Number systems of the world, sorted by complexity of counting (2006) • Hacker News Board

Re: Number systems of the world, sorted by complexity of counting (2006)

#71

Post by yorwba » Thu, Mar 22, 2018, 4:51 PM UTC

Grue3 wrote: post #44

yorwba wrote: post #12

Earlier quoted context omitted.

Classifiers are mostly orthogonal to the number system, and they're really no different from e.g. English using "a herd of cattle" or "a murder of crows" to redundantly encode the kind of thing being talked about. I'm actually not aware of any language that doesn't have different units of measurement for different objects, it's just that some languages effectively make it mandatory to use them. (E.g. in Chinese you c…

Yes, they are different from English. In English you say "one herd of cattle", "two herds of cattle", and so on. You just need to know a plural of "herd" and the regular numbers. In Japanese the numbers themselves depend on the counter. You can't say "one day", "two days", "three days". You can only say "one day (ichinichi)", "foobar (futsuka)", "bazbar (mikka)", and so on. And this counting system is used pretty muc…

The completely different number words used for some things are actually not related to the counter, although it may appear like that because the written form uses the Chinese-style number + counter system. The spoken words are holdouts from ancient Japanese (before Chinese become influential), which TFA discusses separately.

The situation is similar to Latin or Greek numerals in English, which are also applied pretty inconsistently. E.g. duplicate, triplicate, quadruple, ... but pair, triple, quadruple, ...

In general, all languages are riddled with exceptions, ambiguities, contradictions and archaic forms, but it's easier to notice them when you're learning the language later in life and have the "logical" structures of your mother-tongue to compare them to.

Re: Number systems of the world, sorted by complexity of counting (2006)

#72

Post by DonaldFisk » Thu, Mar 22, 2018, 5:04 PM UTC

Khmer is quite complex, and isn't on the list:

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

Up to 30, it's got a base-5 component so, for example, 16 = dap pram muoy (10 5 1). From 30 onwards, like Thai it follows the more straightforward Chinese number system.

The numbers in Scottish Gaelic have recently been changed and are now base 10:

https://gaelicgrammar.org/~gaelic/mediawiki/index.php/Numera...

Re: Number systems of the world, sorted by complexity of counting (2006)

#73

Post by FullyFunctional » Thu, Mar 22, 2018, 5:05 PM UTC

tekkk wrote: post #42

Wow, Tongan number system is simply beautiful. Pure elegance that I'm sure could be defined mathematically very simply. I myself can only scribble a naive implementation for natural numbers in Javascript: const base = ["noa", "taha", "ua", "tolu", "fa", "nima", "ono", "fitu", "valu", "hiva"] const tongan = n => Array.from(n.toString()).map(Number).map(i => base[i]).join(" ") Not as pretty as I thought. Probably would…

I theorize that humans do poorly with too much regularity and we actually benefit from irregularity, unlike computers.

In Haskell, first line would be the same without the const and the other could be

tongan = intercalate " ".reverse.map ((base !!).(`mod` 10)).takeWhile (> 0).iterate (`div` 10)

(ISTM that there must be a better alternative to takeWhile + iterate).

Re: Number systems of the world, sorted by complexity of counting (2006)

#74

Post by Manishearth » Thu, Mar 22, 2018, 5:06 PM UTC

dingo_bat wrote: post #34

jazzyb wrote: post #6

I don't understand how the author is judging complexity. The top one, Huli, is a base-15 number system but looks quite regular otherwise. French, on the other hand, switches from a base-10 to a base-20 at 80 and then switches things up at 97. According to the listing, Welsh sits somewhere between these two but it has separate numbering systems for {20s, 40s, 60s, 80s}, {30s, 70s, 90s}, and {50s}. That seems much more…

Agreed. Hindi is ranked 4th most difficult but the system is identical to English (rank 41). Just the symbols for the digits are different. Even they are similar looking!

Hindi/Marathi are not easy, you almost have to memorize the numbers 1-100.

Hindi and Marathi both have dedicated names for the tens (11, 12, 13, ...) and after that numbers are named in the reverse order of their digits. E.g. 45 will be five - forty.

_except_ the word for five will be different from the word for five in, say, 75. Similarly, the word for "fifty" in the fifties is different for many of them.

There's a lot of variation which you basically don't realize if you speak these languages natively, the variation can't be boxed into "rules" to make it easy to learn, and the end result is that you just end up implicitly memorizing it.

It's hard to realize because you basically end up modeling this subconsciously as there being multiple ways to say "five" and multiple ways to say "seventy", so the numbers seem to be following a fixed scheme, but in reality you've learned which synonym to use where.

In fact when folks talk about french numbers being weird and complex, this is often the counterexample I give.

I suspect this complexity arose from having synonyms for numbers which eventually randomly settled down, and also from having sandhi (rules for melding words together) which got corrupted over time, leading to things like "tay/ees" vs "chau/bees"

The website probably should have used the "different form"/"different word" thing it did for English. But note that the site did consider "twelve" to be its own number, not 10 + 2, which is basically what's happening here too, just extended 1-100.

Re: Number systems of the world, sorted by complexity of counting (2006)

#75

Post by DonaldFisk » Thu, Mar 22, 2018, 5:08 PM UTC

jazzyb wrote: post #6

I don't understand how the author is judging complexity. The top one, Huli, is a base-15 number system but looks quite regular otherwise. French, on the other hand, switches from a base-10 to a base-20 at 80 and then switches things up at 97. According to the listing, Welsh sits somewhere between these two but it has separate numbering systems for {20s, 40s, 60s, 80s}, {30s, 70s, 90s}, and {50s}. That seems much more…

French spoken in Belgium and Switzerland has 70 = septante and 90 = nonante. In parts of Switzerland, 80 = huitante.

Re: Number systems of the world, sorted by complexity of counting (2006)

#76

Post by madmoose » Thu, Mar 22, 2018, 5:10 PM UTC

wodenokoto wrote: post #48

Danish typically ranks high on these lists because the names for some of the tens have etymological roots in base 20. But this doesn't add any complexity, compared to having just named tens. Nobody is doing any kind of everyday counting in base 20 in Denmark. Everything is base 10, with 9 irregular named numbers for the multiples of 10.

As a parent of English/Danish bilingual children I have to tell you that you are very wrong on this.

My children still occasionally make mistakes when saying numbers in the range 50-99 in Danish, they haven't said the English numbers wrong for years.

That the word for 50 contains the word "tre" (three) and the word for 90 contains the word "fem" (five) is very confusing to our children, especially when the English equivalents are so simple in comparison.

Re: Number systems of the world, sorted by complexity of counting (2006)

#77

Post by bassman9000 » Thu, Mar 22, 2018, 5:13 PM UTC

jazzyb wrote: post #6

I don't understand how the author is judging complexity. The top one, Huli, is a base-15 number system but looks quite regular otherwise. French, on the other hand, switches from a base-10 to a base-20 at 80 and then switches things up at 97. According to the listing, Welsh sits somewhere between these two but it has separate numbering systems for {20s, 40s, 60s, 80s}, {30s, 70s, 90s}, and {50s}. That seems much more…

He clearly states it's his opinion. E.g. mandarin is one of the least complex for him, and yet

http://www.sf.airnet.ne.jp/ts/language/number/mandarin.html

Re: Number systems of the world, sorted by complexity of counting (2006)

#78

Post by Manishearth » Thu, Mar 22, 2018, 5:14 PM UTC

dsr_ wrote: post #16

Can any native Hindi speakers comment on the difficulty of doing math in a language where every number 1-100 has its own name?

(Native Marathi, competent Hindi speaker here. Marathi has the same problem)

So, it's not like each number has a different name.

However, it's almost like that.

Basically, the numbers can be broken down into a logical tens and ones place -- e.g. 45 will be five-forty (paintalees -- pai/talees), however the exact way to say "five" will change based on the number, as will the exact way to say "forty".

There's not much logic to it -- some tens series are more regular than others -- which means you effectively end up memorizing it, but subconsciously.

Imagine numbers in English but there were three ways of saying each digit, and each number 1-100 would pick from the synonyms. It's basically like that. That is to say, it's not too hard to deal with -- you'll mentally be associating the numbers with their words so it's not hard to say it out, and because they're synonyms not hard to understand when spoken.

Re: Number systems of the world, sorted by complexity of counting (2006)

#79

Post by no_identd » Thu, Mar 22, 2018, 5:17 PM UTC

xavieralexandre wrote: post #62

no_identd wrote: post #46

A LOT of these have massive errors. I strongly recommend comparing all that to this paper: https://pdfs.semanticscholar.org/5ca1/fa0ffca55e9003053de2f5... - Harald Hammarström - Rarities in Numeral Systems (2009) And this page: https://mpi-lingweb.shh.mpg.de/numeral/ "Numeral Systems of the World's Languages" By the way: If anyone can find a digital copy of this paper from 1840 by Augustin-Louis Cauchy (yes, THAT Cau…

Comptes rendus hebdomadaires des séances de l'Académie des Sciences Tome XI, p.789 (16 novembre 1840) Found in Oeuvres complètes d'Augustin Cauchy 1ère série Tome V III. Notes et articles extraits des comptes rendus hebdomadaires des séances de l'Académie des Sciences. (Suite.) 105. Calculs numériques. sur les moyens d'éviter les erreurs dans les calculs numériques. https://www.e-rara.ch/zut/content/pageview/5702727

Wow. I figured it'd sit online in some archive that I failed to find. Thanks a lot!

PDF of Tome V here:

https://www.e-rara.ch/download/pdf/5702285?name=Tome%2520V%4...

Re: Number systems of the world, sorted by complexity of counting (2006)

#80

Post by jankovicsandras » Thu, Mar 22, 2018, 5:18 PM UTC

Why is hungarian considered more complex than english or norwegian? Hungarian has regular "on ten one" for 11 and "on ten two" for 12, when english and norwegian have different words; and teens are arguably also more complex.