Native Alaskan Language Reshapes Mathematics
Published by Reblogs - Credits in Posts,
The languages we speak influence the way that we see the world, in ways most of us may never recognize. For example, researchers report seeing higher savings rates among people whose native language has limited capacity for a future tense, and one Aboriginal Australian language requires precise knowledge of cardinal directions in order to speak at all. And one Alaskan Inuit language called Iñupiaq is using its inherent visual nature to reshape the way children learn and use mathematics, among other things.
Arabic numerals are widespread and near universal in the modern world, but except perhaps for the number "1", are simply symbols representing ideas. They require users to understand these quantities before being able to engage with the underlying mathematical structure of this base-10 system. But not only are there other bases, but other ways of writing numbers. In the case of the Iñupiaq language, which is a base-20 system, the characters for the numbers are expressed in a way in which information about the numbers themselves can be extracted from their visual representation.
This leads to some surprising consequences, largely that certain operations like addition and subtraction and even long division can be strikingly easy to do since the visual nature of the characters makes it obvious what each answer should be. Often the operations can be seen as being done to the characters themselves, instead of in the Arabic system where the idea of each number must be known before it can be manipulated in this way.
This project was originally started as a way to make sure that the Iñupiaq language and culture wasn’t completely lost after centuries of efforts to eradicate it and other native North American cultures. But now it may eventually get its own set of Unicode characters, meaning that it could easily be printed in textbooks and used in computer programming, opening up a lot of doors not only for native speakers of the language but for those looking to utilize its unique characteristics to help students understand mathematics rather than just learn it.
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57 thoughts on "Native Alaskan Language Reshapes Mathematics"
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Paul says:
Interesting. Biquinary. I wonder if it is borrowed from the abacus, or sprung up independently.
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ced4r says:
I think both come from people often having two hands with five fingers.
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Ostracus says:
Fingermath.
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Yeah yeah nah, otherwise we’d all be working in binary notation. This is just another linguistic curiosity that will go nowhere and eventually be completely forgotten as far as everyday use is concerned, just like all of the languages from Australia, because the way of life that may make them relevant is no longer practiced by anyone.
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Upgrade pi-top [3] says:
"because the way of life that may make them relevant is no longer practiced by anyone" – this is precisely what the end of the article explains isn’t the case…
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DrewTheMachinist says:
Pessimisim here from someone who always uses a username with unspeakable symbols in unicode is indeed ironic
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No Frency says:
Chinese and Japanese people also have it much easier with math thanks to their number system. For example, in Japanese instead of "thirteen" they say "juu san" (ten three) and for "one hundred and thirteen" they’ll say "hyaku juu san" (hundred ten three). All you need to know are numbers between 0 and 10, 100, 1000, 10000, and you easily know all numbers in between. French is probably the worst when it comes to numbers. Something like "eighty four" ends up "quatre vingt quatre" (four twenty four), but then "ninety four" is "quatre vingt quatre orze" (four tenty four orze) haha what the hell is an orze?.. i know i know, it’s actually (four twenty fourtneen) but it’s still stupid. Yay for languages which simply math.
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The Mighty Buzzard says:
That’s easier *talking about* math. They pretty much exclusively use Arabic numbers when *doing* math.
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JohnU says:
And then there’s French numbers…
99 – quatre-vingt-dix-neuf (literally "four twenties plus ten plus nine")
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Kaiser says:
And then there is Danish:
trehalvfems -> tre-(halv-fem)-s -> three and (halv-five)[twentie]s -> 3+4.5×20 -> 93
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bob says:
japanese kanji don’t translate to computers well though, with hundreds or thousands? of different characters and combinations thereof. the 26 + 10 alphabet and decimal system can be supported on a keyboard. maybe it doesn’t matter because technology has developed so that kanji could be entered on a drawing tablet, but in the past the roman alphabet was a massive advantage in computing.
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mac12345 says:
And 94 could be either "quatre vingt quatorze" or "Nonante quatre" depending on the speaker region.
And 14 is quatorze, not quatre orze
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Comedicles says:
Neat. Like Roman Numerals but a lot smarter. I don’t know about so many strokes compared to Arabic, but you write fewer characters.
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robertrapplean says:
This reminds me of something… was it.. maybe the Romans? Nah, they didn’t have a zero.
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evad says:
Bold title.
4 paragraphs dont deliver on it though.
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3L_S4N70 says:
Just one comment: the written numbers have less than 20 years now (they were created in 1994), it is the use of them orally that is ancestral. Interestingly, Canada has considered use them (I don’t know where in the process if the idea they are at the moment).
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Artenz says:
You’re not going to like hearing this, but the people who have trouble grasping the meaning of digits 0-9 are not going to make any difference in the world when you teach them something easier instead. For everybody else, this is just a distraction.
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Daniel Dunn says:
I *highly* doubt these people aren’t also going to be taught 0-9, because cheap calculators and phone keyboards, aka the main way people interact with math, use it.
Maybe it’s just as valuable as the times tables or all the other random math stuff nobody uses that we learn to theoretically help us learn other math, so that a few percent can get a job that actually uses it while everyone else just has a better appreciation of how to use a calculator.
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dudefromthenorth says:
Vigesimal ?
https://en.wikipedia.org/wiki/Vigesimal#Use
example; French umbering is 20 based, 80 being quatre-vingt, aka "four twenties"….
And others -
Isn’t this basically tick marks? |||| with a slash though them for five?
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Dude says:
"The Kaktovik numerals started as a class project to adapt the counting system to a written form. The numerals, based on tally marks, "look like" the Iñupiaq words they represent."
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aki009 says:
Surprisingly many of the numeric systems around the world trace their origins to India and the middle East of 8000 years ago. I personally like how the Sumerian numeric systems prevail until this very day (base 60) in things like the number of minutes in an hour, and the number of degrees in a circle. Numbers don’t lie, and they indicate that there’s a lot to our pre-history that we just haven’t connected yet.
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Dan says:
"Numbers don’t lie"
Err… nope. "Lies, damned lies, and statistics".
The UK census has just "shown" that 1/67 Muslims are trans, and those for whom English is not their first language are 5x more likely to be trans than native speakers. Quite clearly these numbers lie, and almost certainly relate to a badly worded question on the census.
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Dude says:
>Bartley reports that after a year of the students working fluently in both systems, scores on standardized math exams jumped from below the 20th percentile to "significantly above" the national average.
I’m afraid they’ve fallen into a trap. The article desicribes how the system was developed by the students themselves, and then taught alongside arabic numerals, which means the students actually got twice the math training because they were doing the work in double.
Naturally, if you train harder, your scores will improve faster. Whether that makes you any better at math is debatable.
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Upgrade pi-top [3] says:
Did they get twice the amount of training though? If the way human beings learn is primarily through repetition then "twice the training" would indicate "twice the hours". If they only had the same number of hours (not double) then they didn’t have "twice the training" and thus the differentiating factors are the content of what was learned and how they learned it.
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Dude says:
Possibly not twice, but still they went through a lot more trouble to incorporate the new system as opposed to just learning the old. More time spent on the subject, while approaching it through more varied examples, usually leads to greater learning outcomes.
Plus, there’s the Hawthorne effect where the test subjects become more engaged in the topic while they’re being tested, which leads to improvements in performance. When the new system becomes routine, performance drops to previous levels or lower, because the real effect was masked by the greater motivation of the test subjects. Everyone can perform at 110% for some time, but eventually fatigue will set in.
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Upgrade pi-top [3] says:
"More time spent on the subject" – again, if it was the same number of hours, that wasn’t "more time". Remains to be confirmed whether they had the same number of hours, or more.
Everything is relative; even if the effect you describe did happen, it would be in a system where people have still learned to understand Mathematics better through the language used so the general ability in Maths should be improved when compared to the previous system.
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Dude says:
True, but the point is that the results can be explained by other means than by the special base 20 number and symbol system being used.
Learning these kinds of arbitrary patterns can be entirely superfluous, and if the method of teaching is not motivating in the first place it can even become counter-productive with worse learning outcomes; exactly like "new math" where you were actually spending most of your effort learning set theory instead of basic arithmetic.
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Dude says:
Or, another example, in most language studies, the teacher is attempting to teach from the same point of view as they were taught as language teachers. As a result the students are forced to learn concepts and rules – essentially a whole different meta-language that analyzes and describes languages – rather than simply learning to speak in a different language. They have to learn what a concept like "accusative" means before they can follow the teacher’s instructions and answer their questions, which is simply more work and extra cognitive load. Nobody thinks in these terms when they’re actually conversing in a language.
In the same sense, it’s not efficient to teach multiple number notation systems for basic arithmetic. You can get the point across using any one of them, and the question is about keeping the kids interested enough to assimilate the information.
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Dude says:
>whether they had the same number of hours, or more.
Or completed more work in the same number of hours, or more homework, or spent more time on the subject outside of class voluntarily etc.
Usually in a math class, most kids are just trying to avoid work and entertain themselves to make the time pass quickly. Simply engaging them in the work improves results tremendously.
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Dude says:
And it’s not the hours of training really. If you repeat 1 + 1 for two hours, you’re not going to learn it any better – or at least you’ll have diminishing returns. Long term retention requires you to space it apart and "sleep over it".
Repetition leads to boredom, which shifts the brain into "I’ve seen this before" mode and it stops memorizing stuff, but if you pose the same problem from a novel angle, such as learning a different notation for the same thing, the brain goes "Hey, this is new, better pay attention." and you get a dopamine hit, and your brain makes a note to remember it better.
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Upgrade pi-top [3] says:
But that’s still repetition, just from a different angle. If you learn a list of vocabulary the night before a test and get a full score, it’s very easy to forget some of them within a week (perhaps a day, even) if you don’t repeat those words in different contexts.
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Dude says:
Yes, but it is from a different angle which avoids the boredom response.
The most effective form of repetition learning is by introducing the same subject as part of different problems, where the subject acts as a necessary stepping stone to solve the question. The problems themselves can be quite trivial, and should be so. Of course if you simply phrase the question differently like "Johnny has five apples…", it’s not novel – it’s just convoluted.
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Dude says:
What "rote learning" usually means is saturation learning, where you repeat repeat repeat until you can reproduce the correct answer by reflex. I say A, you reply B. That kind of learning is what’s mostly employed in elementary level math classes where you’re filling in sheets and sheets of "5 + _ = 8" type of problems where you simply fill in the correct answer. That’s exceedingly boring and very inefficient.
If you set the students to design their own system of notation, and rules for using it, then automatically you set up a situation where they have to learn the matter that you’re teaching as an instrument for achieving their goal. To think about the matter, they have to think in terms of the fundamental arithmetic, which means they repeat it over and over and automatically memorize it.
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Dude says:
https://www.gse.harvard.edu/news/ed/17/01/bored-out-their-minds
"A 2014 study that followed 424 students at the University of Munich over the course of an academic year found a cycle in which boredom bore lower test results, which bore higher levels of boredom, which bore still lower test results. Boredom accounts for nearly a third of variation in student achievement."
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Reluctant Cannibal says:
I’d like to see a proper system of notation for ternary ie (on), (off) and (both on and off) and get rid of binary in computers. Maybe it exists already?
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Upgrade pi-top [3] says:
Or quarternary, including "neither on, nor off" – a Schrödinger’s Cat-based, quantum system
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Reluctant Cannibal says:
I put your comment into Bard and it came up with this: ‘This system is called Schrödinger’s Cat notation. It is a base-4 number system, which means that it uses four symbols to represent numbers. The symbols are 0, 1, 1/2, and -1/2.’ Using ‘1/2’ is confusing and inappropriate IMO.
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Reluctant Cannibal says:
BTW i then asked Bard: ‘is there such a system as Schrödinger’s Cat notation?’ and they replied ‘no there is not’. So obviously Bard spontaneously invented it and then, only minutes later, forgot about it again.
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Upgrade pi-top [3] says:
I see what Bard did there Although it really ought to have replied:
There is
There isn’t
There is and isn’t
…I’ll show myself out
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Upgrade pi-top [3] says:
Sorry, I forgot the:
There neither is nor isn’t♂️
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Upgrade pi-top [3] says:
A brief DDG search indicates it might possibly be referred to as "Bra-Ket" notation?
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Dan says:
It’s been invented already, and the values are known as "true", "false", and "file not found".
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metan says:
The obvious answer why 60 is the number of minutes per hour is because it has maximal number of dividers up to it’s double, which just makes it convenient and obvious choice. There is nothing magical about it. The same reason goes why people used to count stuff in dozens instead of multiples of ten, e.g. you can divide dozen eggs between three people without a quarrel.
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Upgrade pi-top [3] says:
Huh. A more socialist counting system?
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anon says:
I agree with others here. This is just a bad idea. Unlike language, arabic numerals are near universal which means no matter where anyone is in the world they can write them down and everyone understands. THIS IS AMAZING. Even if by some miracle this was a better system to represent numbers (I’m sure 444 looks awesome using this system), it is not so much better as to cripple children into not learning a universal notation. If a system can make 0.1% more students comprehend math at the cost that all students in that group can not share math with others this is a net negative. If we are teaching students both systems why not just spend 2x as long teaching them the one everyone else uses I’m sure that will have better results.
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Winston says:
I’m for octal or hexadecimal combined with scientific notation. Fewer digits to write/type.
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Winston says:
Oops, make that just hexadecimal with scientific notation.
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LordNothing says:
an interesting system from my state. i think we may have had an assignment on these, but im not sure. i graduated back in 2000 and the system seems to have originated a few years before then. they seem familiar. of course this would have been more taught in village schools, where i went to school in anchorage, so i don’t think it would have been any more than a social studies assignment.
anyway go read the article to see the full matrix. i like that the number system forms its own look up table. such that the ones and fives components define the whole set.
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RunnerPack says:
"centuries of efforts to eradicate it and other native North American cultures" [citation needed]
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