9 ms·

I dislike these pseudo-scientific claims about alternative number systems and methods of paper and pencil arithmetic: > Because of the tally-inspired design, a

by todd8 3y 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 3y ago
Babylonyan Base 60 is superior.
- rendall 3y 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 3y 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)
    - rendall 3y ago
      It's true. I was teasing, but I did work this out once. IIRC it went something like: A = 1 B = 2 C = 3 D = 5 E = 7 F = 11 ... and so on Then any number can be represented in terms of its prime factorization: 4 : BB or B^B 6 : BC 8 : BBBB or B^C 9 : CCC or C^B 10 : BD ... 100 : (BD)^B 101 : # (some arbitrary unique symbol) ...
  - naasking 3y ago
    Actually base e is clearly the superior base as it's the most information-dense number representation.
kragen 3y ago
i had the same thought, but it sounds like starting with a base-20 numeral system makes it easier for the iñupiat students to learn base 10, as evidenced by the reported test score improvements i worked out the multiplication thing in more detail in https://news.ycombinator.com/item?id=35551051 https://news.ycombinator.com/item?id=35551051 myself, i learned mediation and duplation before i learned to multiply with a memorized multiplication table, and though that's a faster algorithm, you could maybe teach it after switching to base 10? also nowadays maybe you'd be better off with a memorized table of briggsian logarithms because if you really need more than two digits of precision you should probably use a calculator mediation and duplation of 69 · 21 21 69 * 10 138 5 276 * 2 552 1 1104 * now we add the starred duplation column items where the mediated multiplicand was odd (corresponding to the 1s in its binary representation, 16+4+1) 1104 276 + 69 ---- 1449 a bit more work than adding up four appropriately shifted table-lookup results but not really that much, doesn't depend on a multiplication table, and you can do it just as easily in roman numerals or kaktovik numerals also people have been multiplying using tables of squares since babylonian times; https://en.wikipedia.org/wiki/Multiplication_algorithm#Quarter_square_multiplication https://en.wikipedia.org/wiki/Multiplication_algorithm#Quart... for this you calculate 69+21 = 90 and 69-21 = 48, look up or remember that ⌊¼90²⌋ = 2025 and ⌊¼48²⌋ = 576, and 2025 - 576 = 1449, the correct answer
- IIAOPSW 3y ago
  So we just wrote very similar comments at the same time. Did you notice this for yourself too, or is there some magic utopia I've never heard of where they teach something other than memorizing math tables? Couldn't help but notice your use of RPN, and the fact that you have specific vocabulary for all the steps.
  - kragen 3y ago
    i learned mediation and duplation (which doesn't involve multiplying by the base of your numeral system!) from a book as a kid (a compendium of knowledge for kids from the 01950s that my grandparents had) but have seen people talk about it several times since then you can get pretty fast at it but you have to do 6.64 halving and n-digit doubling operations per digit of the multiplier, plus about 1.66 n-digit additions, so in my experience it's still slower than computing partial products with a memorized base-10 multiplication table, which requires adding together n recalled multiplication-table entries to get a partial product per digit of the multiplier, and then adding these partial products together just not as much slower as you'd naively expect i derived a shitty version of quarter-square multiplication on my own about 20 or 25 years ago and much later learned about the streamlined version from wikipedia i like rpn but i don't think i used it here?
eyelidlessness 3y ago
> “the students found, with their numerals, they could solve problems a better way, a faster way” > Base 20 is not a popular notation for numbers […] We shouldn't make it harder for these kids So much of what you object to is that something they’ve found more intuitive and engaging isn’t what unintuitive disengaging stuff they’ll encounter. But developing intuition for math is far more valuable than developing conformance to how it’s supposed to be done. Who cares if that intuition is developed with some idiosyncrasy from what you consider normal? The math is math, the principles are consistent, the knowledge is transferable. Insisting they learn the same things a different way is totally arbitrary and counterproductive.
- skywal_l 3y ago
  I think parent's point is not cultural as you are implying but rather practical. Learning in a base that nobody uses could be easier today and an hindrance later. I think, all in all, this should not be a big deal. For the gifted kid, they'll find a way to adapt and become the next Einstein. As for the ungifted, it might give them a better leg up and allow them to perform better than they would have, so it's probably a plus anyways.
  - westurner 3y ago
    Finger binary: https://en.wikipedia.org/wiki/Finger_binary https://en.wikipedia.org/wiki/Finger_binary : > Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: that is, up to 2**5−1 or 2**10−1 respectively. - "How to count to 1000 on two hands" by 3blue1brown https://youtu.be/1SMmc9gQmHQ https://youtu.be/1SMmc9gQmHQ - "Polynesian People Used Binary Numbers 600 Years Ago - Scientific American" https://www.scientificamerican.com/article/polynesian-people-used-binary-numbers-600-years-ago/ https://www.scientificamerican.com/article/polynesian-people... What is the comparative value of radixes like Binary, Octal, andHexadecimal compared to Decimal (radix 10)? Perhaps a radix like eπI would be more useful; though some amost-mystic physicists do tend to radix 9: "nonary" (which is actually ~ also radix-3). List of numeral systems > By culture / time period, By type of notation https://en.wikipedia.org/wiki/List_of_numeral_systems https://en.wikipedia.org/wiki/List_of_numeral_systems : > Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base.
IIAOPSW 3y ago
Memorizing the times table is for suckers. If you can add, you can spend at most 2 additions to get 2, 3 and 4 (2x = x+x, 3x = x+x+x, 4x = (2x+2x)). Multiplying by the base of your numeral system comes for free (just add 0 to the end). Assuming subtraction just as easy as addition, I now know how to multiply by base-1 and base-2 (9 and 8 normally, 19 and 18 in this case). The last trick I need to invoke is division by 2. Assume you've ignored every other lesson in order to focus on being unreasonably fast at cutting numbers in half. So now, coupled with the append zero trick, you have a path to 5 and 10 (5x = (20x/2)/2, 10x = 20x/2). I haven't memorized anything, and I've used at most two operations, and already I can multiply by 2,3,4,5,10,11,18,19,20. With a third operation I can reach 6,8,9,12,15,17. All that's missing is 7,13,14,16. At that point the remaining part of the "table" only has 10 unique elements in it. I can cover it with a 4th and 5th op if I'm truly stuck, but at some point in doing that repeatedly I'd probably end up remembering that chunk of the table anyway. If we were still in base 10, the same tricks would get me the entire single digit table within at most two addition and/or halving operations. It only takes 3 ops if you reject my premise that halving is as easy as doubling / adding. Sure it costs me 3 operations per multiplication, but my operations are only doubling and halving (and arguably appending zero). What I lose in number of steps I gain back by just being faster at those two specific skills. And I didn't even have to waste time memorizing stupid tables!
- charlieyu1 3y ago
  It is still extra mental steps, memorising times table is relatively trivial. The costs of having these extra steps really add up for more complicated problems that involve multiplication
  - jacquesm 3y ago
    Memorizing the multiplication table is a shortcut that works for small numbers, memorizing a quick method for multiplication works for all numbers. The table is just an optimization that can come in handy in the same way that cache memory is handy: it gives you the same answer but only for a limited set of data and in a faster way. Eventually you'll have to venture out of cache memory to reach the rest of the space and if cache memory is all you have you're in trouble. So if you can learn only one of the two the method is the better one, so learn that one first, then memorize, as much or as little as you feel like. Up to 20x20 is doable, much larger is useful for squares, powers of two and some other numbers for order-of-magnitude checks but when I'm lazy I'll just break out the calculator. It's useful to be able to do this in your head up to a certain point and beyond I'll use a tool just because it is convenient and faster.
jacquesm 3y ago
The big advantage would be that you learn to see that there is nothing magical or 'right' of one number base over another. Base 2 has it's uses as does base 10(10). And most computer programmers are familiar with at least one other base besides decimal, and quite a few will be able to use binary, octal and decimal with relative ease. It gets interesting when you go off the beaten path and you re-learn the rules for arithmetic in different bases. In my experience all of this gives you a much better understanding of why decimal is practical and widespread. But it also shows you that it is a convention that won out for both cultural reasons and because it made certain arithmetic easier. If 10x10 = 100 looks natural to you in decimal then it will still be natural to you if you think of it as 16x16 = 256 when you look at the numbers in their hexadecimal representation. You can only get that kind of fluidity by playing around in different number systems. So I'm perfectly ok with students inventing their own number systems, they are definitely not going to get any dumber on account of having done that. Growing up with Inches and degrees Fahrenheit is a cultural issue, most of the rest of the world has moved on from there, for reasons that are far more compelling than those that would apply to using a different number base. Those are arbitrary values, whereas all number bases exist regardless of whether we use them or not. Think of the one as cultural baggage and the others as just another part of number theory.
- kome 3y ago
  great and enlightening comment.
- gladiatr72 3y ago
  Not trolling. Promise. I can't think of a non-computing/math-related context where being cog of base number theory comes into play.
  - revscat 3y ago
    It’s at least partially about recognizing that there are other ways to view the world than the default one we carry around inside our precious egos, ways that are — literally, in this case — equal to our defaults.
  - 3y ago
scrollaway 3y ago
> The times tables, memorized in grade school and fundamental to paper and pencil calculations Am I the only one who never memorized the times tables as a kid (because I found it boring), and yet today I am far better at mental arithmetics than 99% of people? eg. If you ask me what 7 times 5 is I have no idea from memory, but I can tell you half of 7 is 3.5 so it's 10 times that. Or 8 times 9 is 80-8. And so on.
hnbad 3y ago
Your argument could equally be used to say that children should only be taught English, Spanish, Mandarin or Hindi. I'm not sure if you would agree with that, but the sentiment isn't unheard of, especially when it comes to opposition to language preservation.
watwut 3y ago
Practically, they do better with this? > The times tables, memorized in grade school and fundamental to paper and pencil calculations, are now four times larger. Why would you expect them to memorize four time larger table? There is zero reason to do so, just because the base number is larger. Also kids don't memorize the whole 10x10 table anyway. They are taught to calculate majority of it.
rcme 3y ago
This isn’t base 20, though. It’s actually base 5. But groups of 2 digits are written in the same text area. Basically a fancy ligature.
- tobr 3y ago
  The bottom part has 5 digits, but the top part only has 4 (counting blank as digit 0). If both had 5 digits there would have been 5×5=25 positional digits. So it’s kind of base 5, base 4, and base 20 at the same time.
  - deleted 3y ago
    [deleted]
  - rcme 3y ago
    Good point
eternityforest 3y ago
Will they actually need to do pen and paper multiplication in real life? I'm not sure when anyone I know would need to, or if I even still could. Is using a lookup table just as good/almost as good if nobody actually needs to do it fast in the field? Can they just use base 10 for all multiplication, if multiplication isn't needed in whatever problem set this is optimized for that seems to have them so excited?
nulbyte 3y ago
> However, spending time learning base 20 arithmetic has obvious disadvantages that the article ignores. They aren't learning base 20; they already use it in their language. They are learning how to write their language in their writing system. From the article: "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." Not everyone counts in decimal. Base 20 exists in spoken French. For numbers 50-90, Danish uses base 20, in some cases mixed with fractions. There are other bases in other living languages as well.
- saalweachter 3y ago
  The remnants of duodecimal are still in English, for that matter. Eleven, twelve, dozen, gross. Twelve inches to the foot used to be a round number.
  - prometheus76 3y ago
    Come and join the Dozenal Society of America! https://dozenal.org/index.html https://dozenal.org/index.html
neither_color 3y 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 sounds like they objectively are doing better though. Bottom 20th to above average is non-trivial. Even if you look at it from the point of view that learning a different base(binary, hex), any base, teaches you to think differently about math, why not learn the native base for extra confidence?
useerup 3y ago
Actually, many western number systems have traces from base 20. Just consider how you have names for numbers up until 20. In Danish, the way we name numbers are heavily inspired by French, which also exhibit traces from base 20. The name in Danish for 60 and 80 in modern Danish are "tre(d)s" and "firs", respectively. These are shortened forms of "tredsindstyvende" and "firsindstyvende" used historically, literally meaning "3 times 20" and "4 times 20", respectively. The number for 50 is "halvtreds" - derived from "half way to treds (60)" - meaning half way (when the "way" is 20 long) between 40 and 60. In french 80 is quatre-vingt (4-20). If anything, arguably our common system in which we have named numbers up until 20 (i.e. base-20) and then shift to base-10 for numbers above 20 is illogical.
- jessekv 3y ago
  Ha! Although you could also argue that the transition is from twelve to thirteen ("three-ten"). On the other hand, in english, there is "score" for 20.
jgrahamc 3y ago
For most British people of my age learning up to 20^2 would be 2.8x larger as we had to learn times table to 12. https://blog.jgc.org/2010/06/duodecimal.html https://blog.jgc.org/2010/06/duodecimal.html

by todd8 3y ago

Etrnl_President 3y ago

Babylonyan Base 60 is superior.

rendall 3y 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 3y 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)
  - rendall 3y ago
    It's true. I was teasing, but I did work this out once. IIRC it went something like: A = 1 B = 2 C = 3 D = 5 E = 7 F = 11 ... and so on Then any number can be represented in terms of its prime factorization: 4 : BB or B^B 6 : BC 8 : BBBB or B^C 9 : CCC or C^B 10 : BD ... 100 : (BD)^B 101 : # (some arbitrary unique symbol) ...
- naasking 3y ago
  Actually base e is clearly the superior base as it's the most information-dense number representation.

kragen 3y ago

i had the same thought, but it sounds like starting with a base-20 numeral system makes it easier for the iñupiat students to learn base 10, as evidenced by the reported test score improvements i worked out the multiplication thing in more detail in https://news.ycombinator.com/item?id=35551051 https://news.ycombinator.com/item?id=35551051 myself, i learned mediation and duplation before i learned to multiply with a memorized multiplication table, and though that's a faster algorithm, you could maybe teach it after switching to base 10? also nowadays maybe you'd be better off with a memorized table of briggsian logarithms because if you really need more than two digits of precision you should probably use a calculator mediation and duplation of 69 · 21 21 69 * 10 138 5 276 * 2 552 1 1104 * now we add the starred duplation column items where the mediated multiplicand was odd (corresponding to the 1s in its binary representation, 16+4+1) 1104 276 + 69 ---- 1449 a bit more work than adding up four appropriately shifted table-lookup results but not really that much, doesn't depend on a multiplication table, and you can do it just as easily in roman numerals or kaktovik numerals also people have been multiplying using tables of squares since babylonian times; https://en.wikipedia.org/wiki/Multiplication_algorithm#Quarter_square_multiplication https://en.wikipedia.org/wiki/Multiplication_algorithm#Quart... for this you calculate 69+21 = 90 and 69-21 = 48, look up or remember that ⌊¼90²⌋ = 2025 and ⌊¼48²⌋ = 576, and 2025 - 576 = 1449, the correct answer

IIAOPSW 3y ago
So we just wrote very similar comments at the same time. Did you notice this for yourself too, or is there some magic utopia I've never heard of where they teach something other than memorizing math tables? Couldn't help but notice your use of RPN, and the fact that you have specific vocabulary for all the steps.
- kragen 3y ago
  i learned mediation and duplation (which doesn't involve multiplying by the base of your numeral system!) from a book as a kid (a compendium of knowledge for kids from the 01950s that my grandparents had) but have seen people talk about it several times since then you can get pretty fast at it but you have to do 6.64 halving and n-digit doubling operations per digit of the multiplier, plus about 1.66 n-digit additions, so in my experience it's still slower than computing partial products with a memorized base-10 multiplication table, which requires adding together n recalled multiplication-table entries to get a partial product per digit of the multiplier, and then adding these partial products together just not as much slower as you'd naively expect i derived a shitty version of quarter-square multiplication on my own about 20 or 25 years ago and much later learned about the streamlined version from wikipedia i like rpn but i don't think i used it here?

eyelidlessness 3y ago

> “the students found, with their numerals, they could solve problems a better way, a faster way” > Base 20 is not a popular notation for numbers […] We shouldn't make it harder for these kids So much of what you object to is that something they’ve found more intuitive and engaging isn’t what unintuitive disengaging stuff they’ll encounter. But developing intuition for math is far more valuable than developing conformance to how it’s supposed to be done. Who cares if that intuition is developed with some idiosyncrasy from what you consider normal? The math is math, the principles are consistent, the knowledge is transferable. Insisting they learn the same things a different way is totally arbitrary and counterproductive.

skywal_l 3y ago
I think parent's point is not cultural as you are implying but rather practical. Learning in a base that nobody uses could be easier today and an hindrance later. I think, all in all, this should not be a big deal. For the gifted kid, they'll find a way to adapt and become the next Einstein. As for the ungifted, it might give them a better leg up and allow them to perform better than they would have, so it's probably a plus anyways.
- westurner 3y ago
  Finger binary: https://en.wikipedia.org/wiki/Finger_binary https://en.wikipedia.org/wiki/Finger_binary : > Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: that is, up to 2**5−1 or 2**10−1 respectively. - "How to count to 1000 on two hands" by 3blue1brown https://youtu.be/1SMmc9gQmHQ https://youtu.be/1SMmc9gQmHQ - "Polynesian People Used Binary Numbers 600 Years Ago - Scientific American" https://www.scientificamerican.com/article/polynesian-people-used-binary-numbers-600-years-ago/ https://www.scientificamerican.com/article/polynesian-people... What is the comparative value of radixes like Binary, Octal, andHexadecimal compared to Decimal (radix 10)? Perhaps a radix like eπI would be more useful; though some amost-mystic physicists do tend to radix 9: "nonary" (which is actually ~ also radix-3). List of numeral systems > By culture / time period, By type of notation https://en.wikipedia.org/wiki/List_of_numeral_systems https://en.wikipedia.org/wiki/List_of_numeral_systems : > Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base.

IIAOPSW 3y ago

Memorizing the times table is for suckers. If you can add, you can spend at most 2 additions to get 2, 3 and 4 (2x = x+x, 3x = x+x+x, 4x = (2x+2x)). Multiplying by the base of your numeral system comes for free (just add 0 to the end). Assuming subtraction just as easy as addition, I now know how to multiply by base-1 and base-2 (9 and 8 normally, 19 and 18 in this case). The last trick I need to invoke is division by 2. Assume you've ignored every other lesson in order to focus on being unreasonably fast at cutting numbers in half. So now, coupled with the append zero trick, you have a path to 5 and 10 (5x = (20x/2)/2, 10x = 20x/2). I haven't memorized anything, and I've used at most two operations, and already I can multiply by 2,3,4,5,10,11,18,19,20. With a third operation I can reach 6,8,9,12,15,17. All that's missing is 7,13,14,16. At that point the remaining part of the "table" only has 10 unique elements in it. I can cover it with a 4th and 5th op if I'm truly stuck, but at some point in doing that repeatedly I'd probably end up remembering that chunk of the table anyway. If we were still in base 10, the same tricks would get me the entire single digit table within at most two addition and/or halving operations. It only takes 3 ops if you reject my premise that halving is as easy as doubling / adding. Sure it costs me 3 operations per multiplication, but my operations are only doubling and halving (and arguably appending zero). What I lose in number of steps I gain back by just being faster at those two specific skills. And I didn't even have to waste time memorizing stupid tables!

charlieyu1 3y ago
It is still extra mental steps, memorising times table is relatively trivial. The costs of having these extra steps really add up for more complicated problems that involve multiplication
- jacquesm 3y ago
  Memorizing the multiplication table is a shortcut that works for small numbers, memorizing a quick method for multiplication works for all numbers. The table is just an optimization that can come in handy in the same way that cache memory is handy: it gives you the same answer but only for a limited set of data and in a faster way. Eventually you'll have to venture out of cache memory to reach the rest of the space and if cache memory is all you have you're in trouble. So if you can learn only one of the two the method is the better one, so learn that one first, then memorize, as much or as little as you feel like. Up to 20x20 is doable, much larger is useful for squares, powers of two and some other numbers for order-of-magnitude checks but when I'm lazy I'll just break out the calculator. It's useful to be able to do this in your head up to a certain point and beyond I'll use a tool just because it is convenient and faster.

jacquesm 3y ago

The big advantage would be that you learn to see that there is nothing magical or 'right' of one number base over another. Base 2 has it's uses as does base 10(10). And most computer programmers are familiar with at least one other base besides decimal, and quite a few will be able to use binary, octal and decimal with relative ease. It gets interesting when you go off the beaten path and you re-learn the rules for arithmetic in different bases. In my experience all of this gives you a much better understanding of why decimal is practical and widespread. But it also shows you that it is a convention that won out for both cultural reasons and because it made certain arithmetic easier. If 10x10 = 100 looks natural to you in decimal then it will still be natural to you if you think of it as 16x16 = 256 when you look at the numbers in their hexadecimal representation. You can only get that kind of fluidity by playing around in different number systems. So I'm perfectly ok with students inventing their own number systems, they are definitely not going to get any dumber on account of having done that. Growing up with Inches and degrees Fahrenheit is a cultural issue, most of the rest of the world has moved on from there, for reasons that are far more compelling than those that would apply to using a different number base. Those are arbitrary values, whereas all number bases exist regardless of whether we use them or not. Think of the one as cultural baggage and the others as just another part of number theory.

kome 3y ago
great and enlightening comment.
gladiatr72 3y ago
Not trolling. Promise. I can't think of a non-computing/math-related context where being cog of base number theory comes into play.
- revscat 3y ago
  It’s at least partially about recognizing that there are other ways to view the world than the default one we carry around inside our precious egos, ways that are — literally, in this case — equal to our defaults.
- 3y ago

scrollaway 3y ago

> The times tables, memorized in grade school and fundamental to paper and pencil calculations Am I the only one who never memorized the times tables as a kid (because I found it boring), and yet today I am far better at mental arithmetics than 99% of people? eg. If you ask me what 7 times 5 is I have no idea from memory, but I can tell you half of 7 is 3.5 so it's 10 times that. Or 8 times 9 is 80-8. And so on.

hnbad 3y ago

Your argument could equally be used to say that children should only be taught English, Spanish, Mandarin or Hindi. I'm not sure if you would agree with that, but the sentiment isn't unheard of, especially when it comes to opposition to language preservation.

watwut 3y ago

Practically, they do better with this? > The times tables, memorized in grade school and fundamental to paper and pencil calculations, are now four times larger. Why would you expect them to memorize four time larger table? There is zero reason to do so, just because the base number is larger. Also kids don't memorize the whole 10x10 table anyway. They are taught to calculate majority of it.

rcme 3y ago

This isn’t base 20, though. It’s actually base 5. But groups of 2 digits are written in the same text area. Basically a fancy ligature.

tobr 3y ago
The bottom part has 5 digits, but the top part only has 4 (counting blank as digit 0). If both had 5 digits there would have been 5×5=25 positional digits. So it’s kind of base 5, base 4, and base 20 at the same time.
- deleted 3y ago
  [deleted]
- rcme 3y ago
  Good point

eternityforest 3y ago

Will they actually need to do pen and paper multiplication in real life? I'm not sure when anyone I know would need to, or if I even still could. Is using a lookup table just as good/almost as good if nobody actually needs to do it fast in the field? Can they just use base 10 for all multiplication, if multiplication isn't needed in whatever problem set this is optimized for that seems to have them so excited?

nulbyte 3y ago

> However, spending time learning base 20 arithmetic has obvious disadvantages that the article ignores. They aren't learning base 20; they already use it in their language. They are learning how to write their language in their writing system. From the article: "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." Not everyone counts in decimal. Base 20 exists in spoken French. For numbers 50-90, Danish uses base 20, in some cases mixed with fractions. There are other bases in other living languages as well.

saalweachter 3y ago
The remnants of duodecimal are still in English, for that matter. Eleven, twelve, dozen, gross. Twelve inches to the foot used to be a round number.
- prometheus76 3y ago
  Come and join the Dozenal Society of America! https://dozenal.org/index.html https://dozenal.org/index.html

neither_color 3y 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 sounds like they objectively are doing better though. Bottom 20th to above average is non-trivial. Even if you look at it from the point of view that learning a different base(binary, hex), any base, teaches you to think differently about math, why not learn the native base for extra confidence?

useerup 3y ago

Actually, many western number systems have traces from base 20. Just consider how you have names for numbers up until 20. In Danish, the way we name numbers are heavily inspired by French, which also exhibit traces from base 20. The name in Danish for 60 and 80 in modern Danish are "tre(d)s" and "firs", respectively. These are shortened forms of "tredsindstyvende" and "firsindstyvende" used historically, literally meaning "3 times 20" and "4 times 20", respectively. The number for 50 is "halvtreds" - derived from "half way to treds (60)" - meaning half way (when the "way" is 20 long) between 40 and 60. In french 80 is quatre-vingt (4-20). If anything, arguably our common system in which we have named numbers up until 20 (i.e. base-20) and then shift to base-10 for numbers above 20 is illogical.

jessekv 3y ago
Ha! Although you could also argue that the transition is from twelve to thirteen ("three-ten"). On the other hand, in english, there is "score" for 20.

jgrahamc 3y ago

For most British people of my age learning up to 20^2 would be 2.8x larger as we had to learn times table to 12. https://blog.jgc.org/2010/06/duodecimal.html https://blog.jgc.org/2010/06/duodecimal.html