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What we consider "natural" now is not what was originally considered "natural" during the early centuries of the Hindu-Arabic numerals' journey. In fact, we ca

What we consider "natural" now is not what was originally considered "natural" during the early centuries of the Hindu-Arabic numerals' journey. In fact, we can still see the vestiges of the "low order digits first" convention in some languages even today (for example, in German). Even Greek numbers underwent reversals in the early years (earliest known evidence circa 4th century BC).

Someone 2y ago
> In fact, we can still see the vestiges of the "low order digits first" convention in some languages even today (for example, in German). Also in English, with the numbers thirteen through nineteen (and, fairly well hidden, eleven and twelve)
- somat 2y ago
  I always thought eleven and twelve were remnants from when the system was more base twelveish. It was never actually base 12, that would have required inventing 0, But sometimes I wonder if we would not have been better off sticking with base 12. And before someone chimes in with "base 10 is natural because we have 10 fingers" no we have 8 fingers, by that logic we should be using base 8, but the real winner in using base 12 is count using your finger bones(there are twelve of them) and use your thumb to keep your count, use both hands and you can get to 100(144 in base 10). this is probably why base twelveish was so common, shepards counting sheep. try counting to 100 in base 10 on your fingers, not so natural now is it.
  - Someone 2y ago
    > I always thought eleven and twelve were remnants from when the system was more base twelveish. https://www.etymonline.com/search?q=eleven https://www.etymonline.com/search?q=eleven disagrees. It says eleven means “one left” and twelve “two left”, with an implicit “over ten”. That, to me, doesn’t look like base twelve was leading.
- kstenerud 2y ago
  In French it gets even weirder: 80 is "four 20s" (quatrevingt) 92 is "four 20s and 12" (quatrevingt douze) Not sure where that comes from...
  - rsynnott 2y ago
    Oddly, I believe French as spoken in Belgium actually _does_ have a proper word for 80.
    - Someone 2y ago
      Sextante, octante/huitante and nonante are used for 70, 80, 90 in various French-speaking countries/regions (Suisse, Belgium, parts of Canada (https://en.wikipedia.org/wiki/Acadian_French#Numerals https://en.wikipedia.org/wiki/Acadian_French#Numerals)
  - wakawaka28 2y ago
    I forgot about that one and also the English numbers less than twenty. But in any case, if you consider bigger numbers, the most significant units invariably come first.
    - kstenerud 2y ago
      Yes, because by the time that the bigger numbers were in common usage, the world had settled upon "big endian" reading of numbers. But it's hard to kill an already entrenched system, thus vier-tausend-neun-hundert-acht-und-dreißig (four-thousand-nine-hundred-eight-and-thirty)
      - wakawaka28 2y ago
        It's not mere convention. Reading the most significant digits first lets you abbreviate in an ad-hoc fashion and it also supports adding more precision as the number is being written. "Most significant digit" is a clue that those are the figures people consider most important in general. They want to hear those digits first, abbreviate or round to those higher place values, etc. So, big-endian makes a lot of sense for writing and speaking. Little-endian really offers no advantages for speaking or writing. And in doing arithmetic, decimal answers expand in either direction (multiplication to the more significant, division and roots to the less significant), so you can't say one form is universally preferable there either. So big-endian wins!
da_chicken 2y ago
That still doesn't imply "naturalness". Quite the opposite. It implies that both are natural since both are adopted and both have been switched to after previously adopting the other. Remember, too, that most people consider every system that they learn first as "natural". Like it's equally true that historically people did not select base 10 very often. Base 12 and base 60 were both popular as well if they're even using positional numbering at all. Nevermind how long we went in positional numbering without a zero. Is zero then unnatural? I think it must be. Is "naturalness" even virtuous then?
- kstenerud 2y ago
  "naturalness" is a rather pointless thing to argue over. I only mentioned it in response to the parent (and I only mentioned it in the article to highlight how arbitrary it is). My point in the article was that the numbering system was originally little endian because it made things easier when multidigit numbers grow in magnitude in the same direction as you write (least significant digit to the right in this case as it was a right-to-left writing system at the time). This written ordering was then maintained for compatibility reasons in the parts of the world that eventually settled on left-to-right. And the vocalizations ultimately followed those of the dominant cultures of the times - which used left-to-right (with some vestigial exceptions - see my sister comment).
AnimalMuppet 2y ago
> What we consider "natural" now is not what was originally considered "natural" during the early centuries of the Hindu-Arabic numerals' journey. Which no doubt affected the byte order that the early Hindus and Arabs used for their processors. For processors made in the 20th and 21st centuries, however, the numeral order used by people in those centuries is a more relevant data point. By raw human nature, humans can do it either way. For the humans we have now, with their background, one way is definitely more "natural" than the other. That is, it's more natural to them, because they come with a cultural background.
wakawaka28 2y ago
Do you have any evidence that, say, "three million, one hundred twenty-five thousand, two hundred sixty-nine" would have ever been spoken starting with "nine" and ending with "three million"? I guess that wouldn't be the dumbest thing humans have ever done, but it sure sounds impractical.
- kstenerud 2y ago
  The "dumbness" depends entirely on what you're used to. There's no actual need to lead off with the most significant digit other than convention. "three million, one hundred twenty-five thousand, two hundred sixty-nine" "nine, sixty, two hundred, thousands five, twenty, one hundred, millions three" It could work either way. And in fact, in the early days of the Hindu-Arabic numeral system's penetration into Europe, they actually DID lead off with the least significant digit (although numbers larger than thousands were rarely used, and the archaic wordings have only survived in the ones and tens digits - if at all for a particular language).
  - wakawaka28 2y ago
    >It could work either way. Yes but one of those ways does not support abbreviation or interruption, or fractions. If you see a 9 digit number for example, you might want to just round off to one or two significant digits while reading it. Having the smallest components first presents obstacles to speech in much the same way Roman numerals do.
    - kstenerud 2y ago
      That's also convention talking. Looking at the number 443937215, it's trivial to identify the first two or the last two digits. And for counting digits to get an idea of the magnitude, we use separators like so: 443,937,215 (or 443.937.215 depending on what country you're in). The only difference is whether you estimate this number as "about four hundred and forty million" or "about ten and five hundred million"
      - 2y ago

Someone 2y ago

> In fact, we can still see the vestiges of the "low order digits first" convention in some languages even today (for example, in German). Also in English, with the numbers thirteen through nineteen (and, fairly well hidden, eleven and twelve)

somat 2y ago
I always thought eleven and twelve were remnants from when the system was more base twelveish. It was never actually base 12, that would have required inventing 0, But sometimes I wonder if we would not have been better off sticking with base 12. And before someone chimes in with "base 10 is natural because we have 10 fingers" no we have 8 fingers, by that logic we should be using base 8, but the real winner in using base 12 is count using your finger bones(there are twelve of them) and use your thumb to keep your count, use both hands and you can get to 100(144 in base 10). this is probably why base twelveish was so common, shepards counting sheep. try counting to 100 in base 10 on your fingers, not so natural now is it.
- Someone 2y ago
  > I always thought eleven and twelve were remnants from when the system was more base twelveish. https://www.etymonline.com/search?q=eleven https://www.etymonline.com/search?q=eleven disagrees. It says eleven means “one left” and twelve “two left”, with an implicit “over ten”. That, to me, doesn’t look like base twelve was leading.
kstenerud 2y ago
In French it gets even weirder: 80 is "four 20s" (quatrevingt) 92 is "four 20s and 12" (quatrevingt douze) Not sure where that comes from...
- rsynnott 2y ago
  Oddly, I believe French as spoken in Belgium actually _does_ have a proper word for 80.
  - Someone 2y ago
    Sextante, octante/huitante and nonante are used for 70, 80, 90 in various French-speaking countries/regions (Suisse, Belgium, parts of Canada (https://en.wikipedia.org/wiki/Acadian_French#Numerals https://en.wikipedia.org/wiki/Acadian_French#Numerals)
- wakawaka28 2y ago
  I forgot about that one and also the English numbers less than twenty. But in any case, if you consider bigger numbers, the most significant units invariably come first.
  - kstenerud 2y ago
    Yes, because by the time that the bigger numbers were in common usage, the world had settled upon "big endian" reading of numbers. But it's hard to kill an already entrenched system, thus vier-tausend-neun-hundert-acht-und-dreißig (four-thousand-nine-hundred-eight-and-thirty)
    - wakawaka28 2y ago
      It's not mere convention. Reading the most significant digits first lets you abbreviate in an ad-hoc fashion and it also supports adding more precision as the number is being written. "Most significant digit" is a clue that those are the figures people consider most important in general. They want to hear those digits first, abbreviate or round to those higher place values, etc. So, big-endian makes a lot of sense for writing and speaking. Little-endian really offers no advantages for speaking or writing. And in doing arithmetic, decimal answers expand in either direction (multiplication to the more significant, division and roots to the less significant), so you can't say one form is universally preferable there either. So big-endian wins!

da_chicken 2y ago

That still doesn't imply "naturalness". Quite the opposite. It implies that both are natural since both are adopted and both have been switched to after previously adopting the other. Remember, too, that most people consider every system that they learn first as "natural". Like it's equally true that historically people did not select base 10 very often. Base 12 and base 60 were both popular as well if they're even using positional numbering at all. Nevermind how long we went in positional numbering without a zero. Is zero then unnatural? I think it must be. Is "naturalness" even virtuous then?

kstenerud 2y ago
"naturalness" is a rather pointless thing to argue over. I only mentioned it in response to the parent (and I only mentioned it in the article to highlight how arbitrary it is). My point in the article was that the numbering system was originally little endian because it made things easier when multidigit numbers grow in magnitude in the same direction as you write (least significant digit to the right in this case as it was a right-to-left writing system at the time). This written ordering was then maintained for compatibility reasons in the parts of the world that eventually settled on left-to-right. And the vocalizations ultimately followed those of the dominant cultures of the times - which used left-to-right (with some vestigial exceptions - see my sister comment).

AnimalMuppet 2y ago

> What we consider "natural" now is not what was originally considered "natural" during the early centuries of the Hindu-Arabic numerals' journey. Which no doubt affected the byte order that the early Hindus and Arabs used for their processors. For processors made in the 20th and 21st centuries, however, the numeral order used by people in those centuries is a more relevant data point. By raw human nature, humans can do it either way. For the humans we have now, with their background, one way is definitely more "natural" than the other. That is, it's more natural to them, because they come with a cultural background.

wakawaka28 2y ago

Do you have any evidence that, say, "three million, one hundred twenty-five thousand, two hundred sixty-nine" would have ever been spoken starting with "nine" and ending with "three million"? I guess that wouldn't be the dumbest thing humans have ever done, but it sure sounds impractical.

kstenerud 2y ago
The "dumbness" depends entirely on what you're used to. There's no actual need to lead off with the most significant digit other than convention. "three million, one hundred twenty-five thousand, two hundred sixty-nine" "nine, sixty, two hundred, thousands five, twenty, one hundred, millions three" It could work either way. And in fact, in the early days of the Hindu-Arabic numeral system's penetration into Europe, they actually DID lead off with the least significant digit (although numbers larger than thousands were rarely used, and the archaic wordings have only survived in the ones and tens digits - if at all for a particular language).
- wakawaka28 2y ago
  >It could work either way. Yes but one of those ways does not support abbreviation or interruption, or fractions. If you see a 9 digit number for example, you might want to just round off to one or two significant digits while reading it. Having the smallest components first presents obstacles to speech in much the same way Roman numerals do.
  - kstenerud 2y ago
    That's also convention talking. Looking at the number 443937215, it's trivial to identify the first two or the last two digits. And for counting digits to get an idea of the magnitude, we use separators like so: 443,937,215 (or 443.937.215 depending on what country you're in). The only difference is whether you estimate this number as "about four hundred and forty million" or "about ten and five hundred million"
    - 2y ago