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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)

#52

Post by Mimino123 »

A small correction to the Georgian language: it belongs to the south Caucasian/Kartvelian(not Georgian) language family. What's interesting here is that Kartvelian does literally mean Georgian in translation, but since it is a term it should not be translated.

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

#53

Post by Robin_Message »

stromgo wrote: post #26
Robin_Message wrote: post #14

Earlier quoted context omitted.

Also, Swiss French, which has proper words for seventy and ninety, is considered more complex than French French, even though I'd consider having specific words simpler (especially given the complexity of 97 (which is said as 4 x 20 + 10 + 7)

Did you interpret the table backwards? Swiss French is considered simpler: 1. (most complex) 19. French 33. Swiss French 69. (simplest)

Yes, yes I did! Thanks, that makes a lot more sense!

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

#54

Post by Coincoin »

oblio wrote: post #22
Robin_Message wrote: post #14

Earlier quoted context omitted.

Also, Swiss French, which has proper words for seventy and ninety, is considered more complex than French French, even though I'd consider having specific words simpler (especially given the complexity of 97 (which is said as 4 x 20 + 10 + 7)

67 isn't much better, either. It's 60 + 10 + 7.

Also, number triads ending in 1 or 11 smaller than 80 need an 'and' conjunction. And numbers ending in 1 need to concord in gender. What a mess.

Before the 1990s there were also all sort of over-complicated hyphen rules. Thank god it's now simpler; hyphens everywhere.

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

#55

Post by davedunkin »

oblio wrote: post #22
Robin_Message wrote: post #14

Earlier quoted context omitted.

Also, Swiss French, which has proper words for seventy and ninety, is considered more complex than French French, even though I'd consider having specific words simpler (especially given the complexity of 97 (which is said as 4 x 20 + 10 + 7)

67 isn't much better, either. It's 60 + 10 + 7.

77?

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

#56

Post by hinkley »

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’s a whole theory of learning that suggested that some languages were more suited to mental gymnastics for a particular field of study (math, logic, biology) and that maybe we could further human progress by teaching children the curriculum in that language.

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

#57

Post by drewmate »

I didn't see Russian listed anywhere on there, but I suspect it would be in the top 20 on this list. It is a pretty straightforward base 10 complicated by archaic phonetic rules that change the pronunciation and stress of words with logical roots in unintuitive ways.

In addition, countable nouns (like cars, people, cities, but also including multiples of 100, 1000, etc...) change form depending on how many of them there are (1, 2-4, 5-20, 21-24, 25-30 etc...) Usually these separate forms are phonetically related, but sometimes there is no connection at all. These rules don't come in to play when strictly counting numbers until 200, but is an integral part of what makes it hard to count things in Russian.

There are also wrinkles like the word for 40 (сорок) and 90 (девяносто) that don't fit in the usual tens pattern like 20 (двадцать - two * ten) or 30 (тридцать - three * ten). Any Russian speakers care to explain what's going on with those two?

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

#58

Post by settrans »

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

Moreover, Japanese has TWO parallel number systems (as does Korean). The Sinitic system, enumerated here, is used for naming numbers, counting with most counter words, and counting large quantities, whereas the native Japanese system is used with certain common counter words.

Compare:

     Ｊａｐ　　Ｓｉｎ
  1  ひとつ　　イチ
  2  ふたつ　　ニ
  3  みっつ　　サン
  4  よっつ　　ヨン
  5　 いつつ　　ゴ
  6　 むっつ　　ロク
  7　 ななつ　　シチ
  8　 やっつ　　ハチ
  9  ここのつ　キュウ
  10　とお　　　ジュウ
The native Japanese numerals are themselves variable: I have listed the forms they assume when paired with the つ counter. For example, two days is rendered as ふつか and six days as むいか.

Further reading: https://en.wikipedia.org/wiki/Japanese_numerals https://japanese.stackexchange.com/questions/14959/are-there...

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

#60

Post by joshuamorton »

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…

>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

5 * 9 = 5 * (10 - 1) = 50 - 5 = 45

Specifically, you need to know everything in the 5x5 area, and how to multiply by 10.

More generally, any digit 6-9 can be rewritten as (10 - (10 - digit)) and then you can apply distribution rules to clean things up. Here's a three by two digit example:

247 * 68 =

    (10 - 3) * (10 - 2) +         // 7 * 8
    10 * (10 - 3) * (10 - 4) +    // 7 * 60
    10 * 4 * (10 - 2) +           // 40 * 8
    10 * 10 * 4 * (10 - 4) +      // 40 * 60
    10 * 10 * 2 * (10 - 2) +      // 200 * 8
    10 * 10 * 10 * 2 * (10 - 4)   // 200 * 60
evaluating we get

    100 - 50 + 6 +
    10 * (100 - 70 + 12) + 
    10 * (40 - 8) + 
    100 * (40 - 16) + 
    100 * (20 - 4) + 
    1000 * (20 - 8)
And then to finish up:

    00056 +
    00420 +
    00320 + 
    02400 +
    01600 +
    12000 =
16796, which is the correct answer.

Edit:

The fun thing to think about is conceptually why this works. If you consider numbers as just bits, all you're doing is converting the highest bit from base to sign, without actually changing it, doing the multiplications on the lower bits, and then tracking the sign to know whether or not to add or subtract later.

Or to put it another way, you're shifting your set of numbers from being +0 - +10 to being -5 - +5. This makes the lookup table smaller, but requires you to do some additional intermediate lookups (up to four, one in each "quadrant" of the 10x10 table) to be as powerful.

Fun to conceptualize that way.

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