Numeral Systems of the World's Languages (2021) | Hacker News Reader

Numeral Systems of the World's Languages (2021)

lingweb.eva.mpg.de

49 pointslgessler24 comments

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) for instance Hindi (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.

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.

Ah yes. "Not". Thanks for pointing out.

Isn't what you're describing for Hindi just base-100 numbers?

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.

erm, french is a bit weird on this IIRC.

Yes, French has some remnants of a base-20 system that was there in one of the languages that went before. Interestingly, this only manifests for numbers greater than 60; so while numbering from 0 to 60 looks mostly like in English, the numbers 60-79 are essentially "sixty - sixty-ten (70) - sixty-eleven(71) - sixty-nineteen(79)" (soixante un - soixante dix - soixante onze - soixante dix neuf), and then for 80-99 you have "four twenties - four-twenties-and-10 - four-twenties-and-99" (quatre vingt - quatre vingt dix - quatre vingt dix neuf).

Other European languages also have interesting numbering, such as Danish, with constructions such as 50 being "three less a half [twenties]" (halvtreds).

There are dialects of French that don't use that numeral system, Swiss French uses septante, huitante, nonante for 70, 80, 90.

Hindi and other Indo-Aryan languages are incredibly irregular, but when laid out on a chart it doesn't seem as daunting of a task as the initial prospect of learning 100 numerals for 0-100 would be. For example, if you know 22 is 'bais' and you know the tens place for thirty is 'tis' and sixty is 'sath' you can probably figure out what 'battis' and 'basath' are, although if you know 29 is 'untis' you won't be able to figure out what 'unsath' is from the examples provided in this post.

Irregularity isn't too uncommon though, just not to the same degree. Many Germanic languages have special words for eleven and twelve, with remnants of vigesimal are common throughout Europe. French and Danish were mentioned previously, with Danish having exceptions on top of that system. 23 being '3 and 20th' or 67 being '7 and 3 score' which makes sense, but 34 '3 and 30' and 45 '4 and 5 10s' breaking the rule, and numbers like 78 '8 and 3 score and half fourth score' really stretching the limits. The Celtic languages still use vigesimal and Breton at least has similar degrees of irregularity as Danish. Japanese numerals are also a mess, but that mostly stems from the differences in readings.

There's probably many more examples, but these are the ones that I can think of off the top of my head. The one notable exception being the Pirahã language, which has words for 'one' 'two' and 'many' and that's about it.

https://en.wikipedia.org/wiki/Hindustani_numerals

https://en.wikipedia.org/wiki/Danish_language#Numerals

https://en.wikipedia.org/wiki/Japanese_numerals

Reminiscent of Borges' story 'Funes the memorious', whose title character has a completely eidetic memory and invents his own number system where each number is its own distinct word or phrase - a system described rather beautifully (in the English translation) as 'a rhapsody of incoherent terms ... precisely the opposite of a system of numbers'

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.

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.

Spare a thought for those of us who grew up on the Dicsworld(mud) https://dwwiki.mooo.com/wiki/Currency

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.

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

* Fas (Fas): binary system (base 2) https://lingweb.eva.mpg.de/channumerals/Momu-Fas.htm

* Pazeh (Austronesian): quinary (base 5) https://lingweb.eva.mpg.de/channumerals/Pazeh.htm

* Amis (Austronesian): decimal (base 10) https://lingweb.eva.mpg.de/channumerals/Amis.htm

* Ron (Afro-Asiatic, Chadic): duodecimal (base 12) https://lingweb.eva.mpg.de/channumerals/Ron-Chadic.htm

* Barapasi (East Geelvink Bay): vigesimal (base 20) https://lingweb.eva.mpg.de/channumerals/Barapasi.htm

* Meyah (East Bird Head-Sentani): mixed-quinary/vigesimal https://lingweb.eva.mpg.de/channumerals/Meyah.htm

[1]: https://linguistics.stackexchange.com/questions/2652/which-m...

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"

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.

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

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.

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.

"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!

Ancient Babylonia is somewhat responsible for the base 60 of minutes, seconds, and degrees.

https://en.wikipedia.org/wiki/Sexagesimal

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

Yes. I discovered this when playing with Forth's BASE word.

Reply on news.ycombinator.com