Kaktovic Numerals in Unicode

April 17, 2023 9:08 PM

'Almost 30 years ago, a group of Kaktovik students invented a numbering system that reflected the way they counted in Iñupiaq and made math more intuitive for them.' The numerals are now part of Unicode (PDF).
posted by Fiasco da Gama (19 comments total)

This is cool! And using a unary tally structure to form numerals is the kind of brilliant idea that's simple in hindsight; do any other systems do it?

(I do kinda wish humans had a fifth arm, so the system would have ended up base-25 for regularity. Adding on dextrous mandibles / chelicerae would do too.)
posted by away for regrooving at 9:38 PM on April 17, 2023 [2 favorites]

Okay but where is the sideways w?

(This is very cool.)
posted by constraint at 10:18 PM on April 17, 2023

That'd be for base 21
posted by grokus at 10:47 PM on April 17, 2023

base-25 for regularity

I used to work as a stocktaker, and base-5 for counting (i.e. tally) is how that work is done. We look at a group of objects and can see that there are five of them without having to add, where for most people as soon as there are more, it's a set of four and two, or three and three. So you make tallies of fives, then you bundle the fives in fives, then you bundle four five-fives and that's a hundred, which is a typical price-per-item count for consumer commodities, whether it's chip packets or t-shirts or galvanised bolts. It's fast and you rarely if ever lose count. Finger counting works.
posted by Fiasco da Gama at 10:51 PM on April 17, 2023 [11 favorites]

Side note: “base n” means a numeration system where you have place value, with a 1s digit/place, an ‘n’s digit/place, an ‘n^2’ digit/place, etc. Base five numerals look like 234 = (2 x 25) + (3 x 5) + (4 x 1). Basic tally numeration, while commonly grouped in groups of five, is not base five. The system described above where groups of five individual tallies are also grouped into five-fives gets closer, but if you are only grouping four groups of five-fives at the next level, you’ve broken the ‘base five’ structure.
posted by eviemath at 11:26 PM on April 17, 2023 [6 favorites]

Kudos to these students who not only invented a neat system but (according to the article) made math more appealing!

do any other systems do it?

Quite a few of them. Numerals usually do derive from tally marks. Chinese still has 一 二 三; as for our system, the Brahmi script started with | || |||. A few centuries later they were placed on their sides, like the Chinese characters. By the ninth century or so people were connecting the strokes, giving something like 𑁧 𑁨 𑁩 which became our 1 2 3.

Georges Ifrit thinks the other Indian numbers also derive from tally marks, greatly simplified. (We can actually see how that happened with Ancient Egyptian.)
posted by zompist at 11:31 PM on April 17, 2023 [20 favorites]

Oh, and though mathematicians talk about bases, it's more complicated for languages. Iñupiaq is base 20... but if you look at the number names, and the new number symbols, they're based on 5's, then 20's. Michael Closs would call this a 5-20 system. Classical Maya numerals are 5-20 while the number names are 10-20.
posted by zompist at 11:44 PM on April 17, 2023 [7 favorites]

I used to work as a stocktaker, and base-5 for counting (i.e. tally) is how that work is done. We look at a group of objects and can see that there are five of them without having to add, where for most people as soon as there are more, it's a set of four and two, or three and three. So you make tallies of fives, then you bundle the fives in fives, then you bundle four five-fives and that's a hundred, which is a typical price-per-item count for consumer commodities, whether it's chip packets or t-shirts or galvanised bolts. It's fast and you rarely if ever lose count. Finger counting works.

I worked in a print shop, and when it was necessary to count paper, we'd do it in fives for a similar reason. After a while you can just "feel" each group of five, so it is very fast and automatic. Then you are just tracking groups of five and then hundreds up to 500. I almost never had to hand-count more than that but if you did, you'd be tracking in reams at that point. (Very large quantities would be weighed, not counted.)
posted by Dip Flash at 5:50 AM on April 18, 2023 [2 favorites]

there are \ð kinds of people:

those that count in Kaktovic numerals,
those that belong to EmpressCallipygos,
embalmed ones,
those that are trained,
suckling infants,

mermaids,
fabulous ones,
those that none know are stray dogs on the internet,
those included in the present classification,
those that tremble as if they were mad,

innumerable ones,
those drawn with a very fine camelhair brush,
others,
those that have just broken a flower vase,
those that from a long way off look like flies,

those that count in quinary,
those that count in quaternary,
those that count in ternary,
those that count in binary,
and those who don't count.
posted by ApplAuD at 6:00 AM on April 18, 2023 [11 favorites]

Adding on dextrous mandibles / chelicerae would do too.

Interviewer: "So, if I understand this correctly, you decided to grow two sets of hinged mandibles and a skull crest in order to simplify basic arithmetic for yourself, is that correct?"

Me, glancing up from the boar I'm devouring: ".... Yes. Math."
posted by mhoye at 6:01 AM on April 18, 2023 [11 favorites]

This is way more interesting than the Zoom planning meeting I'm currently on.
posted by outgrown_hobnail at 6:34 AM on April 18, 2023 [3 favorites]

...using them in math problems was easier than Arabic numbers, Solomon said. Just by looking at the Kaktovik numerals, students could see how to add, subtract and even divide. For example, for long division, students used colored pencils to match the strokes of the divisor in the dividend.
“The numbers almost gave themselves away,” Bartley said.

I would be interested to see how that works
posted by MtDewd at 10:20 AM on April 18, 2023 [3 favorites]

I was curious too. In this video the explanation of how arithmetic works starts around 3:50, and there are a number of other videos about it that I haven't had time yet to watch. It's really impressive!
posted by trig at 2:17 PM on April 18, 2023 [4 favorites]

Numeration systems predate a lot of recorded history, so there’s quite a lot we still don’t know about their initial development or the spread of various useful ideas for representing numbers. From the bits I’ve read, it seems that tally numeration systems arose independently many places, zero was discovered/invented independently a few times but also spread along trade routes, positional notation also seems to be something that came from a combination of arising independently multiple places and spreading through trade and migration. And base 60 seems to crop up independently multiple times (60 is divisible by a lot of numbers and thus makes various computations more convenient; and may also have been usefully aligned with natural/cosmological cycles?). There also seems to be a lot of confidently stated just-so stories about the origins of numeration systems, that are reasonable hypotheses and probably what folks who actually research this personally believe, but which we simply don’t have enough evidence to conclude with certainty? Since the history is not my area of specialization, I don’t have a good resource to directly answer your question or give a comprehensive overview of what is known. But here are a couple basic introductions (from some open math education textbooks) that list sources that could be followed up on, or give definitions/terminology that may be helpful for a more in-depth search:

The Evolution of Numeration Systems

Number Systems

I haven’t read it yet, but have heard good reviews, so likely see also: Zero: The biography of a dangerous idea
posted by eviemath at 4:18 PM on April 18, 2023 [4 favorites]

Shorter article that gives a flavour of some of what is and isn’t known about ancient history of numeration systems: A history of zero
posted by eviemath at 4:28 PM on April 18, 2023

More: The Origin of the Number Zero
posted by eviemath at 4:33 PM on April 18, 2023

Cuneiform also has a tally system, in base sixty. (But it’s really 10s, then 6 of those).
posted by nat at 6:21 PM on April 18, 2023

That is a brilliantly simple system. I wonder how English-speaking students who struggle with traditional math might fare using Kaktovic numerals , considering their visual power.
posted by Big Al 8000 at 10:38 PM on April 18, 2023

I wonder how English-speaking students who struggle with traditional math might fare using Kaktovic numerals

That's an interesting idea; given that our symbolic systems are not in themselves "math" but are how we express and communicate math, that different symbolic systems present different accessibility properties to their audiences.
posted by mhoye at 6:08 AM on April 19, 2023 [1 favorite]