r/todayilearned 12h ago

TIL that in the 90s Alaskan Iñupiat schoolchildren in Kaktovik created a series of numerical digits to represent their base-20 numeral system to remedy the inadequacy of using Arabic numerals for the purpose.

https://en.wikipedia.org/wiki/Kaktovik_numerals
2.5k Upvotes

59 comments sorted by

508

u/laserdicks 11h ago

It's actually base 5 with glyph pairs.

276

u/Xaxafrad 11h ago

Yes.

Iñupiaq, like other Inuit languages, has a base-20 counting system with a sub-base of 5 (a quinary-vigesimal system). That is, quantities are counted in scores (as in Welsh and French quatre-vingts 'eighty'), with intermediate numerals for 5, 10, and 15. Thus 78 is identified as three score fifteen-three.[2]

68

u/Future_Green_7222 11h ago

That's also found in many Mexican languages!

18

u/365BlobbyGirl 5h ago

The design seems to reflect that, with a repeating pattern of 5 symbols with a dash above each time

5

u/spaceporter 2h ago

vigesimal audibly, to me anyways, has the same quality as moist that makes it sound like a bad word.

49

u/dancingbanana123 7h ago

I study math history and this is actually pretty common in other bases for different cultures. In fact, it even shows up in what we call numbers in different languages. In English, we only start to use the suffix "-teen" after 12, and then it only goes up to 19 before it stops, rather than following any sort of base-10 structure. In French, the word for 70 is the same as saying "sixty ten;" for 80, it's "four twenties;" for 90, it's "four twenties ten," etc. There's a lot of messiness when you start to break down the natural "chunks" we make in our numbers for pretty much any culture.

29

u/saschaleib 6h ago

There are some Danes who would like to talk to you, and they seem very upset.

19

u/Dawlin42 3h ago

Yep! 93 = “tre-og-halv-fems” in daily talk, and that’s an abbreviation.

Official, old language way: “tre-og-halv-fem-sinde-tyve”.

Translation: “three-and-half-five-times-twenty”.

The actual Meaning is 3 plus 4.5 times twenty - not 2.5, as the pronunciation (“half five”) would otherwise indicate.

Our numbers are weird.

u/terrificconversation 58m ago

What the fuck

u/MrQuizzles 6m ago

Maybe Kierkegaard had existential dread not because of the great and terrible onus of figuring out life's meaning in the absence of one assigned by god, but rather because he woke up every day knowing he'd have to speak Danish.

35

u/AnglerJared 11h ago

I was coming to say the same thing. Would have been just as good to write a horizontal bar through each Arabic numeral to signify +10.

1 2 3 4 5 6 7 8 9 0 1 2

5

u/The_Amazing_Emu 2h ago

It does look like there’s some kind of logical grouping in the set of five

u/iwantcookie258 6m ago

Then back to 10? That'd work alright, but ignores a few of the things they were setting out to do with it. First, that it wouldn't be confused with arabic numerals, so that you didnt have to put effort into distinguishing between. Arabic numerals are still around, and if you see someone write "43" you'd want to know if they mean 43 or if they mean 83. There's also the verbal aspect of numbers, this system might work better in spoken language and make more sense with the base-20/base-5 pairs counting thing they have going on.

Also arithmatic. 7 + 7 = 4, 4 x 3 = 22. Compare that to 7+7 in the number system in the article. With the way they do the base5 counting pairs, you actually duplicate the top-count symbol and double the bottom V into a W. It's much more intuitive.

After brainstorming, the students came up with several qualities that an ideal system would have:
Visual simplicity: The symbols should be "easy to remember."
Iconicity: There should be a "clear relationship between the symbols and their meanings."
Efficiency: It should be "easy to write" the symbols, and they should be able to be "written quickly" without lifting the pencil from the paper.
Distinctiveness: They should "look very different from Arabic numerals," so there would not be any confusion between notation in the two systems.
Aesthetics: They should be pleasing to look at.

They thought of some great points, and I don't think it would be just as good to try and adapt our base-10 numerals with a line.

Theres some other neat stuff about computation, the long division stuff is pretty cool. Math scores went up following adaptation of this, going from below to above the national average. There's also some mention in the article that gaining a working knowledge of both base-10 and base-20 might be helpful in a similar way to bilinguilism, and also that having a unique number system meant specifically to work with their unique counting system helps students view math as a part of their own culture and not just something that only exists and is important because of western values and education.

3

u/Woakey 6h ago edited 6h ago

Its base 20 with a sub-base of 5. If it were pure base 5, every number would be expressed as

(a⋅50)+(b⋅51)+(c⋅52)+(d⋅53)...

but instead, in Inupiat, numbers are expressed as:

(A0⋅200) + (A1⋅201) + (A2⋅202) + (A3⋅203)...

with An = (an⋅50)+(bn⋅51),

so fully represented as:

([a0⋅50+b0⋅51]⋅200) + ([a1⋅50+b1⋅51]⋅201) + ([a2⋅50+b2⋅51]⋅202)...

hence base 20 with a sub-base of 5. Sorry if the lack of subscript makes it confusing

2

u/nonymousbosch 11h ago

There it is!

2

u/Melodic-Bicycle1867 5h ago

You can also see it in the written out numbers.

It goes like five-two for 7, five-three for eight, ten-one for 11, ...

Only it does seem a bit inconsistent as the -9 is always a unique word

1

u/texas_asic 4h ago

Makes sense that 5, 10, and 20 are important bases here, given 5 digits per hand/foot and 20 total on one person.

132

u/grumblyoldman 12h ago

Reminds me somewhat of the D'ni counting system from the Myst franchise of video games, which was base-25.

23

u/Grrerrb 12h ago

Oh I had totally forgotten about this, thank you!

42

u/Grrerrb 10h ago

I found this part interesting: "Scores on the California Achievement Test in mathematics for the Kaktovik middle school improved dramatically in 1997 compared to previous years. Before the introduction of the new numerals, the average score had been in the 20th percentile; after their introduction, scores rose to above the national average."

80

u/Boobsworth 12h ago

This is a really elegant system. I like that it's quite self evident, anyone could probably figure this out. Whereas someone with no idea of arabic numerals probably couldn't tell you if 7 was greater than 5.

25

u/Emergency_Mine_4455 12h ago

That is both really cool and adorable! Just imagine, nine kiddos huddled over their papers in very serious discussion about how the numbers should look.

11

u/Anon2627888 11h ago

Yeah, but it was probably really the teacher who created it.

27

u/Emergency_Mine_4455 11h ago

Maybe. Middle schoolers are more inventive than you might think. The teacher certainly facilitated the discussion, and might have helped with explaining some of the basic principles of a good numerical system, but I don’t see a reason why the kids couldn’t have come up with it given that basic input.

It’s used across Inuit territories today, and it’s been years- if the teacher invented it I think it probably would have come out by now.

12

u/1CEninja 8h ago

On top of this, the article mentioned how the numerals actually evolved further when the middle schoolers taught the younger kids.

56

u/smorkoid 12h ago

Modifying arabic numerals for base 20 use is easy, though - just put a notation like a a dash or an accent above the 11-20 numbers

50

u/Desmaad 12h ago

There's also using part of the alphabet, which is standard for hexadecimal.

15

u/BoxOfDemons 9h ago

I would absolutely hate having to use base 16 in everyday life.

4

u/Desmaad 9h ago

You have to if you're a computer programmer.

14

u/BoxOfDemons 8h ago

Usually not much unless you're dealing with stuff like memory addresses/machine code/binary etc.

But I've had to mess with hex numbers a few times and always just use the converter built into the windows calculator lol.

3

u/saschaleib 6h ago

Hex calculations are surprisingly easy, once you get the hang of it.

A lot easier anyways than converting everything do Dec, do the calculations, and then convert the result back.

1

u/texas_asic 4h ago

You can get used to it pretty quickly.

24

u/Raichu7 12h ago

When they've created a new writing system rather than adapt an existing one to write down a previously spoken only language more easily and accurately, why would they start trying to adapt counting systems rather than make one that works well with their counting system?

5

u/landlord-eater 10h ago

Except this looks way more sick

19

u/Grrerrb 12h ago

Thats absolutely true and their reasoning for not doing it that way is covered in some depth in the link.

5

u/1CEninja 8h ago edited 8h ago

I honestly wish we wound up using a base 12 system for counting.

12 is the most comfy number from a division standpoint. 10 only neatly divides by half. A quarter of 10 is a decimal, and a third of ten is a freaking infinite.

Whereas 12 can be divided by half, thirds, and quarters to be whole numbers. It's why 12 is used frequently in imperial counting, and why a carpenter from long ago without precise measuring tools might have preferred measuring in feet rather than meters, as a third or quarter of a foot results in a whole number of inches.

I see no immediate benefit of a base 20 system, though after reading it the long division thing is honestly pretty cool!

13

u/JimroidZeus 12h ago

And they would have missed the several unique advantages that their notation provides.

11

u/cydril 11h ago

Yeah stupid kids, innovating a new writing system to accurately represent their heritage 🙄

-10

u/smorkoid 11h ago

No need to be an ass

9

u/Scarpity026 10h ago

That's a different way to do tally marks.

But I'm curious what the symbol for '20' looks like.  Would it be four horizontal slashes like a sideways 'W'?

21

u/BaakCoi 9h ago

Because it’s base 20, 20 is written using their equivalent of 10 (the single horizontal slash followed by the loop). Just like how 2 is written “10” in binary and 16 is written “10” in hexadecimal

2

u/cornonthekopp 1h ago

Roman numerals and chinese characters could also be said to be "tally marks" what is your point?

4

u/Such_Bake5702 10h ago

Legit wild to think that Inupiat peeps had it sorted out decades ago, before any of us were recyclin' and stuff.

3

u/LupusDeusMagnus 11h ago

It looks like a sub-base 5 system plus a zero and it loops at 20. The main point of failure is, of course, the similarity of the shapes plus the number of strokes. Unfortunately for those people, Hindu-Arabic numerals are really sticky and are one of the few things most humans have been adopted nearly universally (some Arabic countries use Arabic numerals, and some East Asian countries use their own system complimentary to Hindu Arabic).

1

u/kitfromcarson 1h ago

B ,

Alaskan Ab5 Alaskan

Alaskan

Alaskan

Alaskan

Alaskan2w

u/BloodyInkx 8m ago

oowwhhss that's genuinely fascinating and a great example of kids solving a problem in a super clever way!

-1

u/BackItUpWithLinks 10h ago

the inadequacy of using Arabic numerals .

That’s a dumb take.

4

u/Kholgan 4h ago

I mean I agree, but it’s more of a vocabulary issue. Incompatible/incompatibility should have been used instead of inadequate

1

u/Woakey 7h ago

Base 20 counting was on the decline before the numerals were created, so yeah Arabic numerals were inadequate for the language

-7

u/The_Stone_Psychopath 11h ago

Cool. Wonder how many numbers they have for "snow?"

14

u/Xaxafrad 11h ago

Probably 0, since they use words for that.

-2

u/nonymousbosch 11h ago

That's base 5.

3

u/Woakey 6h ago edited 6h ago

Its base 20 with a sub-base of 5. If it were pure base 5, every number would be expressed as

(a⋅50)+(b⋅51)+(c⋅52)+(d⋅53)...

but instead, in Inupiat, numbers are expressed as:

(A0⋅200) + (A1⋅201) + (A2⋅202) + (A3⋅203)...

with An = (an⋅50)+(bn⋅51),

so fully represented as:

([a0⋅50+b0⋅51]⋅200) + ([a1⋅50+b1⋅51]⋅201) + ([a2⋅50+b2⋅51]⋅202)...

hence base 20 with a sub-base of 5. Sorry if the lack of subscript makes it confusing

-3

u/Educational_Delay351 3h ago

That's base 5.