5 ms·

Numeral Systems of the World's Languages (2021)

49 points by lgessler 3y ago

lgessler 3y ago
Some unusual systems documented on these pages, pointed out by Gaston Ümlaut in his StackExchange answer[1]: * Orokaiva (Trans–New Guinea): digit-tally system https://lingweb.eva.mpg.de/channumerals/Orokaiva.htm https://lingweb.eva.mpg.de/channumerals/Orokaiva.htm * Fas (Fas): binary system (base 2) https://lingweb.eva.mpg.de/channumerals/Momu-Fas.htm https://lingweb.eva.mpg.de/channumerals/Momu-Fas.htm * Pazeh (Austronesian): quinary (base 5) https://lingweb.eva.mpg.de/channumerals/Pazeh.htm https://lingweb.eva.mpg.de/channumerals/Pazeh.htm * Amis (Austronesian): decimal (base 10) https://lingweb.eva.mpg.de/channumerals/Amis.htm https://lingweb.eva.mpg.de/channumerals/Amis.htm * Ron (Afro-Asiatic, Chadic): duodecimal (base 12) https://lingweb.eva.mpg.de/channumerals/Ron-Chadic.htm https://lingweb.eva.mpg.de/channumerals/Ron-Chadic.htm * Barapasi (East Geelvink Bay): vigesimal (base 20) https://lingweb.eva.mpg.de/channumerals/Barapasi.htm https://lingweb.eva.mpg.de/channumerals/Barapasi.htm * Meyah (East Bird Head-Sentani): mixed-quinary/vigesimal https://lingweb.eva.mpg.de/channumerals/Meyah.htm https://lingweb.eva.mpg.de/channumerals/Meyah.htm [1]: https://linguistics.stackexchange.com/questions/2652/which-modern-spoken-languages-do-not-use-the-decimal-number-system https://linguistics.stackexchange.com/questions/2652/which-m...
- ithkuil 3y ago
  Fas doesn't appear to be base-2 number system in that it's not a positional number system. "Base" refers to the base of a positional number system. It's an unary system, where one quantity is grouped (2) like in a sign-value system but also used when speaking and not just in symbolic notation. It's like if our 10-centric languages we'd say thirty five as "ten ten ten five". In fas you'd say thirty five as "two two two two two two two two two two two two two two two two two one"
  - tobbe2064 3y ago
    Its a bit surprising that none seems to have invented base 2. It should be the most expressive way to count using fingers since it allows 32 number to be expressed with a single hand and 1024 numbers with two hands. But I guess that would be overengineering and annoying for most early cultures.
    - ithkuil 3y ago
      In 2nd century BC, the the indian scholar Pingala wrote Chandaḥśāstra where he developed a positional little endian (least significant digit on the left) base-2 system using a sanskrit short syllable for 0 and long syllable for one
crvdgc 3y ago
The Chinese footnote: > 未经本人电邮及书面授权，不得复制中文译名 states that one is not allowed to copy the Chinese translated names without an email and written consent of the author. It's the first time I see an attempt to copyright translated names, which would defeat the purpose of translation itself. Let alone most names are just translated by pronunciations. It's really weird to see the author being overly protective and the wording is much milder in English.
- numpad0 3y ago
  Does it say you have to ask author, though? Machine translations might take it as such, being only able to handle word-perfect transpositions that aren't guaranteed to make sense, but 本人 is not a typical first person pronoun in Chinese vocabulary. I think it just means you'll have to make sure the transliteration is accepted by primary person - bearers of translated names. That'd make sense, CJK transliterations are all but canonical.
readthenotes1 3y ago
"All the data on this site needs further checking for typos and errors before being distributed and share to linguists and related scholars." Good sense of humor!
1letterunixname 3y ago
Ancient Babylonia is somewhat responsible for the base 60 of minutes, seconds, and degrees. https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal
1letterunixname 3y ago
If you can/could make change in the Carolingian monetary system (pre-decimalization British coinage), then you're either a cabbie, a genius, or Brian May (who I assume is both). 1 £ equivalents --------------- 1/135th or 4/21st 5 guineas (depended on the context) 1/27th or 20/21st 1 guineas 2/27th or 40/21st half guineas 3/27th or 60/21st third guineas 4/27th or 80/21st quarter guineas 1 sovereign = 1 pound ("quid") 2 half sovereigns 4 crowns 5 double florins 8 half crowns 10 florins 20 shillings 40 sixpences 60 fourpences 80 thruppences (threepences) 160 twopences 240 pennies 480 halfpennies 960 farthings 1920 half farthings 2880 third farthings 3840 quarter farthings The values changed in 1971. These are the ancient values.
- gumby 3y ago
  My grandfather (born around 1910, died 1969) used to earn extra money on week ends by going to the horse track and calculating odds for the bookies. They’d take a big bet and he would tell them how to adjust the odds and what offsetting bets to make to hedge risk. This was in guineas, pounds, shillings, farthings etc. He did all the calculations in his head. He’d only attended school through part of year 5. Not surprisingly, the one of his kids who went to uni (my dad) got two maths degrees and two EE degrees.
- totetsu 3y ago
  Spare a thought for those of us who grew up on the Dicsworld(mud) https://dwwiki.mooo.com/wiki/Currency https://dwwiki.mooo.com/wiki/Currency
- canjobear 3y ago
  One fun thing about reading Ulysses is that a lot of Leopold Bloom's interior monologue revolves around money in the old system and he does a lot of calculations in his head. You start to get a sense of what it was like. The impression I got is that it all revolves around the shilling, which seems to have been worth something like $5 around the time of the book: 1 crown = 5 shillings 1 pound = 20 shillings 1 guinea = 21 shillings 1 shilling = 12 pence Guinea is the weird one, but it has the function of allowing you to give tips. If someone charges you 3 pounds and you pay them 3 guineas then you are giving a 5% tip.
sagaro 3y ago
It is interesting how many languages originating in different parts of the world all somehow figured to have a base and name the numbers by base. For instance if you know 1 to 9. And then you know 10, 20, 30, 40... 90. And then 100, 200, 300... you will be able to say the numbers 57 (fifty, seven) or 69 (sixty nine) or 237 (two hundred, thirty, seven). But all the languages under Indo-Iranian(https://lingweb.eva.mpg.de/channumerals/Indoeuro.htm https://lingweb.eva.mpg.de/channumerals/Indoeuro.htm) for instance Hindi (https://lingweb.eva.mpg.de/channumerals/Hindi.htm https://lingweb.eva.mpg.de/channumerals/Hindi.htm) have 1-100 as different numbers and then follow the base principle. 20 in Hindi is 'bis'. 2 is 'do'. But 22 is 'bais'. Know 30 and knowing 7 in Hindi or any of those Indo-Iranian language will not help you tell 37. But knowing 100 and 37 will be enough to say 137 in those languages. 100 in hindi is ek sau. And 37 is 'senthis'. So you will be able to say 'ek sau senthis'. It is fascinating that those languages chose to not follow base till 100 and then followed the base while naming their numbers.
- unwind 3y ago
  Cool! I think you had an unfortunate typo: [...] will now help [...] That should read "will not help", right? Else I'm even more confused than normal.
  - sagaro 3y ago
    Ah yes. "Not". Thanks for pointing out.
- simiones 3y ago
  Isn't what you're describing for Hindi just base-100 numbers?
  - sagaro 3y ago
    That is an interesting way of looking at it. Kind of makes sense considering unlike western units, 100k in Hindi is "ek lakh". And in India, the numbers are expressed as xx,xx,xx,xxx. So 100 is sau (hundred), 1,000 is hazar (thousand) 1,00,000 is lakh (hundred thousand) 1,00,00,000 is crore (10 million) Somehow the first split is 1000, then on every order of 100 gets a name. It sure is confusing, but there must be some reason to this.
BerislavLopac 3y ago
And just as a reminder, never to forget: all bases are base 10. ;)
- timbit42 3y ago
  Yes. I discovered this when playing with Forth's BASE word.

49 points by lgessler 3y ago

Some unusual systems documented on these pages, pointed out by Gaston Ümlaut in his StackExchange answer[1]: * Orokaiva (Trans–New Guinea): digit-tally system https://lingweb.eva.mpg.de/channumerals/Orokaiva.htm https://lingweb.eva.mpg.de/channumerals/Orokaiva.htm * Fas (Fas): binary system (base 2) https://lingweb.eva.mpg.de/channumerals/Momu-Fas.htm https://lingweb.eva.mpg.de/channumerals/Momu-Fas.htm * Pazeh (Austronesian): quinary (base 5) https://lingweb.eva.mpg.de/channumerals/Pazeh.htm https://lingweb.eva.mpg.de/channumerals/Pazeh.htm * Amis (Austronesian): decimal (base 10) https://lingweb.eva.mpg.de/channumerals/Amis.htm https://lingweb.eva.mpg.de/channumerals/Amis.htm * Ron (Afro-Asiatic, Chadic): duodecimal (base 12) https://lingweb.eva.mpg.de/channumerals/Ron-Chadic.htm https://lingweb.eva.mpg.de/channumerals/Ron-Chadic.htm * Barapasi (East Geelvink Bay): vigesimal (base 20) https://lingweb.eva.mpg.de/channumerals/Barapasi.htm https://lingweb.eva.mpg.de/channumerals/Barapasi.htm * Meyah (East Bird Head-Sentani): mixed-quinary/vigesimal https://lingweb.eva.mpg.de/channumerals/Meyah.htm https://lingweb.eva.mpg.de/channumerals/Meyah.htm [1]: https://linguistics.stackexchange.com/questions/2652/which-modern-spoken-languages-do-not-use-the-decimal-number-system https://linguistics.stackexchange.com/questions/2652/which-m...

ithkuil 3y ago
Fas doesn't appear to be base-2 number system in that it's not a positional number system. "Base" refers to the base of a positional number system. It's an unary system, where one quantity is grouped (2) like in a sign-value system but also used when speaking and not just in symbolic notation. It's like if our 10-centric languages we'd say thirty five as "ten ten ten five". In fas you'd say thirty five as "two two two two two two two two two two two two two two two two two one"
- tobbe2064 3y ago
  Its a bit surprising that none seems to have invented base 2. It should be the most expressive way to count using fingers since it allows 32 number to be expressed with a single hand and 1024 numbers with two hands. But I guess that would be overengineering and annoying for most early cultures.
  - ithkuil 3y ago
    In 2nd century BC, the the indian scholar Pingala wrote Chandaḥśāstra where he developed a positional little endian (least significant digit on the left) base-2 system using a sanskrit short syllable for 0 and long syllable for one

crvdgc 3y ago

The Chinese footnote: > 未经本人电邮及书面授权，不得复制中文译名 states that one is not allowed to copy the Chinese translated names without an email and written consent of the author. It's the first time I see an attempt to copyright translated names, which would defeat the purpose of translation itself. Let alone most names are just translated by pronunciations. It's really weird to see the author being overly protective and the wording is much milder in English.

numpad0 3y ago
Does it say you have to ask author, though? Machine translations might take it as such, being only able to handle word-perfect transpositions that aren't guaranteed to make sense, but 本人 is not a typical first person pronoun in Chinese vocabulary. I think it just means you'll have to make sure the transliteration is accepted by primary person - bearers of translated names. That'd make sense, CJK transliterations are all but canonical.

readthenotes1 3y ago

"All the data on this site needs further checking for typos and errors before being distributed and share to linguists and related scholars." Good sense of humor!

1letterunixname 3y ago

Ancient Babylonia is somewhat responsible for the base 60 of minutes, seconds, and degrees. https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal

1letterunixname 3y ago

If you can/could make change in the Carolingian monetary system (pre-decimalization British coinage), then you're either a cabbie, a genius, or Brian May (who I assume is both). 1 £ equivalents --------------- 1/135th or 4/21st 5 guineas (depended on the context) 1/27th or 20/21st 1 guineas 2/27th or 40/21st half guineas 3/27th or 60/21st third guineas 4/27th or 80/21st quarter guineas 1 sovereign = 1 pound ("quid") 2 half sovereigns 4 crowns 5 double florins 8 half crowns 10 florins 20 shillings 40 sixpences 60 fourpences 80 thruppences (threepences) 160 twopences 240 pennies 480 halfpennies 960 farthings 1920 half farthings 2880 third farthings 3840 quarter farthings The values changed in 1971. These are the ancient values.

gumby 3y ago
My grandfather (born around 1910, died 1969) used to earn extra money on week ends by going to the horse track and calculating odds for the bookies. They’d take a big bet and he would tell them how to adjust the odds and what offsetting bets to make to hedge risk. This was in guineas, pounds, shillings, farthings etc. He did all the calculations in his head. He’d only attended school through part of year 5. Not surprisingly, the one of his kids who went to uni (my dad) got two maths degrees and two EE degrees.
totetsu 3y ago
Spare a thought for those of us who grew up on the Dicsworld(mud) https://dwwiki.mooo.com/wiki/Currency https://dwwiki.mooo.com/wiki/Currency
canjobear 3y ago
One fun thing about reading Ulysses is that a lot of Leopold Bloom's interior monologue revolves around money in the old system and he does a lot of calculations in his head. You start to get a sense of what it was like. The impression I got is that it all revolves around the shilling, which seems to have been worth something like $5 around the time of the book: 1 crown = 5 shillings 1 pound = 20 shillings 1 guinea = 21 shillings 1 shilling = 12 pence Guinea is the weird one, but it has the function of allowing you to give tips. If someone charges you 3 pounds and you pay them 3 guineas then you are giving a 5% tip.

sagaro 3y ago

It is interesting how many languages originating in different parts of the world all somehow figured to have a base and name the numbers by base. For instance if you know 1 to 9. And then you know 10, 20, 30, 40... 90. And then 100, 200, 300... you will be able to say the numbers 57 (fifty, seven) or 69 (sixty nine) or 237 (two hundred, thirty, seven). But all the languages under Indo-Iranian(https://lingweb.eva.mpg.de/channumerals/Indoeuro.htm https://lingweb.eva.mpg.de/channumerals/Indoeuro.htm) for instance Hindi (https://lingweb.eva.mpg.de/channumerals/Hindi.htm https://lingweb.eva.mpg.de/channumerals/Hindi.htm) have 1-100 as different numbers and then follow the base principle. 20 in Hindi is 'bis'. 2 is 'do'. But 22 is 'bais'. Know 30 and knowing 7 in Hindi or any of those Indo-Iranian language will not help you tell 37. But knowing 100 and 37 will be enough to say 137 in those languages. 100 in hindi is ek sau. And 37 is 'senthis'. So you will be able to say 'ek sau senthis'. It is fascinating that those languages chose to not follow base till 100 and then followed the base while naming their numbers.

unwind 3y ago
Cool! I think you had an unfortunate typo: [...] will now help [...] That should read "will not help", right? Else I'm even more confused than normal.
- sagaro 3y ago
  Ah yes. "Not". Thanks for pointing out.
simiones 3y ago
Isn't what you're describing for Hindi just base-100 numbers?
- sagaro 3y ago
  That is an interesting way of looking at it. Kind of makes sense considering unlike western units, 100k in Hindi is "ek lakh". And in India, the numbers are expressed as xx,xx,xx,xxx. So 100 is sau (hundred), 1,000 is hazar (thousand) 1,00,000 is lakh (hundred thousand) 1,00,00,000 is crore (10 million) Somehow the first split is 1000, then on every order of 100 gets a name. It sure is confusing, but there must be some reason to this.

BerislavLopac 3y ago

And just as a reminder, never to forget: all bases are base 10. ;)

timbit42 3y ago
Yes. I discovered this when playing with Forth's BASE word.