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Kaktovik Numerals
- arketyp 4y agoSeems like it could be generalized to something more like a base 5 where the positions are rotated.
- kmill 4y agoThis sort of rotation-and-superposition number system also appears (in base 5 too!) in the game Riven: https://dni.fandom.com/wiki/D%27ni_Numerals https://dni.fandom.com/wiki/D%27ni_Numerals It's sort of funny how both Kaktovik and the D'ni numerals were invented around the same time (1994 for Kaktovik and 1997 for when Riven was released).
- 082349872349872 4y agoTIL a new way to write sheep counts (spoken system: https://en.wikipedia.org/wiki/Yan_tan_tethera https://en.wikipedia.org/wiki/Yan_tan_tethera )
- 6502nerdface 4y agoAs employed so hauntingly by Jake Thackray in "Molly Metcalfe": https://youtu.be/TiXINuf5nbI https://youtu.be/TiXINuf5nbI
- pimlottc 4y agoLovely story and song! Thanks for sharing!
- monopoliessuck 4y agoI'd be in support of stopping at 15 and moving to a base 16 metric. Hexadecimal numbers being discrete from alpha glyphs would be a bonus.
- deleted 4y ago[deleted]
- scotty79 4y agoStopping at 10 is nice too and also an option.
- downvotetruth 4y ago16 is not a colossally abundant number
- hui-zheng 4y agoso these numerals notation were invented in 1994. How does the Iñupiaq people do numeric calculation in the past without numerals notation?
- kerpotgh 4y agoProbably like a lot of other hunter gatherer groups, worked with 10 numbers at most- what they could count on their fingers.
- tom-thistime 4y agoI don't think they'd necessarily have a base-20 system built into the language if they didn't work with numbers larger than 10.
- pavlov 4y agoThere's another set of countables on feet, for a total of 20.
- Ancapistani 4y agoBase-20 works well on one hand. Using your thumb, start counting on the first bone in each finger. That gets you to four. Continue with the first joint (8), then the second bone (12), then the second joint (16) and finally the tips (20).
- Schiphol 4y agoAnd 32 with your fingers only, if you use each finger as a bit :)
- Turing_Machine 4y agoIf you use all 10, you can count up to 1024. :-)
- Panoramix 4y agohttps://en.wikipedia.org/wiki/Maya_numerals https://en.wikipedia.org/wiki/Maya_numerals The Mayan numerals are also base 20 but like 2000 years older.
- ithkuil 4y agoTIL Maya used a mixed radix system for calendars, using base 18 for most significant digits and base 20 for least significant digits. The real world is messy
- thaumasiotes 4y agoWe also use a mixed radix system for calendars, which is why we separate the digits of a date with non-numeric separators.
- nayuki 4y agoI see similarities with Chinese https://en.wikipedia.org/wiki/Counting_rods https://en.wikipedia.org/wiki/Counting_rods
- scotty79 4y agoFont that supports Kaktovik numerals: https://languagetools-153419.appspot.com/ik/downloads/ https://languagetools-153419.appspot.com/ik/downloads/
- kej 4y agoWhy stop at base-20 when base-1000 is available? https://en.wikipedia.org/wiki/Cistercian_numerals https://en.wikipedia.org/wiki/Cistercian_numerals
- kibwen 4y agoHow inefficient! It only takes 10 distinct black-and-white pixels to represent 1000 distinct glyphs. Even low-res bitmap fonts are usually at least 6x6 pixels in size, meaning that we can use them to represent numbers in base 2^36. And with modern high-DPI screens we have easily enough room for glyphs that are 30 pixels square, letting us represent numbers in base 2^900. But why limit ourselves to black and white? We have the full 8-bit color space to work with, letting us devise a numeral system that can easily represent (2^24)^900 numbers using the space of a single glyph. :)
- Turing_Machine 4y agoBase e would be the most efficient, if one assumes that the cost of representing a number in a particular radix is proportional to the radix. If you restrict the radix to natural numbers (e-state devices being rather hard to construct), base 3 would be more efficient. As it happens, we've learned to make two-state devices way more cheaply than three-state devices, so binary wins in the real world, but if we figured out how to make three-state devices for at most 1.5 times the cost of two-state devices, base three would win. It's fun to prove that base e and base 3 are theoretically more efficient than base 2 (and not all that difficult...only basic calculus is necessary).
- l- 4y ago> Base e would be the most efficient Only in one dimension.
- vintermann 4y ago> The Iñupiaq language has a base-20 numeral system, as do the other Eskimo–Aleut languages of Alaska and Canada (and formerly Greenland). Arabic numerals, which were designed for a base-10 system, are inadequate for Iñupiaq and other Inuit languages. To remedy this problem, students in Kaktovik, Alaska, invented a base-20 numeral notation Nobody suggest this to the Danes, please.
- ithkuil 4y ago"However, Danish numerals are not vigesimal since it is only the names of some of the tens that are etymologically formed in a vigesimal way. In contrast with e.g. French quatre-vingt-seize, the units only go from zero to nine between each ten which is a defining trait of a decimal system."
- deleted 4y ago[deleted]
- timerol 4y agoThis character set was only added to Unicode last September, as mentioned on the page. I first learned about them via this video https://www.youtube.com/watch?v=EyS6FfczH0Q https://www.youtube.com/watch?v=EyS6FfczH0Q
- dhosek 4y agoThat’s how I learned about them—I’m always curious about what’s new in each release of Unicode and how it impacts my Rust Unicode library (finl_unicode).
- lgdw 4y agoI remember this being in a NACLO problem last year.
- ChrisMarshallNY 4y ago> Arabic numerals, which were designed for a base-10 system, are inadequate for Iñupiaq and other Inuit languages. I am curious as to why Arabic numerals (or any number system, for that matter) are inadequate for a language.
- dragonwriter 4y agoIt explains the problem: they are not a good way to express a base-20 numbering system used in the language. (Now, you could easily augment or modify them to do that—and the creators [0] of this system initially tried that but were unsatisfied—the common way of expressing base-16 using arabic numerals plus the first six letters of the alphabet as added numerals is an example, but if you aren't using a language whose existing writing system conventionally users Arabic numerals, why would you?) [0] middle school students!
- ChrisMarshallNY 4y agoI guess I was confused about that. I didn't think that a numbering system was considered part of a language. I always thought that a numbering system was more of an ADAPTER pattern (like Hexadecimal, binary, and octal are all "addons" to the English language).
- dragonwriter 4y agoThe way that a language constructs number words can have an implied base; English has an implied based 10 in most of the language (though 0-19 uses a different structure that could imply base 20 if it continued.) Most germanic and romance languages I think do something similar, though, e.g. French (FR-fr, but not some other dialects) breaks back into an implicit base-20 at 60-99. Having numerals that map well to words reduces friction for practical arithmetic.
- Turing_Machine 4y agoIt used to be common to count by scores (twenties) in English, though this has mostly disappeared other than for poetical/literary usage (e.g., "Four score and seven years ago"). Dozens (twelves) were also quite common, and are still in everyday use for certain commodities (eggs, donuts, etc.).
- jasonwatkinspdx 4y agoWorth noting this detail towards the bottom of the article: > 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. It is theorized that being able to work in both base-10 and base-20 might have comparable advantages to those bilingual students have from engaging in two ways of thinking about the world.
- hgsgm 4y agoIt's seems much more likely that the new system was easier to use because it's an iconic tally system (vertical stroke = 1, horizontal = 5) that doesn't require leaerning 9 digit symbols or place value.
- jasonwatkinspdx 4y agoYeah, I think the wiki statement might be poorly worded, but the way I interpret it is something like: - they learned base 20 counting verbally at home, possibly simple additions, multiplications, and such too - they learned base 10 english counting as well, and eventually written arithmetic with Arabic numerals - but there was a missing link in having to translate bases that made it harder for them to understand the underlying patterns of written arithmetic or even algebra - having the new written numerals provided that missing bridge, allowing them to round out their understanding To be clear that's just armchair speculation on my part, but that's how I interpreted it. They went from having a challenge of a missing mental connection, to having the advantage of two perspectives. But certainly there's confounders, like perhaps the new numeral system motivated more interest and family support in math.
- aaron695 4y ago[dead]
- retrac 4y agoOr perhaps engaging with this topic so practically - understanding their native language's counting system and then devising a notation - sparked an interest in what is often perceived as a useless and boring topic. I had a few "ooh, this is not only useful, but intellectually fun" experiences with math in school. Positional number systems was one of them. Distinct aha moment. So much of what had not made sense before suddenly did, including why we had just spent weeks on logarithms. Without at least a few experiences like that, I am sure I would have been even more tuned out in class, destined to hate math for life. I found the way it was taught most of the time to be a form of low-grade torture.
- 29athrowaway 4y agoNice for steganography applications.
- ycombinaor 4y agoYour comment made me really curious, could you please elaborate how this number system can be used in Steganography? I have a basic idea of steganography, but I want to know more
- voxelghost 4y agoI think we can assume that parent made a typo, or suffered autocorrect , and most likely meant stenography
- 29athrowaway 4y agoYou assumed wrongly this time.
- voxelghost 4y agoWell color me surprised
- 29athrowaway 4y agoThese glyphs are not immediately recognizable as numbers by most people. This can assist the purpose of hiding information visually. It can also be used to avoid computer vision solutions from detecting numbers in an image, avoiding OCR, etc.
- yawaramin 4y agoThis reminds me of the Birkana artificial hexadecimal numerals: https://yawar.blogspot.com/2016/10/the-birkana-hexadecimal-number-symbols.html https://yawar.blogspot.com/2016/10/the-birkana-hexadecimal-n...
- akdor1154 4y agoThe long division example in there is a massive WTF, getting towards the level of the inverse square root float/int thing.
- kenshoen 4y agoSub-base 5 makes the multiplication table actually smaller than decimal. Nice.