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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)

#111

Post by jacobolus »

pierrebai wrote: post #101
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:…

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.

Most everything is easier with negative digits. Easier addition, easier rounding, easier multiplication, much easier subtraction. The one part that needs slightly more distinct techniques vs. what you are used to is division, but it's still probably easier overall.

The grandparent poster's example only looks more complicated because we don't have standard glyphs for the negative digits.

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

#112

Post by jacobolus »

gkya wrote: post #89
andreareina wrote: post #86

Earlier quoted context omitted.

Just the names doesn't account for 80 + 10, 80 + 11, ..., 80 + 19.

Isn't it like quatre-vingts and ten, eleven, etc?

97 is pronounced like "four-score-ten-seven".

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

#113

Post by jacobolus »

yorwba wrote: post #10
gbrown_ wrote: post #3

The base 60 Sexagesimal system used by the Sumerians is always an interesting one. https://en.wikipedia.org/wiki/Sexagesimal

TFA has a section on Assyrian, but that's a decimal system, which made me wonder where the sexagesimal came from. It appears that although Assyrian and earlier Akkadian were written in cuneiform, they are Semitic languages that adopted their writing system from the otherwise unrelated Sumerian language, and apparently didn't bother to adapt the numerals to the decimal system. https://en.wikipedia.org/wiki/Akkadian

Akkadians et al. kept using both decimal and sexagesimal arithmetic in parallel.

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

#114

Post by jacobolus »

jacobolus wrote: post #112
gkya wrote: post #89

Earlier quoted context omitted.

Isn't it like quatre-vingts and ten, eleven, etc?

97 is pronounced like "four-score-ten-seven".

Who is downvoting this, and why? Quatre-vingt-dix-sept is literally the French version of four-score-ten-seven.

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

#115

Post by wodenokoto »

madmoose wrote: post #76
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 eq…

Fair enough. As a child I could never remember if it was 50 or 60 that had "halv" (50 is halvtreds, 60 is treds, neither word have any resemblance to 5, 6 or 10, but 50 sounds a bit like it ought to be half of 60), but my point is that the number system has nothing to do with base 20 except a few etymological roots of some names, that for all intents and purposes might as well be random.

But you are right: they are worse than random, since they are named close enough to other entities to be confuseaable.

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

#116

Post by dalbuschat »

German is much more complex in counting than Japanese in that table, which I would wager is not true. In Japanese, you have to decide which counting words you use depending on what you are counting, and most of those words are highly irregular. There's no such complexity in German, it's only irregular for 10, 11 and 12.

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

#117

Post by hvidgaard »

gkya wrote: post #49
hvidgaard wrote: post #32

Earlier quoted context omitted.

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.

"Und" is "and" in English, and "og" in Danish, and is used in Danish as well. I think Danish and German is quite similar as you say. It's been 20 odd years since I learned to speak German and it's long since forgotten.

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

#118

Post by tom_mellior »

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…

> A LOT of these have massive errors. I strongly recommend comparing all that to this paper

As you have already found those errors and done that comparison, could you share some of what you've found?

EDIT: For whatever it's worth, I checked French on https://mpi-lingweb.shh.mpg.de/numeral/, and it lists the same forms for 70 and 90 for French and Belgian French. Which is incorrect.

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

#119

Post by Moru »

hmd_imputer wrote: post #69
Moru wrote: post #40

Earlier quoted context omitted.

I bet they use card instead... In Germany you stand in line waiting for everyone to find exactly the right change, be them young or old. Most people pay with cash even though it seems to get more common to use card. Euro has at least eight different coins. Sweden has 1, 2, 5, 10 as coins but most people still pay with card because it's easier and people are not burned by the big brother syndrome of the WW1/2 :-) Woul…

Another Germany related comment today. Made my day :) It really becomes annoying when you have to wait a minute because an old lady needs to count all her coins in Lidl. Back to the original topic, as someone who can speak a few languages, I find the arguments stated in the article quite interesting. Obviously, just because one speaks Chinese doesn't mean they will definitely be a wunder-kind in math. Yet, it plays a…

It's not only old ladies that have to count their coins, everyone young or old stands there with the head deep down over the purse trying to find those microscopic coins :-)

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

#120

Post by kzrdude »

jacobolus wrote: post #114
jacobolus wrote: post #112

Earlier quoted context omitted.

97 is pronounced like "four-score-ten-seven".

Who is downvoting this, and why? Quatre-vingt-dix-sept is literally the French version of four-score-ten-seven.

but with notes:

- quatre-vingt is the name for 80 - dix-sept is the name for 17

so we could also say it's eighty-seventeen.

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