13 ms·

A number system invented by Inuit schoolchildren

210 points by nathandaly 4y ago

foota 4y ago
I find it interesting but unsurprising that learning a second base system makes you better at math, much in the same way as learning a second language as a child has benefits.
- readthenotes1 4y ago
  From what I recall, the early success of the Dvorak keyboard was mostly the success of retraining someone on a keyboard. The new system does seem more visually accessible for arithmetic. I wouldn't be surprised if it's easier to teach children than the Arabic numerals
- photochemsyn 4y ago
  Grasping the concept of number regardless of base system is an interesting exercise (linked to modular arithmetic), see Mathologer on times tables in any number base: https://youtu.be/qhbuKbxJsk8 https://youtu.be/qhbuKbxJsk8
- cat_plus_plus 4y ago
  Second base in math classes would have better motivated me, that's for sure. Would that be a number system with 21 digits?
nashashmi 4y ago
Could our computers handle it? Makes me remember the count by 5 system. In this case, the 4 sticks are connected into a W. And the tick across the 4 sticks becomes a bar on top. The bar on top can count from 1-4. And then it goes to the next digit. So instead of base 16, we have a base 20.
- wolfram74 4y ago
  Much like mayan, a base 20 system, very nice for addition subtraction, need to be a bit cleverer for multiplication. I made a little javascript module to convert arab to mayan numerals and render an SVG to go with them. Here's a fun demo https://wolfram74.github.io/ArabIntToMayaInt/countdown.html https://wolfram74.github.io/ArabIntToMayaInt/countdown.html
- codebje 4y ago
  > Could our computers handle it? It's been a very long time since computers were anything other than binary, and unless quantum computing takes a, haha, quantum leap forward it will be a very long time yet until they're doing anything else. But they can handle converting to and from this numeral system for the few humans who find it more natural to work with just fine.
- kens 4y ago
  Yes, computers can handle base 20. The IBM 1401 business computer (1959) could optionally support pounds/shillings/pence in hardware, where there were 20 shillings in a pound and 12 pence in a shilling. (Britain switched to decimal currency in 1971 for reasons that should be clear.) It could add, subtract, multiply, divide, and format pounds/shillings/pence as well as its normal base-10 arithmetic. So it was doing base-12 and base-20 arithmetic. I should point out that this was implemented in hardware with transistors (lots of germanium transistors), not microcode or software. In other words, the three fundamental hardware datatypes of the IBM 1401 were arbitrary-length decimal numbers, arbitrary-length strings, and pounds/shillings/pence. Of course there were two conflicting standards on how to represent pounds/shillings/pence, so there was a knob on the computer's front panel to select the standard. (This isn't directly related to the Inuit base-20, but I'm sure IBM would have supported Inuit base-20 if customers would pay for it.)
boomboomsubban 4y ago
Wouldn't extending the system to 25 make more sense? I understand that it started as a representation of their previous system, but it stopping before W on W seems counterintuitive. No clue if that'd ruin the arithmetic benefits.
- thro1 4y ago
  I see it would be more consistent in base 25.. if we could make up the missing 5 fingers. For me base 20 is already to difficult as I'm not so good in counting with my toes.
  - boomboomsubban 4y ago
    Wrists, ankles, neck. They're easier to count than toes unless you have unusually good control of your individual toes.
behnamoh 4y ago
Sounds like typical SV hype tbh. Who needs to do number arithmetics anyway? Most math involves working with symbols (x, y, etc.) for which this number system is useless. And as for actual number arithmetics: calculators.
- eternityforest 4y ago
  Actually doing arithmetic is mostly useless in the modern world where everyone has phones, but teachers all seem convinced you still need to learn and understand it. Symbolic math is also not directly used much(or at all) by most non-STEM people, since there's an app for almost everything, but we still learn it even though it's a specialist kind of thing. Plus, if the kids are excited about it, maybe it's somehow relevant in the region in a way that's not obvious to people in the city, the same way that tradespeople actually like fractional units for some reason I don't really understand.
LudwigNagasena 4y ago
> Math is called the “universal language,” but a unique dialect is being reborn It is not a unique dialect. It is just a yet another numeral system. > Because of the tally-inspired design, arithmetic using the Kaktovik numerals is strikingly visual. Ok, so is there any reason to think that it is better than other similar systems like the Mayan system? I am not even convinced that “strikingly visual” system is any better than our modern way to represent numbers in bases above ten using letters (…, 8, 9, A, B, …). If numbers look similar, you are more likely to mix them up.
- cuteboy19 4y ago
  It is a straight downgrade from Hindu numerals and base 10
  - gpvos 4y ago
    Maybe some people would agree with you if you brought along some arguments.
- bawolff 4y ago
  2 used to be fairly visual https://upload.wikimedia.org/wikipedia/commons/c/c6/Evolution2glyph.png https://upload.wikimedia.org/wikipedia/commons/c/c6/Evolutio... I think the benefit, is its confusing to convert between systems. The point is to match the base ti the one the language/culture generally uses. English uses base-10, this particular language/cultural group did not, so constantly converting back and forth to base 10 was confusing.
- atlas_hugged 4y ago
  Please try thinking of something positive for a change. I was going to say more but your comments are just full of negativity. That can’t be healthy.
  - Gordonjcp 4y ago
    Please don't tone police people. It's not a great way to communicate, and it stifles discussion. You don't need to demonstrate your privilege at every opportunity you get.
andrewstuart 4y ago
Some of the earliest human civilizations used base 60 for their number system, which comes from counting fingers and knuckles, somehow.
- numbol 4y ago
  This is more to that! 60 is https://en.wikipedia.org/wiki/Superior_highly_composite_number https://en.wikipedia.org/wiki/Superior_highly_composite_numb... which means that lot of fractional numbers can be represnted in nice way. And because one year is around 360 days and 12 (another superior highly composite number) is roughly correspond to number of lunar months in the year, people used those to based their calendar and angular measurments around that. And 60 is very close to 64, so it could be nicely represented in binary... (10 is kinda akward, too big for 8 and too small for 16)
  - numbol 4y ago
    also https://en.wikipedia.org/wiki/Colossally_abundant_number https://en.wikipedia.org/wiki/Colossally_abundant_number
- kneebonian 4y ago
  3 knuckles on each digit. 5 digits per appendage, 4 appendages. 3 * 5 * 4 = 60 Actually quite intuitive and impressive.
  - andrewstuart 4y ago
    I think it’s more like this info: https://mathsciencehistory.com/2021/11/09/count-to-60-with-your-phalanges/ https://mathsciencehistory.com/2021/11/09/count-to-60-with-y... They counted to 60 by counting the 3 phalanges on each finger on one hand and with their other hand they indicated each time they added 12 more numbers to their count. So by adding 12 numbers 5 times they were able to count to 60! This is base 60, also known as the sexagesimal number system.
  - galleywest200 4y ago
    Thumbs have two knuckles?
bawolff 4y ago
That's cool and all, but the computer aspect of this is it just got encoded into unicode and someone is making a font. Great for users of this system of course but ultimately not exactly the most exciting.
- jonny_eh 4y ago
  > not exactly the most exciting What was the last novel number system that impressed you?
  - bawolff 4y ago
    Idk, Base64 i guess. Actually the UTF-8 encoding is pretty ingenious. However, that's beside the point. This number system this article is talking about is 30 years old. The article is actually about encoding some glyphs in unicode not the number system. The number system is interesting. Adding a bunch of glyphs to unicode is not particularly.
  - cat_plus_plus 4y ago
    Binary and 2s compliment negative numbers / normalized floats, took some out of the box thinking.
KingLancelot 4y ago
[dead]
photochemsyn 4y ago
> "The Alaskan Inuit language, known as Iñupiaq, uses an oral counting system built around the human body. Quantities are first described in groups of five, 10, and 15 and then in sets of 20." So, sounds fundamentally like Mayan numerals? https://en.wikipedia.org/wiki/Maya_numerals https://en.wikipedia.org/wiki/Maya_numerals
- galleywest200 4y ago
  Sure, but without the need to draw an entire seashell to represent zero.
- tragomaskhalos 4y ago
  Interesting challenge: do arithmetic using only the 'head variant' Mayan forms!
- kzrdude 4y ago
  French counting numbers are also still partly 20-based, as are danish and welsh. It's said it's a remnant of an earlier common numerical system. It's then even possible that human languages came from a common origin with a 20-based system, and some kept it.
  - rvense 4y ago
    Danish counting is no more base 20 than English (that is, it is until 20). The words for 50, 60, 70, 80, and 90 are derived from an old word for twenty, but it's really no different than English having "twenty", "thirty" and "fifty" instead of "twoty", "threety" and "fivety". It's not like French where 99 is 80+19.
    - kzrdude 4y ago
      In french, 90 is 4 x 20 + 10 and in danish, 90 is "4½" x 20, seems similar to me. You can ignore that and just learn the words as opaque names for concepts, but then you don't see the underlying structure.
8note 4y ago
The examples listed feel contrived to get the best case results rather than the worst case. I think the most interesting checks is with exponentials though? How does this represent e? Pi? Complex number rotations?
- sp332 4y ago
  e and pi wouldn't really be different. Not worse, anyway. I don't have a way to draw with those numerals here, but just swap in the digits: (2) . (14) (7) (6) (5) (1) (17) (0) (8) (11) (0) (12) (9) (5)... (3) . (2) (16) (12) (14) (16) (9) (16) (11) (17) (19) (9) (13) (2)...
- lelanthran 4y ago
  > The examples listed feel contrived to get the best case results rather than the worst case. They're cherry-picked. For addition, it only "makes sense visually" the way the article says it does if the answer lies within the sub-base-5 digit (i.e. the answer is, worst case, less than 5 numbers away). There's also arbitrary rules in the so-called "easy visual arithmetic" - for some divisions (not all), some strokes have to be rotated. For the long division example, the visual indication of the remainder is reversed - i.e. it's a mirror image of the actual digit. While I like the idea (the base-20 with sub-bases-5 makes counting easier, and having sub-bases means less memory overhead in memorising all 20 digits), the article itself is spinning wildly to make this seem like "the children came up with it on their own". The title says "A number system invented by schoolchildren", while the article says that this was the result of a teacher-lead class project which came up with symbols for an existing numbering system. Aside: With the exception of zero this numbering system is only slightly different from roman numerals - use the number of strokes and the special symbol to determine what number you are at. Counting is easier, and simple addition/subtraction/division is easier with roman numerals as well, but as soon as you need to do common things (approximate VAT for any figure[1]) then base-10 is so much easier. For really easy arithmetic, using a base-12 counting system is even better (hence, the rise and popularity of imperial measures, which layers a base-12 system on top of base-10). [1] VAT is 15% where I am, so mentally approximating VAT of $FOO is "10% of $FOO + 1/2 of 10% of $FOO). When it was 14% it was just as easy, do the above and remove 1%.
- 4y ago
joseph_grobbles 4y ago
[dead]
egberts1 4y ago
Base 20, with stick figures; got it.
todd8 4y ago
I dislike these pseudo-scientific claims about alternative number systems and methods of paper and pencil arithmetic: > Because of the tally-inspired design, arithmetic using the Kaktovik numerals is strikingly visual. Addition, subtraction and even long division become almost geometric. The Hindu-Arabic digits are an awkward system, Bartley says, but “the students found, with their numerals, they could solve problems a better way, a faster way.” I think the students can be praised for having come up with simple to understand and write number system that corresponds to the conventions for counting in Alaskan Inuit language, and it seems appropriate to capture these notations in upcoming Unicode standards. However, spending time learning base 20 arithmetic has obvious disadvantages that the article ignores. The times tables, memorized in grade school and fundamental to paper and pencil calculations, are now four times larger. Base 20 is not a popular notation for numbers. One important advantage of the number system (Hindu-Arabic) that most of the world uses is that most of the world uses it. I grew up with inches and degrees Fahrenheit and had to learn the metric system to pursue my science education. I'm glad I didn't have to learn how to count as well. We shouldn't make it harder for these kids to enjoy the rest of the world's books, journals, and internet resources about math and science.
- Etrnl_President 4y ago
  Babylonyan Base 60 is superior.
  - rendall 4y ago
    Your joke was misinterpreted as a dig, unfortunately. I mean, it's obvious that a prime-number base is best above all: 1 = 1 10 = 2 100 = 3 1000 = 5 10000 = 7 100000 = 11 etc
    - rocqua 4y ago
      You get non-canonical representations such as 11=3 You could go multiplicative based. So 11 = 2×3. But then you get very difficult addition, comparison, and you need numerals inside your numerals. (E.g. 2048 would be 11 as in a single 11 in the first symbol spot)
cat_plus_plus 4y ago
The decimal system is already based on the human body, most people are just not great at bending their toes one by one and find it convenient to have them covered by footwear. If you want a special symbol for one full hand, just use Roman numerals. This reminds me of retro computing. Amiga or BeOS had some amazing concepts for the time, and quite possibly Wintel dominance was achieved by predatory tactics. It can be interesting to study old platforms and some enjoy creating new software up to this day. But if you limit yourself to these, don't expect modern living. At best you can hook up an old computer to a modern one as a thin client and fool yourself into thinking that harpooning a whale from a motor boat is traditional living. For whatever reason the world have move on and it's not possible for could have been possibilities to ever catch up with limited number of participants, since the rest of the world will also not stand still.
- magic_hamster 4y ago
  As a retro computing aficionado, this is where I disagree. Learning about old computers has always taught me something useful about modern systems. Going back to the first IBMs and Apple architectures has a lot of merit. It's like reading a book from the beginning, instead of jumping in the middle and trying to make sense of everything. You can probably continue reading, but you won't know why some things are the way they are. Obviously, developing software for obsolete systems is not a great income stream, but as an exercise, this too has merit. You learn a lot about constraints and limitations, which today are rarely considered, but could still teach you how to optimize code. You learn how to produce software which can run surprisingly fast on machines from 30 or 40 years ago, and that is transferrable to modern coding. You learn a lot about memory, how to use it efficiently and what can be achieved with just 640K, which as we all know, "is all the memory anyone should ever need". You learn that by introducing limitations a sort of game happens in which you need to be more creative to implement things which have since become obvious. And this makes you a better problem solver. There is a lot to learn from old computers, and while some people will always disagree, I think it makes you a better software engineer.
- anthk 4y ago
  Both Aros and Haiku support open standards.
asjfka 4y ago
I like it. Remove the last column and you have a far better hexadecimal notation than using 0123456789ABCDEF
witrak 4y ago
Sorry, but I don't understand the basis for the opinion presented by a couple of people that the Kaktovik numeral system is similar to the Roman one. Is that because both of them use short lines as the sole element to build digits/numbers?! But Kaktovik is a positional system while Roman is not!
MPlus88 4y ago
[dead]
n4r9 4y ago
Last year someone on HN linked to a sample set of problems from the International Linguistics Olympiad. I really enjoyed working through a few of them and found it an approachable challenge despite having no training in linguistics. About 2/3 of the way down there's a problem on Inuktitut Numbers, which I recommend attempting before reading the attached article if possible: https://ioling.org/booklets/samples.en.pdf https://ioling.org/booklets/samples.en.pdf
- majou 4y ago
  The one time I read the article before the comments...
  - n4r9 4y ago
    The problems on Kazakh and Basque numbers also look fun :)
2d8a875f-39a2-4 4y ago
"... a two-dimensional positional value system with a primary base of 20 and a sub-base of 5" Saved you a click.
ricardobeat 4y ago
What I found interesting is that you could write these right-to-left and bottom-up, as long as you allow the top part to point in either direction, which makes the whole thing a lot easier. For example, 171: \ (1) \/\ \ (60 + 1) > \/\ \ (70 + 1, add 10 to the right digit) / > \/\ \ (171, add 100 to the left digit) Hopefully this makes sense, utf-8 will need to catch-up :)
aaron695 4y ago
[dead]
candiodari 4y ago
Kids invent numbering systems all the time. Usually they see the point of numbers very early on and use their fingers to count. But occasionally they're very creative. I have 3 kids. I remember an instance where the middle one asked for candy. So I said "how much". And she got her box of marbles and stones she collected (quite a collection), and wanted that many.
c3534l 4y ago
This is quite similar to Sumerian numerals and countless other tally-based numerals. I fail to see what's totally unique about this number system.
OJFord 4y ago
It works with the cherry-picked examples. 9-8 for example gives not 1 but its mirror image.
red75prime 4y ago
Looks like diversity for diversity's sake. An alternative number system that will never be widely adopted due to switching barriers. Cool. Whatever.
thro1 4y ago
We have no glyph for \/\, with glyph we have it could be: | V N W or 1 V N W, but with unique glyphs: | /| X| |X|
c7b 4y ago
The visual logic sure seems nice, and the test results seem to speak for themselves (would be interesting to see studies on its impact). But I can't help but feel that if we are going to introduce a new number system with a different base at all, then that base should be 12. It's a highly composite number, it's divisible by 2, 3, 4 and 6, meaning that 1/2, 1/3, 1/4 and 1/6 (and their multiples) all have finite-digit representations, which would simplify a lot of everyday calculations. Several pop science articles have been written about the case for base 12: https://www.scienceabc.com/eyeopeners/why-we-should-already-use-base-12-instead-of-base-10.html https://www.scienceabc.com/eyeopeners/why-we-should-already-... https://gizmodo.com/why-we-should-switch-to-a-base-12-counting-system-5977095 https://gizmodo.com/why-we-should-switch-to-a-base-12-counti... If we're happy to use 11 new symbols instead of just 2, we could even keep the ideas from this system of using ticks and sub-bases to make computations more 'visual'.
WakoMan12 4y ago
[dead]
Maursault 4y ago
Invented... or discovered!
nathandaly 4y ago
These are so neat. It seems like they would make arithmetic much easier! If you ever played Riven, I think the Kaktovik numerals inspired the numbering system from the game. Spoilers: https://lparchive.org/Riven/Update%2015/ https://lparchive.org/Riven/Update%2015/
- waldothedog 4y ago
  Wow, I can still remember the puzzle in this game that got me stuck, never solved it! Thanks for the memory-trip 0__0
  - petermcneeley 4y ago
    There is an entire alphabet in the school (located in the middel of the lake) https://omniglot.com/conscripts/dni.htm https://omniglot.com/conscripts/dni.htm
    - duskwuff 4y ago
      IIRC, the D'ni text you find in the school is written in their own (constructed) language. The player isn't expected to decipher it; I'm not sure if there's even enough information in the game to do so.
      - petermcneeley 4y ago
        I spent hours trying though ...
- readthenotes1 4y ago
  So long. So long ago. I remember why I never finished it--too much life to live at the time...
- duskwuff 4y ago
  D'ni numerals were base 25, not 20. Each digit is composed of two base-5 "sub-digits" superimposed at 90° to each other -- the digits are designed such that this is unambiguous.

210 points by nathandaly 4y ago

I find it interesting but unsurprising that learning a second base system makes you better at math, much in the same way as learning a second language as a child has benefits.

readthenotes1 4y ago
From what I recall, the early success of the Dvorak keyboard was mostly the success of retraining someone on a keyboard. The new system does seem more visually accessible for arithmetic. I wouldn't be surprised if it's easier to teach children than the Arabic numerals
photochemsyn 4y ago
Grasping the concept of number regardless of base system is an interesting exercise (linked to modular arithmetic), see Mathologer on times tables in any number base: https://youtu.be/qhbuKbxJsk8 https://youtu.be/qhbuKbxJsk8
cat_plus_plus 4y ago
Second base in math classes would have better motivated me, that's for sure. Would that be a number system with 21 digits?

nashashmi 4y ago

Could our computers handle it? Makes me remember the count by 5 system. In this case, the 4 sticks are connected into a W. And the tick across the 4 sticks becomes a bar on top. The bar on top can count from 1-4. And then it goes to the next digit. So instead of base 16, we have a base 20.

wolfram74 4y ago
Much like mayan, a base 20 system, very nice for addition subtraction, need to be a bit cleverer for multiplication. I made a little javascript module to convert arab to mayan numerals and render an SVG to go with them. Here's a fun demo https://wolfram74.github.io/ArabIntToMayaInt/countdown.html https://wolfram74.github.io/ArabIntToMayaInt/countdown.html
codebje 4y ago
> Could our computers handle it? It's been a very long time since computers were anything other than binary, and unless quantum computing takes a, haha, quantum leap forward it will be a very long time yet until they're doing anything else. But they can handle converting to and from this numeral system for the few humans who find it more natural to work with just fine.
kens 4y ago
Yes, computers can handle base 20. The IBM 1401 business computer (1959) could optionally support pounds/shillings/pence in hardware, where there were 20 shillings in a pound and 12 pence in a shilling. (Britain switched to decimal currency in 1971 for reasons that should be clear.) It could add, subtract, multiply, divide, and format pounds/shillings/pence as well as its normal base-10 arithmetic. So it was doing base-12 and base-20 arithmetic. I should point out that this was implemented in hardware with transistors (lots of germanium transistors), not microcode or software. In other words, the three fundamental hardware datatypes of the IBM 1401 were arbitrary-length decimal numbers, arbitrary-length strings, and pounds/shillings/pence. Of course there were two conflicting standards on how to represent pounds/shillings/pence, so there was a knob on the computer's front panel to select the standard. (This isn't directly related to the Inuit base-20, but I'm sure IBM would have supported Inuit base-20 if customers would pay for it.)

boomboomsubban 4y ago

Wouldn't extending the system to 25 make more sense? I understand that it started as a representation of their previous system, but it stopping before W on W seems counterintuitive. No clue if that'd ruin the arithmetic benefits.

thro1 4y ago
I see it would be more consistent in base 25.. if we could make up the missing 5 fingers. For me base 20 is already to difficult as I'm not so good in counting with my toes.
- boomboomsubban 4y ago
  Wrists, ankles, neck. They're easier to count than toes unless you have unusually good control of your individual toes.

behnamoh 4y ago

Sounds like typical SV hype tbh. Who needs to do number arithmetics anyway? Most math involves working with symbols (x, y, etc.) for which this number system is useless. And as for actual number arithmetics: calculators.

eternityforest 4y ago
Actually doing arithmetic is mostly useless in the modern world where everyone has phones, but teachers all seem convinced you still need to learn and understand it. Symbolic math is also not directly used much(or at all) by most non-STEM people, since there's an app for almost everything, but we still learn it even though it's a specialist kind of thing. Plus, if the kids are excited about it, maybe it's somehow relevant in the region in a way that's not obvious to people in the city, the same way that tradespeople actually like fractional units for some reason I don't really understand.

LudwigNagasena 4y ago

> Math is called the “universal language,” but a unique dialect is being reborn It is not a unique dialect. It is just a yet another numeral system. > Because of the tally-inspired design, arithmetic using the Kaktovik numerals is strikingly visual. Ok, so is there any reason to think that it is better than other similar systems like the Mayan system? I am not even convinced that “strikingly visual” system is any better than our modern way to represent numbers in bases above ten using letters (…, 8, 9, A, B, …). If numbers look similar, you are more likely to mix them up.

cuteboy19 4y ago
It is a straight downgrade from Hindu numerals and base 10
- gpvos 4y ago
  Maybe some people would agree with you if you brought along some arguments.
bawolff 4y ago
2 used to be fairly visual https://upload.wikimedia.org/wikipedia/commons/c/c6/Evolution2glyph.png https://upload.wikimedia.org/wikipedia/commons/c/c6/Evolutio... I think the benefit, is its confusing to convert between systems. The point is to match the base ti the one the language/culture generally uses. English uses base-10, this particular language/cultural group did not, so constantly converting back and forth to base 10 was confusing.
atlas_hugged 4y ago
Please try thinking of something positive for a change. I was going to say more but your comments are just full of negativity. That can’t be healthy.
- Gordonjcp 4y ago
  Please don't tone police people. It's not a great way to communicate, and it stifles discussion. You don't need to demonstrate your privilege at every opportunity you get.

andrewstuart 4y ago

Some of the earliest human civilizations used base 60 for their number system, which comes from counting fingers and knuckles, somehow.

numbol 4y ago
This is more to that! 60 is https://en.wikipedia.org/wiki/Superior_highly_composite_number https://en.wikipedia.org/wiki/Superior_highly_composite_numb... which means that lot of fractional numbers can be represnted in nice way. And because one year is around 360 days and 12 (another superior highly composite number) is roughly correspond to number of lunar months in the year, people used those to based their calendar and angular measurments around that. And 60 is very close to 64, so it could be nicely represented in binary... (10 is kinda akward, too big for 8 and too small for 16)
- numbol 4y ago
  also https://en.wikipedia.org/wiki/Colossally_abundant_number https://en.wikipedia.org/wiki/Colossally_abundant_number
kneebonian 4y ago
3 knuckles on each digit. 5 digits per appendage, 4 appendages. 3 * 5 * 4 = 60 Actually quite intuitive and impressive.
- andrewstuart 4y ago
  I think it’s more like this info: https://mathsciencehistory.com/2021/11/09/count-to-60-with-your-phalanges/ https://mathsciencehistory.com/2021/11/09/count-to-60-with-y... They counted to 60 by counting the 3 phalanges on each finger on one hand and with their other hand they indicated each time they added 12 more numbers to their count. So by adding 12 numbers 5 times they were able to count to 60! This is base 60, also known as the sexagesimal number system.
- galleywest200 4y ago
  Thumbs have two knuckles?

bawolff 4y ago

That's cool and all, but the computer aspect of this is it just got encoded into unicode and someone is making a font. Great for users of this system of course but ultimately not exactly the most exciting.

jonny_eh 4y ago
> not exactly the most exciting What was the last novel number system that impressed you?
- bawolff 4y ago
  Idk, Base64 i guess. Actually the UTF-8 encoding is pretty ingenious. However, that's beside the point. This number system this article is talking about is 30 years old. The article is actually about encoding some glyphs in unicode not the number system. The number system is interesting. Adding a bunch of glyphs to unicode is not particularly.
- cat_plus_plus 4y ago
  Binary and 2s compliment negative numbers / normalized floats, took some out of the box thinking.

KingLancelot 4y ago

[dead]

photochemsyn 4y ago

> "The Alaskan Inuit language, known as Iñupiaq, uses an oral counting system built around the human body. Quantities are first described in groups of five, 10, and 15 and then in sets of 20." So, sounds fundamentally like Mayan numerals? https://en.wikipedia.org/wiki/Maya_numerals https://en.wikipedia.org/wiki/Maya_numerals

galleywest200 4y ago
Sure, but without the need to draw an entire seashell to represent zero.
tragomaskhalos 4y ago
Interesting challenge: do arithmetic using only the 'head variant' Mayan forms!
kzrdude 4y ago
French counting numbers are also still partly 20-based, as are danish and welsh. It's said it's a remnant of an earlier common numerical system. It's then even possible that human languages came from a common origin with a 20-based system, and some kept it.
- rvense 4y ago
  Danish counting is no more base 20 than English (that is, it is until 20). The words for 50, 60, 70, 80, and 90 are derived from an old word for twenty, but it's really no different than English having "twenty", "thirty" and "fifty" instead of "twoty", "threety" and "fivety". It's not like French where 99 is 80+19.
  - kzrdude 4y ago
    In french, 90 is 4 x 20 + 10 and in danish, 90 is "4½" x 20, seems similar to me. You can ignore that and just learn the words as opaque names for concepts, but then you don't see the underlying structure.

8note 4y ago

The examples listed feel contrived to get the best case results rather than the worst case. I think the most interesting checks is with exponentials though? How does this represent e? Pi? Complex number rotations?

sp332 4y ago
e and pi wouldn't really be different. Not worse, anyway. I don't have a way to draw with those numerals here, but just swap in the digits: (2) . (14) (7) (6) (5) (1) (17) (0) (8) (11) (0) (12) (9) (5)... (3) . (2) (16) (12) (14) (16) (9) (16) (11) (17) (19) (9) (13) (2)...
lelanthran 4y ago
> The examples listed feel contrived to get the best case results rather than the worst case. They're cherry-picked. For addition, it only "makes sense visually" the way the article says it does if the answer lies within the sub-base-5 digit (i.e. the answer is, worst case, less than 5 numbers away). There's also arbitrary rules in the so-called "easy visual arithmetic" - for some divisions (not all), some strokes have to be rotated. For the long division example, the visual indication of the remainder is reversed - i.e. it's a mirror image of the actual digit. While I like the idea (the base-20 with sub-bases-5 makes counting easier, and having sub-bases means less memory overhead in memorising all 20 digits), the article itself is spinning wildly to make this seem like "the children came up with it on their own". The title says "A number system invented by schoolchildren", while the article says that this was the result of a teacher-lead class project which came up with symbols for an existing numbering system. Aside: With the exception of zero this numbering system is only slightly different from roman numerals - use the number of strokes and the special symbol to determine what number you are at. Counting is easier, and simple addition/subtraction/division is easier with roman numerals as well, but as soon as you need to do common things (approximate VAT for any figure[1]) then base-10 is so much easier. For really easy arithmetic, using a base-12 counting system is even better (hence, the rise and popularity of imperial measures, which layers a base-12 system on top of base-10). [1] VAT is 15% where I am, so mentally approximating VAT of $FOO is "10% of $FOO + 1/2 of 10% of $FOO). When it was 14% it was just as easy, do the above and remove 1%.
4y ago

joseph_grobbles 4y ago

[dead]

egberts1 4y ago

Base 20, with stick figures; got it.

todd8 4y ago

I dislike these pseudo-scientific claims about alternative number systems and methods of paper and pencil arithmetic: > Because of the tally-inspired design, arithmetic using the Kaktovik numerals is strikingly visual. Addition, subtraction and even long division become almost geometric. The Hindu-Arabic digits are an awkward system, Bartley says, but “the students found, with their numerals, they could solve problems a better way, a faster way.” I think the students can be praised for having come up with simple to understand and write number system that corresponds to the conventions for counting in Alaskan Inuit language, and it seems appropriate to capture these notations in upcoming Unicode standards. However, spending time learning base 20 arithmetic has obvious disadvantages that the article ignores. The times tables, memorized in grade school and fundamental to paper and pencil calculations, are now four times larger. Base 20 is not a popular notation for numbers. One important advantage of the number system (Hindu-Arabic) that most of the world uses is that most of the world uses it. I grew up with inches and degrees Fahrenheit and had to learn the metric system to pursue my science education. I'm glad I didn't have to learn how to count as well. We shouldn't make it harder for these kids to enjoy the rest of the world's books, journals, and internet resources about math and science.

Etrnl_President 4y ago
Babylonyan Base 60 is superior.
- rendall 4y ago
  Your joke was misinterpreted as a dig, unfortunately. I mean, it's obvious that a prime-number base is best above all: 1 = 1 10 = 2 100 = 3 1000 = 5 10000 = 7 100000 = 11 etc
  - rocqua 4y ago
    You get non-canonical representations such as 11=3 You could go multiplicative based. So 11 = 2×3. But then you get very difficult addition, comparison, and you need numerals inside your numerals. (E.g. 2048 would be 11 as in a single 11 in the first symbol spot)

cat_plus_plus 4y ago

The decimal system is already based on the human body, most people are just not great at bending their toes one by one and find it convenient to have them covered by footwear. If you want a special symbol for one full hand, just use Roman numerals. This reminds me of retro computing. Amiga or BeOS had some amazing concepts for the time, and quite possibly Wintel dominance was achieved by predatory tactics. It can be interesting to study old platforms and some enjoy creating new software up to this day. But if you limit yourself to these, don't expect modern living. At best you can hook up an old computer to a modern one as a thin client and fool yourself into thinking that harpooning a whale from a motor boat is traditional living. For whatever reason the world have move on and it's not possible for could have been possibilities to ever catch up with limited number of participants, since the rest of the world will also not stand still.

magic_hamster 4y ago
As a retro computing aficionado, this is where I disagree. Learning about old computers has always taught me something useful about modern systems. Going back to the first IBMs and Apple architectures has a lot of merit. It's like reading a book from the beginning, instead of jumping in the middle and trying to make sense of everything. You can probably continue reading, but you won't know why some things are the way they are. Obviously, developing software for obsolete systems is not a great income stream, but as an exercise, this too has merit. You learn a lot about constraints and limitations, which today are rarely considered, but could still teach you how to optimize code. You learn how to produce software which can run surprisingly fast on machines from 30 or 40 years ago, and that is transferrable to modern coding. You learn a lot about memory, how to use it efficiently and what can be achieved with just 640K, which as we all know, "is all the memory anyone should ever need". You learn that by introducing limitations a sort of game happens in which you need to be more creative to implement things which have since become obvious. And this makes you a better problem solver. There is a lot to learn from old computers, and while some people will always disagree, I think it makes you a better software engineer.
anthk 4y ago
Both Aros and Haiku support open standards.

asjfka 4y ago

I like it. Remove the last column and you have a far better hexadecimal notation than using 0123456789ABCDEF

witrak 4y ago

Sorry, but I don't understand the basis for the opinion presented by a couple of people that the Kaktovik numeral system is similar to the Roman one. Is that because both of them use short lines as the sole element to build digits/numbers?! But Kaktovik is a positional system while Roman is not!

MPlus88 4y ago

[dead]

n4r9 4y ago

Last year someone on HN linked to a sample set of problems from the International Linguistics Olympiad. I really enjoyed working through a few of them and found it an approachable challenge despite having no training in linguistics. About 2/3 of the way down there's a problem on Inuktitut Numbers, which I recommend attempting before reading the attached article if possible: https://ioling.org/booklets/samples.en.pdf https://ioling.org/booklets/samples.en.pdf

majou 4y ago
The one time I read the article before the comments...
- n4r9 4y ago
  The problems on Kazakh and Basque numbers also look fun :)

2d8a875f-39a2-4 4y ago

"... a two-dimensional positional value system with a primary base of 20 and a sub-base of 5" Saved you a click.

ricardobeat 4y ago

What I found interesting is that you could write these right-to-left and bottom-up, as long as you allow the top part to point in either direction, which makes the whole thing a lot easier. For example, 171: \ (1) \/\ \ (60 + 1) > \/\ \ (70 + 1, add 10 to the right digit) / > \/\ \ (171, add 100 to the left digit) Hopefully this makes sense, utf-8 will need to catch-up :)

aaron695 4y ago

[dead]

candiodari 4y ago

Kids invent numbering systems all the time. Usually they see the point of numbers very early on and use their fingers to count. But occasionally they're very creative. I have 3 kids. I remember an instance where the middle one asked for candy. So I said "how much". And she got her box of marbles and stones she collected (quite a collection), and wanted that many.

c3534l 4y ago

This is quite similar to Sumerian numerals and countless other tally-based numerals. I fail to see what's totally unique about this number system.

OJFord 4y ago

It works with the cherry-picked examples. 9-8 for example gives not 1 but its mirror image.

red75prime 4y ago

Looks like diversity for diversity's sake. An alternative number system that will never be widely adopted due to switching barriers. Cool. Whatever.

thro1 4y ago

We have no glyph for \/\, with glyph we have it could be: | V N W or 1 V N W, but with unique glyphs: | /| X| |X|

c7b 4y ago

The visual logic sure seems nice, and the test results seem to speak for themselves (would be interesting to see studies on its impact). But I can't help but feel that if we are going to introduce a new number system with a different base at all, then that base should be 12. It's a highly composite number, it's divisible by 2, 3, 4 and 6, meaning that 1/2, 1/3, 1/4 and 1/6 (and their multiples) all have finite-digit representations, which would simplify a lot of everyday calculations. Several pop science articles have been written about the case for base 12: https://www.scienceabc.com/eyeopeners/why-we-should-already-use-base-12-instead-of-base-10.html https://www.scienceabc.com/eyeopeners/why-we-should-already-... https://gizmodo.com/why-we-should-switch-to-a-base-12-counting-system-5977095 https://gizmodo.com/why-we-should-switch-to-a-base-12-counti... If we're happy to use 11 new symbols instead of just 2, we could even keep the ideas from this system of using ticks and sub-bases to make computations more 'visual'.

WakoMan12 4y ago

[dead]

Maursault 4y ago

Invented... or discovered!

nathandaly 4y ago

These are so neat. It seems like they would make arithmetic much easier! If you ever played Riven, I think the Kaktovik numerals inspired the numbering system from the game. Spoilers: https://lparchive.org/Riven/Update%2015/ https://lparchive.org/Riven/Update%2015/

waldothedog 4y ago
Wow, I can still remember the puzzle in this game that got me stuck, never solved it! Thanks for the memory-trip 0__0
- petermcneeley 4y ago
  There is an entire alphabet in the school (located in the middel of the lake) https://omniglot.com/conscripts/dni.htm https://omniglot.com/conscripts/dni.htm
  - duskwuff 4y ago
    IIRC, the D'ni text you find in the school is written in their own (constructed) language. The player isn't expected to decipher it; I'm not sure if there's even enough information in the game to do so.
    - petermcneeley 4y ago
      I spent hours trying though ...
readthenotes1 4y ago
So long. So long ago. I remember why I never finished it--too much life to live at the time...
duskwuff 4y ago
D'ni numerals were base 25, not 20. Each digit is composed of two base-5 "sub-digits" superimposed at 90° to each other -- the digits are designed such that this is unambiguous.