" numbers without actually focusing on them, then putting the most-significant digit first in the stream makes sense. 30 is easy to see, even if you look at the 3 you can at least tell there's two digits. 12,048 is pretty easy. Even 8,293,254 isn't that hard to order-of-magnitude from the near-fovea while you're focused on the 8. By the time you get into the larger numbers that are hard, well, they're hard under either order so it's a wash.
- restalis 12y ago
  At reading, one may be indeed hit at first by the most significant digit ('8' in your last example) that is somewhat useful, but the reader can't easily figure out digit's order of magnitude without reading the entire number. There's actually more. The reader can't spell the number right away, as it has to be read entirely and compiled in mind first. This compilation involves counting all digits in the given number to determine the number's size, then starting again by interpreting and spelling accordingly in its order each digit and its designation. This double-pass doesn't appear that efficient to me. On the other hand, if the number from your last example would be written backwards (452'392'8), its reading and interpretation would come efficiently in one pass ("four fifty and two hundred, three ninety and two hundred thousand, and eight million"). Even when all we're interested in would be the most significant digit and its order of magnitude, that would still be faster to determine (i.e. again, in one pass).
  - jerf 12y ago
    "but the reader can't easily figure out digit's order of magnitude without reading the entire number." Yes, they can; that was my entire point. Human-sized numbers fit within the eye's fovea. Numbers that don't fit easily within the fovea require effort under either scheme. Your model of having to go digit-by-digit is a computer's scanning model, not a human perception model; we do not scan that way, we scan in fovea-sized chunks, which are smaller than people may think because the brain is very good at interpolating before the information hits the conscious mind, but is still large enough to fit "millions" in quite comfortably.
chucksmash 12y ago
> Would it have been practical? My gut feeling is that it would have been less so than the current solution. Our current representation is great for skimming in a language written LtR. Placing the most significant digit all the way to the right would be like putting the lead paragraph of an article last.
- aikah 12y ago
  I wonder if some languages write figures RtL , I'm curious about it.
  - zerocrates 12y ago
    Arabic, which is of course normally right-to-left, uses left-to-right ordering for numerals.
_kst_ 11y ago
It wasn't exactly a deliberate choice. The number system we use was imported to Europe from Arabia. In Arabic, the number 1234 is written with the most significant digit on the left -- but Arabic is written right-to-left, so it's actually little-endian. When they were introduced to Europe (with the help of Fibonacci), the convention of putting the most significant digit on the left was retained, but since European languages are written left-to-right the notation magically became big-endian. The fact that the Roman numeral system that it replaced was also big-endian was likely an influence.

jerf 12y ago

If you take into account the fact that you can obtain the order-of-magnitude for most "human" numbers without actually focusing on them, then putting the most-significant digit first in the stream makes sense. 30 is easy to see, even if you look at the 3 you can at least tell there's two digits. 12,048 is pretty easy. Even 8,293,254 isn't that hard to order-of-magnitude from the near-fovea while you're focused on the 8. By the time you get into the larger numbers that are hard, well, they're hard under either order so it's a wash.

restalis 12y ago
At reading, one may be indeed hit at first by the most significant digit ('8' in your last example) that is somewhat useful, but the reader can't easily figure out digit's order of magnitude without reading the entire number. There's actually more. The reader can't spell the number right away, as it has to be read entirely and compiled in mind first. This compilation involves counting all digits in the given number to determine the number's size, then starting again by interpreting and spelling accordingly in its order each digit and its designation. This double-pass doesn't appear that efficient to me. On the other hand, if the number from your last example would be written backwards (452'392'8), its reading and interpretation would come efficiently in one pass ("four fifty and two hundred, three ninety and two hundred thousand, and eight million"). Even when all we're interested in would be the most significant digit and its order of magnitude, that would still be faster to determine (i.e. again, in one pass).
- jerf 12y ago
  "but the reader can't easily figure out digit's order of magnitude without reading the entire number." Yes, they can; that was my entire point. Human-sized numbers fit within the eye's fovea. Numbers that don't fit easily within the fovea require effort under either scheme. Your model of having to go digit-by-digit is a computer's scanning model, not a human perception model; we do not scan that way, we scan in fovea-sized chunks, which are smaller than people may think because the brain is very good at interpolating before the information hits the conscious mind, but is still large enough to fit "millions" in quite comfortably.

chucksmash 12y ago

> Would it have been practical? My gut feeling is that it would have been less so than the current solution. Our current representation is great for skimming in a language written LtR. Placing the most significant digit all the way to the right would be like putting the lead paragraph of an article last.

aikah 12y ago
I wonder if some languages write figures RtL , I'm curious about it.
- zerocrates 12y ago
  Arabic, which is of course normally right-to-left, uses left-to-right ordering for numerals.

_kst_ 11y ago

It wasn't exactly a deliberate choice. The number system we use was imported to Europe from Arabia. In Arabic, the number 1234 is written with the most significant digit on the left -- but Arabic is written right-to-left, so it's actually little-endian. When they were introduced to Europe (with the help of Fibonacci), the convention of putting the most significant digit on the left was retained, but since European languages are written left-to-right the notation magically became big-endian. The fact that the Roman numeral system that it replaced was also big-endian was likely an influence.