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Yes, and those European languages use base-10 numerals. This specific base-20 numeral system has a simple representation which allows some numeric operations t

by dalke 6y ago

Yes, and those European languages use base-10 numerals. This specific base-20 numeral system has a simple representation which allows some numeric operations to be done by pattern matching.[0] See the YT video I linked to. Think I+II = III in Roman numerals, or as the examples show, think V+V=W (for 2+2=4). Though unlike Roman numerals, this uses base-20 positional system, with a subbase-5 system. That composition feature isn't present in the Arabic numerals. And I'm annoyed there's no way to represent it in standard Unicode! [0] I haven't looked into it enough. I suspect the simple pattern matching approach only works for some numbers. But even so, it gives an intermediate/bootstrap step to learning (say) division that feels helpful for beginners.

gus_massa 6y ago
> That composition feature isn't present in the Arabic numerals. "1" +"2" = "3", Can you see the composition? The original representation was "-" + "=" = "≡" but someone got too lazy and rotate 1, wrote the two lines of 2 without lifting up the pen, and the three lines of 3 without lifting up the pen. I'm not an expert in number history, but these are some nice graphics of the evolution of the number system https://www.archimedes-lab.org/numeral.html https://www.archimedes-lab.org/numeral.html and in particular the evolution of the representation of three https://kk.org/cooltools/the-universal-h/ https://kk.org/cooltools/the-universal-h/ This alternative is a nice and ordered number system, but after a few centuries of use some will get lazy and change the shape to write them faster or to make them more different. > And I'm annoyed there's no way to represent it in standard Unicode! Every few years there is a post about someone who added a few characters to Unicode. Take a look at https://news.ycombinator.com/item?id=11958682 https://news.ycombinator.com/item?id=11958682 > I haven't looked into it enough. I suspect the simple pattern matching approach only works for some numbers. But even so, it gives an intermediate/bootstrap step to learning (say) division that feels helpful for beginners. The part of the video about sum and rest make sense, it is slightly easier, but there are many other representations for example with points. I'm a strong proponent of "Use your fingers", but you must learn by heath the tables soon (but not too soon). In the video they didn't explain too many operations with carry. This is possible with this notation, but it is not easier than with the current notation, and you must remember to use 5 for the bottom-to-top transition and 4 for the digit-to-digit transitions, so it may be a problem to remember. The part of the video about division makes no sense. Division is just horrible in any representation. Try 76829/5. (And I pick 5 because 5 is an easy case. If you think it is too easy try with 3 or 7.)

by dalke 6y ago

gus_massa 6y ago

> That composition feature isn't present in the Arabic numerals. "1" +"2" = "3", Can you see the composition? The original representation was "-" + "=" = "≡" but someone got too lazy and rotate 1, wrote the two lines of 2 without lifting up the pen, and the three lines of 3 without lifting up the pen. I'm not an expert in number history, but these are some nice graphics of the evolution of the number system https://www.archimedes-lab.org/numeral.html https://www.archimedes-lab.org/numeral.html and in particular the evolution of the representation of three https://kk.org/cooltools/the-universal-h/ https://kk.org/cooltools/the-universal-h/ This alternative is a nice and ordered number system, but after a few centuries of use some will get lazy and change the shape to write them faster or to make them more different. > And I'm annoyed there's no way to represent it in standard Unicode! Every few years there is a post about someone who added a few characters to Unicode. Take a look at https://news.ycombinator.com/item?id=11958682 https://news.ycombinator.com/item?id=11958682 > I haven't looked into it enough. I suspect the simple pattern matching approach only works for some numbers. But even so, it gives an intermediate/bootstrap step to learning (say) division that feels helpful for beginners. The part of the video about sum and rest make sense, it is slightly easier, but there are many other representations for example with points. I'm a strong proponent of "Use your fingers", but you must learn by heath the tables soon (but not too soon). In the video they didn't explain too many operations with carry. This is possible with this notation, but it is not easier than with the current notation, and you must remember to use 5 for the bottom-to-top transition and 4 for the digit-to-digit transitions, so it may be a problem to remember. The part of the video about division makes no sense. Division is just horrible in any representation. Try 76829/5. (And I pick 5 because 5 is an easy case. If you think it is too easy try with 3 or 7.)