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Kaktovik Iñupiaq Numerals (wikipedia.org)
26 points by dalke 10 months ago | hide | past | favorite | 11 comments

Came across it looking up "Radix" in Wikipedia. Meant to do "Radix sort". Then saw the list of other radix systems. Clicked on this one, found it was made in the 1990s, by middle school students, and read how it's greatly improved math test scores of Iñupiat students.

I see jermaustin1 posted https://news.ycombinator.com/item?id=21992791 linking to an Artifexian video at https://www.youtube.com/watch?v=EyS6FfczH0Q but with no comments or up-votes thought it was too interesting for people to overlook.

Base 20 is not so rare, there are even some remains of this in European languages, for example 80 is French is something like "four-twenties" https://en.wikipedia.org/wiki/Vigesimal#Use

I think Danish has a more complicated system. 1 - 20 is similar to most Germanic languages, by extension Indo European in general. But, then it gets weirder the closer you get to 100:

20 - Tyve (Swedish tjugo, Norwegian: tjue) / 30 - Tredive (Swedish: trettio, Norwegian: tretti) / 40 - Fyrre (Swedish: fyrtio, Norwegian: førti) / 50 - Halvtreds (Swedish: femtio, Norwegian: femti) / 60 - tres (Swedish: sextio, Norwegian: seksti) / 70 - halvfjerds (Swedish: sjuttio, Norwegian: sytti) / 80 - firs (Swedish: åttio, Norwegian: åtti) / 90 - halvfems (Swedish: nittio, Norwegian: nitti) / 100 - hundrede (Swedish: hundra, Norwegian: hundre)

If I understand correctly, the numbers are contractions of longer words... for example, 60 is tres, sixtieth is tresindstyvende, which means something like "three lots of twenty"-th. Weird? Yeah. But no idea what halvfjerds means... it's making my brain hurt trying to work it out.

Okay I googled it - and it does make sense.

Apparently "halvanden" means one and a half (halv = half, andan = 2nd, but for this "2".)

So, 50 is actually "halvtredsindstyve", which is ((3 - 0.5) * 20)... okay.. this is completely messed up! Only the Danes... only the Danes... making their language even less intelligible. ;-)

For the record, 60 is tredsindstyve, which is 3 * 20.. at least that makes some sense. The issue comes that 70 is halvfjerdsindstyve ((4 - 0.5) * 20) and 80 is firsindstyve (4 * 20), but fjerd and fir look like different words! They inbuilt extra confusion to make it even harder! 90 is halvfemsindstyve ((5 - 0.5) * 20).

It all makes some sense if you understand what is going on. Buy why?!?

Yes, and those European languages use base-10 numerals.

This specific base-20 numeral system has a simple representation which allows some numeric operations to be done by pattern matching.[0] See the YT video I linked to.

Think I+II = III in Roman numerals, or as the examples show, think V+V=W (for 2+2=4). Though unlike Roman numerals, this uses base-20 positional system, with a subbase-5 system.

That composition feature isn't present in the Arabic numerals.

And I'm annoyed there's no way to represent it in standard Unicode!

[0] I haven't looked into it enough. I suspect the simple pattern matching approach only works for some numbers. But even so, it gives an intermediate/bootstrap step to learning (say) division that feels helpful for beginners.

> That composition feature isn't present in the Arabic numerals.

"1" +"2" = "3", Can you see the composition? The original representation was "-" + "=" = "≡" but someone got too lazy and rotate 1, wrote the two lines of 2 without lifting up the pen, and the three lines of 3 without lifting up the pen. I'm not an expert in number history, but these are some nice graphics of the evolution of the number system https://www.archimedes-lab.org/numeral.html and in particular the evolution of the representation of three https://kk.org/cooltools/the-universal-h/ This alternative is a nice and ordered number system, but after a few centuries of use some will get lazy and change the shape to write them faster or to make them more different.

> And I'm annoyed there's no way to represent it in standard Unicode!

Every few years there is a post about someone who added a few characters to Unicode. Take a look at https://news.ycombinator.com/item?id=11958682

> I haven't looked into it enough. I suspect the simple pattern matching approach only works for some numbers. But even so, it gives an intermediate/bootstrap step to learning (say) division that feels helpful for beginners.

The part of the video about sum and rest make sense, it is slightly easier, but there are many other representations for example with points. I'm a strong proponent of "Use your fingers", but you must learn by heath the tables soon (but not too soon). In the video they didn't explain too many operations with carry. This is possible with this notation, but it is not easier than with the current notation, and you must remember to use 5 for the bottom-to-top transition and 4 for the digit-to-digit transitions, so it may be a problem to remember.

The part of the video about division makes no sense. Division is just horrible in any representation. Try 76829/5. (And I pick 5 because 5 is an easy case. If you think it is too easy try with 3 or 7.)

Actually quatre-vingt (four twenties) in French is a relatively recent development, almost limited to French from France.

Other francophone countries just say octante (Belgium, Canada, some areas of France) or huitante (mainly Switzerland).

That's very interesting! Is there an easy explanation of the reason? A link to an explanation?

Celtic/Norman cultures/languages were vigesimal, but with the Romans came Latin which is decimal. French evolved from Latin in uneven ways due to economic, cultural, geographic and political factors.

The best in depth explanation is here [0] but it's in French.

Actually reading it my original statement is wrong; it's way more complicated. More likely decimal and vigesimal forms originated at the same time, depending on the factors I mentioned above.

[0] https://french.stackexchange.com/questions/187/quelles-parti...

Thanks for the link. It is difficult to read, because the autotranlation is too smart and translate all the versions of "eighty" in French to the same word in English. But I read the autotranlation and then read the original version.

[Hi from Argentina! I can guess what the text in French says, but with the autotranslation is much easier.]

The "naturally occuring" bases people come up with are quite a bit stranger.

https://en.wikipedia.org/wiki/Telefol_language#Counting_syst... base 27

https://en.wikipedia.org/wiki/Kaugel_language base 24

https://en.wikipedia.org/wiki/Ngiti_language base 32 (well, CS people like that one)

More at https://en.wikipedia.org/wiki/List_of_numeral_systems#Standa... notes base 23 and others (https://www.preposterousuniverse.com/podcast/2020/03/23/89-l... mentions base 87 or 81, but unfortunately got interrupted before she could name the language)

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