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

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

#41

Post by abhishekjha »

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?

I am a native Hindi speaker and I don't think Hindi is very different from base-10 number system(as the article acknowledges) thus there shouldn't be any difficulty as such. Although I can't say that I have done any kind of mathematical calculation in Hindi script/numerals ever.

NOTE: Hindi has its own script for numbers as well which the article is missed to point out.

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

#42

Post by tekkk »

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 look better in functional language.

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

#43

Post by paganel »

kmm wrote: post #24
hmd_imputer wrote: post #19

Another article that was published a while ago had an interesting take on it. There is a quite high correlation between numbering system of a language and how quickly/well kids speaking that language learn counting and math skills. Apparently, the article itself is taken down, but I found an archived version. https://web.archive.org/web/20141215072819/http://playthink....

Maybe it's been taken down because it reeks of bad linguistics and bad anthropology. Not to mention the obvious that being good at counting doesn't make one good at academic subjects. I studied math and didn't see a number larger than 10 after I got my BSc.

> I studied math and didn't see a number larger than 10 after I got my BSc.

Presumably you were not a kid anymore at that time. The OP was mentioning about how easy is for kids to acquire/improve their maths skills if counting is made easier by the language itself. That probably doesn't correlate that well with those kids' academic performances 15 or 20 years later, but that was not the point.

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

#44

Post by Grue3 »

yorwba wrote: post #12
empath75 wrote: post #7

I think they're understanding the complexity of the Japanese number system by quite a lot: https://en.wikipedia.org/wiki/Japanese_counter_word

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 much only for days. Except similar words to "foo" and "baz" here are also used to count some things. But not the others.

Also the rules of combining a numeral and the counter are very inconsistent. Here's my implementation of Japanese counters, suffices to say the English version would be like 5 lines of code:

https://github.com/tshatrov/ichiran/blob/master/dict-counter...

And here's the pronounciation generator for so called "regular" numbers.

https://github.com/tshatrov/ichiran/blob/master/numbers.lisp...

I.e. 1000 = issen (ichi+sen) 3000 = sanzen (san + sen), 800 = happyaku (hachi + hyaku).

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

#45

Post by Cmerlyn »

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?

It's not that difficult. The names are different but they "make sense". It's like 'fifteen', 'sixteen' and 'seventeen' stretched up to 100. Different names, but the pattern is sort of obvious with a few exceptions here and there.

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

#46

Post by no_identd »

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 Cauchy!):

https://scholar.google.com/scholar?cites=6877129426190119313...

I'd very much appreciate it.

Donald E. Knuth cites it in TAOCP while discussing Balanced Ternary:

"Cauchy pointed out that negative digits make it unneccesary for a person to memorize the multiplication table past 5x5." [Comptes Rendus Acad. Sci. 11 (Paris, 1840), 789-798]

But he doesn't elaborate on it further, and neither does anyone else from what I can tell, and I have yet to figure out the trick. (I currently try to teach myself to EFFICIENTLY do all my mental arithmetic in balanced ternary - not an easy task!)

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

#47

Post by gkya »

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…

In french it's base ten only. AFAIK it's just the names, particularly in France, that are a bit confusing. I don't think francophones think of quatre-vingts as 20 20 20 20, but as 80. Just like english is not base-12 because its eleven and twelve, and not oneteen and twoteen.

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

#48

Post by wodenokoto »

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.

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

#49

Post by gkya »

hvidgaard wrote: post #32
julian_t wrote: post #21

I'd put traditional Danish numbering a bit further up the list... it's pretty strange ( http://www.olestig.dk/dansk/numbers.html )

I was surprised to see Danish so high on the list, but after a short while it's not too surprising. It's base-20 for the first 20, like English. Then it's backwards base-10 up to 99 with special names for the whole 10s, 42 is pronounced as "2 and 40". Above 99 it's base-10, 420 is "400 20". But if it's 428 it's "400 8 and 20", but 512 would be "500 12". It's not difficult, it's just a special rule for 1-20, backwards…

That's nearly exactly how german works, 428 is "4-vier 100-hundert 8-acht and-und 20-zwanzig", 512 is "5-fünf 100-hundert 12-zwölf" (excuse my rusty german). The und thing is a germanic thing I think.

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

#50

Post by FabHK »

hmd_imputer wrote: post #19

Another article that was published a while ago had an interesting take on it. There is a quite high correlation between numbering system of a language and how quickly/well kids speaking that language learn counting and math skills. Apparently, the article itself is taken down, but I found an archived version. https://web.archive.org/web/20141215072819/http://playthink....

There are a few articles linked on the bottom of the page (dead links unfortunately) that purport to show the same.

> "Surprisingly enough, it's proven that Chinese-speaking children are better at counting numbers than English-speaking counterparts because of their language. Bilingual children are better at counting when they think in Chinese than in English. The irregularity of the English number system makes it harder for children to count numbers properly."

Not sure I'd give much credence to that hypothesis, though. Hard to disentangle the many factors influencing the results. Having said that, the Chinese numbers are pleasantly short and logical, by and large.

English has the advantage again in big numbers, where we have million, billion, trillion, quadrillion, etc., with the Latin prefix N indicating 10^6N (long scale, old British usage and continental Europe) or 10^(3+3N) (short scale, American usage).

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

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