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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)

#101

Post by pierrebai »

joshuamorton wrote: post #60
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:…

I think this is one instance where using a larger look-up table (i.e. multiplication table up to 10x10) yields clear benefit. The technqiue using only 5x5 increases the number of intermediary results to keep in one's head.

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

#102

Post by dahart »

Numberwang wrote: post #99
joshuamorton wrote: post #60

Earlier quoted context omitted.

>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:…

Is this the best way to do quick arithmetic, or are there other ways?

There are lots of ways, depending on what you want to calculate.

Here's a fantastic book on the subject:

https://www.amazon.com/Dead-Reckoning-Calculating-Without-In...

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

#103

Post by Manishearth »

rlpb wrote: post #39
abhishek0318 wrote: post #27

Earlier quoted context omitted.

Every number doesn't have its own name. If you observe closely there is a pattern. From 21 to 99, you can observe that every digit at tens place decides the suffix and the digit at ones place decides the prefix.

Further, the author says "because of a lot of irregular pronunciation, you have to memorize 100 different words as if it were a centesimal system". But I could say the same for English. We won't say "three-ty-three", we say "thirty-three". Hindi's irregularities are pretty much at the same level.

No, for English the thirty series is always "thirty-foo", and numbers ending in three are always "foo-three". It is true that you don't use the same word for the number when it's in the tens place (like Chinese), but that's as complex as it gets (and the teens, of course).

In Hindi 40 and 41 use a different word for 40. 51 and 53 use a different word for 50. 55 and 45 use a different word for 5. Plus there are smaller but still significant differences between pretty much every number -- e.g. it's chauBees, but puchees and chauNtees.

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

#104

Post by kjaer »

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 wrote it in Scala below; it's a bit shorter, and I really like the map(base). Getting the digits from a number turns out to be most of the work, and the int->string->int conversion also seems to be the best approach.

  val base = List("noa", "taha", "ua", "tolu", "fa", "nima", "ono", "fitu", "valu", "hiva")
  def tongan(n: Int) = n.toString.map(_.asDigit).map(base).mkString(" ")

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

#105

Post by thaumasiotes »

DonaldFisk wrote: post #81
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…

Someone just made these up in the middle ages: https://www.quora.com/Why-is-a-group-of-crows-called-a-murde... I have never heard or read the words "a murder of crows" (or "a parliament of owls" and similar contrivances) except in lists of collective nouns.

The example was poorly chosen, but obligatory measure words are very much a feature of English; compare "a pair of pants" / "a pair of scissors" / "a pair of glasses" / "a loaf of bread". Note that all of those "pairs" refer to a single object.

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

#106

Post by kccqzy »

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…

English numbers aren't much harder.

    englishNumbers n = ten9 !! (n - 1)
      where infixr 7 >
            (>) = liftA2 ()
            ten1 = ["one", "two", "three", "four", "five", "six", "seven", "eight", "nine"]
            ten2 = ten1  ["ten", "eleven", "twelve"]  (["thir", "four"]  prefixes) > ["teen"]  (["twen", "thir", "for"]  prefixes) > ["ty"] > ([[]]  ten1)
              where prefixes = ["fif", "six", "seven", "eigh", "nine"]
            ten3 = ten2  ten1 > ["hundred"] > ([[]]  ten2)
            ten6 = ten3  ten3 > ["thousand"] > ([[]]  ten3)
            ten9 = ten6  ten3 > ["million"] > ([[]]  ten6)

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

#107

Post by dingo_bat »

Manishearth wrote: post #74
dingo_bat wrote: post #34

Earlier quoted context omitted.

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…

> Hindi and Marathi both have dedicated names for the tens (11, 12, 13, ...)

Same deal with English.

> and after that numbers are named in the reverse order of their digits. E.g. 45 will be five - forty.

Which is similar in complexity to English, just the order of speaking is reversed.

> _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.

Now I realize what you're saying. It seems that I have memorized every number. Because I never thought of this.

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

#108

Post by Manishearth »

dingo_bat wrote: post #107
Manishearth wrote: post #74

Earlier quoted context omitted.

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…

> Hindi and Marathi both have dedicated names for the tens (11, 12, 13, ...) Same deal with English. > and after that numbers are named in the reverse order of their digits. E.g. 45 will be five - forty. Which is similar in complexity to English, just the order of speaking is reversed. > _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…

> Same deal with English.

>

> Which is similar in complexity to English, just the order of speaking is reversed.

Yes, I was mentioning these to paint an accurate picture, not to contrast with English :)

-----

As a native Marathi / nonnative Hindi speaker, I can tell you that the Hindi numbers are pretty hard to get, and took me forever to get used to, even though the variations are almost the same as the ones Marathi has.

(However if you asked me about Marathi I'd have the exact same response as you, "what complexity? oh wait I see I've memorized everything oops")

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

#109

Post by kristianov »

Taniwha wrote: post #83
amelius wrote: post #29

Nice to see that Mandarin and Japanese have simple number systems compared to English. It might be worthwhile to learn them and impress your friends while you're reading numbers from restaurant menu-cards :)

the one thing missing is the two mandarin words for 2 (essentially 2 and couple, used in different contents)

Every numeral in Mandarin does have 2 words. It's like NATO phonetic alphabet "Alpha, Bravo, Charlie, ...". "零一二三四五六七八九" maps to "洞幺两参肆伍六拐八勾".

What's more, there are multiple characters for the same numeral, mostly used to counter tempering in bookkeeping.

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

#110

Post by jacobolus »

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…

If you normalize your numbers to be written with digits from -5 to +5 instead of 0 to 9 in each place, then the multiplication table is more symmetrical so you can memorize a table 1/4 as big and then just remember the signs of each quadrant.
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