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> 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

> 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.
- harshreality 4y ago
  Sometimes you need "negativity" (though GP's was very mild) to dissuade people from bad ideas that will have negative consequences later. Prioritizing emotional state now over consequences later has worse consequences than reasoned negativity. If this numeral and base system is used to supplement children's understanding of basic principles, that's fine. I think there were lessons on alternate bases, and there was plenty of interaction with cuisenaire rods, when I was in pre-k/kindergarten/1st and maybe 2nd grade. The emphasis placed on Kaktovic numerals and number system by the article, suggests something more than a supplement. If teaching this system distracts at all from children building a core fluency in arabic numerals and base-10 arithmetic, it does them a great disservice, and makes more advanced math more challenging than it would otherwise be. Arabic numerals and base 10 (which is also based on digits, but only hand-digits and not hand+feet digits) are not fundamentally better than anything else, but they are the primary system used to communicate concrete math, and as such have to be the primary system taught in school, or children suffer far more than any negativity you're worried about in these hackernews comments.
  - gpvos 4y ago
    Appatently[0] it doesn't affect arithmetic with standard numerals negatively, since their math scores went way up. [0] That was a typo, but I'm keeping it.
    - harshreality 4y ago
      > At first students would convert their assigned math problems into Kaktovik numerals to do calculations, but middle school math classes in Kaktovik began teaching the numerals in equal measure with their Hindu-Arabic counterparts in 1997. 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. It's not clear to me what that paragraph is saying. One interpretation is: - They were using standardized textbooks with problems that used standard arabic numerals. - Students converted to kaktovik numbers (in words, since they didn't have the symbols until 1994?) before working the problem, and back to arabic after solving it. - The change in 1997 was to teach students to solve problems directly using arabic numerals in addition to being able to solve problems directly using newly-arrived kaktovik numerals I realize that interpretation goes against the tone of the article, but I wouldn't put it past journalists to gloss over an inconvenient fact in an article that's intended to champion an alternative number representation system. It would make a lot of sense that students would do better on (timed) standardized tests after they're fluent in arabic numerals, which was the entire point and concern in my earlier post. I don't care what else is taught to supplement basic arithmetic, or to reinforce concepts, but students have to be fluent in using arabic numerals for arithmetic, without conversion to some other system, or they will suffer. By the article's own admission there, students were using kaktovik numerals before 1997, and their scores were lower, so whatever change was made in 1997 did not involve students learning kaktovik numerals when they didn't know about them before. Were they taught them better, so they understood abstract concepts in basic arithmetic better... or were they taught arabic numerals better, allowing them to use those numerals natively to solve problems? My speculation, as above, is the latter. There's nothing inherent about learning kaktovik numerals that would help on standardized tests.
kragen 4y ago
http://www.unicode.org/L2/L2021/21058-kaktovik-numerals.pdf http://www.unicode.org/L2/L2021/21058-kaktovik-numerals.pdf is the accepted proposal to add the numerals to unicode; it includes samples from two computer fonts and a photograph from a kindergarten. it's a shame they're not in the bmp given that there are only 20 of them. also it cites https://www.youtube.com/watch?v=EyS6FfczH0Q https://www.youtube.com/watch?v=EyS6FfczH0Q which is better than the article i agree that it's disappointing that the sciam author, amory tillinghast-raby, knew so little about math that they didn't understand that what's supposed to be universal about math isn't the system of numerals; such ignorance or malicious disregard for truth is astounding in this context as for why it's better, if we count 0 as 3 strokes (backslash, left, slash) and a base-20 digit as 4.32 bits, the kaktovik digits average 1.18 bits per stroke, versus what I calculate as 1.11 bits per stroke for our western arabic digits (using the stroke counts [3, 1, 3, 4, 3, 4, 3, 2, 4, 3]) averaging the number of strokes required per number up to 268 (a randomly selected number) we get 6.30 strokes per number with the kaktovik numerals or 6.79 strokes per number for western arabic numerals, an 8% advantage for the kaktovik numerals the mayan base-20 numerals are more immediately comprehensible than the kaktovik numerals but i think they are harder to write and more error-prone to read a way that base 20 is worse is that the multiplication table is substantially more unwieldy to memorize; however, if you can overcome that, both multiplication and division become more practical. for example, numbers between 1000 and 8000 have four base-10 digits but only three base-20 digits, so multiplying two of them in the usual way in base 10 will require 16 multiplication-table lookups and summing four partial products of usually 5 digits, while doing it in base 20 requires 9 lookups and summing three partial products of usually 4 digits, about 40% less work (aside from the number of strokes required) in the limit, representing a large number in base 10 requires about 30.1% more digits than base 20, and so about 69% more work in the standard multiplication algorithm, but beyond about 5 digits you should be using karatsuba multiplication anyway a way in which the kaktovik numerals are worse than western arabic numerals is that you definitely wouldn't want to use them to write a check; all numbers except for 20ⁿ-1 (0, 19, 399, 7999, etc.) can be increased by adding a single extra stroke to an existing digit the chinese (base 10) system, which has a less extreme version of this problem, has a separate set of high-security "大写" or "financial" numerals for contexts where this matters https://en.wikipedia.org/wiki/Chinese_numerals#Standard_numbers https://en.wikipedia.org/wiki/Chinese_numerals#Standard_numb...
lelanthran 4y ago
> Ok, so is there any reason to think that it is better than other similar systems like the Mayan system? It has 'zero'? It's almost identical to roman numerals (count the strokes and the special symbol for certain multiples of 5 - V, X, etc) so I expect that it has all the downfalls of roman numerals. I think that these primitive systems are what you get when you optimise for linear and incremental counting - you're optimising for easy and quick recognition of numbers not for convenient arithmetic. Base-12 is what you get when you optimise for easy and convenient arithmetic. I have no idea what you will get if you optimise for easy and convenient calculus[1] :-) [1] There's probably a research paper of Phd thesis in that goal.
moi2388 4y ago
Define “better”. It is visual, so at least basic addition and subtraction don’t have to be done as calculation, they are purely visual. This could be a benefit for everyday tasks. Of course the representation nor the base actually matters mathematically, so in that regard it’s useless

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.
harshreality 4y ago
Sometimes you need "negativity" (though GP's was very mild) to dissuade people from bad ideas that will have negative consequences later. Prioritizing emotional state now over consequences later has worse consequences than reasoned negativity. If this numeral and base system is used to supplement children's understanding of basic principles, that's fine. I think there were lessons on alternate bases, and there was plenty of interaction with cuisenaire rods, when I was in pre-k/kindergarten/1st and maybe 2nd grade. The emphasis placed on Kaktovic numerals and number system by the article, suggests something more than a supplement. If teaching this system distracts at all from children building a core fluency in arabic numerals and base-10 arithmetic, it does them a great disservice, and makes more advanced math more challenging than it would otherwise be. Arabic numerals and base 10 (which is also based on digits, but only hand-digits and not hand+feet digits) are not fundamentally better than anything else, but they are the primary system used to communicate concrete math, and as such have to be the primary system taught in school, or children suffer far more than any negativity you're worried about in these hackernews comments.
- gpvos 4y ago
  Appatently[0] it doesn't affect arithmetic with standard numerals negatively, since their math scores went way up. [0] That was a typo, but I'm keeping it.
  - harshreality 4y ago
    > At first students would convert their assigned math problems into Kaktovik numerals to do calculations, but middle school math classes in Kaktovik began teaching the numerals in equal measure with their Hindu-Arabic counterparts in 1997. 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. It's not clear to me what that paragraph is saying. One interpretation is: - They were using standardized textbooks with problems that used standard arabic numerals. - Students converted to kaktovik numbers (in words, since they didn't have the symbols until 1994?) before working the problem, and back to arabic after solving it. - The change in 1997 was to teach students to solve problems directly using arabic numerals in addition to being able to solve problems directly using newly-arrived kaktovik numerals I realize that interpretation goes against the tone of the article, but I wouldn't put it past journalists to gloss over an inconvenient fact in an article that's intended to champion an alternative number representation system. It would make a lot of sense that students would do better on (timed) standardized tests after they're fluent in arabic numerals, which was the entire point and concern in my earlier post. I don't care what else is taught to supplement basic arithmetic, or to reinforce concepts, but students have to be fluent in using arabic numerals for arithmetic, without conversion to some other system, or they will suffer. By the article's own admission there, students were using kaktovik numerals before 1997, and their scores were lower, so whatever change was made in 1997 did not involve students learning kaktovik numerals when they didn't know about them before. Were they taught them better, so they understood abstract concepts in basic arithmetic better... or were they taught arabic numerals better, allowing them to use those numerals natively to solve problems? My speculation, as above, is the latter. There's nothing inherent about learning kaktovik numerals that would help on standardized tests.

kragen 4y ago

http://www.unicode.org/L2/L2021/21058-kaktovik-numerals.pdf http://www.unicode.org/L2/L2021/21058-kaktovik-numerals.pdf is the accepted proposal to add the numerals to unicode; it includes samples from two computer fonts and a photograph from a kindergarten. it's a shame they're not in the bmp given that there are only 20 of them. also it cites https://www.youtube.com/watch?v=EyS6FfczH0Q https://www.youtube.com/watch?v=EyS6FfczH0Q which is better than the article i agree that it's disappointing that the sciam author, amory tillinghast-raby, knew so little about math that they didn't understand that what's supposed to be universal about math isn't the system of numerals; such ignorance or malicious disregard for truth is astounding in this context as for why it's better, if we count 0 as 3 strokes (backslash, left, slash) and a base-20 digit as 4.32 bits, the kaktovik digits average 1.18 bits per stroke, versus what I calculate as 1.11 bits per stroke for our western arabic digits (using the stroke counts [3, 1, 3, 4, 3, 4, 3, 2, 4, 3]) averaging the number of strokes required per number up to 268 (a randomly selected number) we get 6.30 strokes per number with the kaktovik numerals or 6.79 strokes per number for western arabic numerals, an 8% advantage for the kaktovik numerals the mayan base-20 numerals are more immediately comprehensible than the kaktovik numerals but i think they are harder to write and more error-prone to read a way that base 20 is worse is that the multiplication table is substantially more unwieldy to memorize; however, if you can overcome that, both multiplication and division become more practical. for example, numbers between 1000 and 8000 have four base-10 digits but only three base-20 digits, so multiplying two of them in the usual way in base 10 will require 16 multiplication-table lookups and summing four partial products of usually 5 digits, while doing it in base 20 requires 9 lookups and summing three partial products of usually 4 digits, about 40% less work (aside from the number of strokes required) in the limit, representing a large number in base 10 requires about 30.1% more digits than base 20, and so about 69% more work in the standard multiplication algorithm, but beyond about 5 digits you should be using karatsuba multiplication anyway a way in which the kaktovik numerals are worse than western arabic numerals is that you definitely wouldn't want to use them to write a check; all numbers except for 20ⁿ-1 (0, 19, 399, 7999, etc.) can be increased by adding a single extra stroke to an existing digit the chinese (base 10) system, which has a less extreme version of this problem, has a separate set of high-security "大写" or "financial" numerals for contexts where this matters https://en.wikipedia.org/wiki/Chinese_numerals#Standard_numbers https://en.wikipedia.org/wiki/Chinese_numerals#Standard_numb...

lelanthran 4y ago

> Ok, so is there any reason to think that it is better than other similar systems like the Mayan system? It has 'zero'? It's almost identical to roman numerals (count the strokes and the special symbol for certain multiples of 5 - V, X, etc) so I expect that it has all the downfalls of roman numerals. I think that these primitive systems are what you get when you optimise for linear and incremental counting - you're optimising for easy and quick recognition of numbers not for convenient arithmetic. Base-12 is what you get when you optimise for easy and convenient arithmetic. I have no idea what you will get if you optimise for easy and convenient calculus[1] :-) [1] There's probably a research paper of Phd thesis in that goal.

moi2388 4y ago

Define “better”. It is visual, so at least basic addition and subtraction don’t have to be done as calculation, they are purely visual. This could be a benefit for everyday tasks. Of course the representation nor the base actually matters mathematically, so in that regard it’s useless