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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 teac

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 4y 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?
- IIAOPSW 4y ago
  >6.64 halving and n-digit doubling operations per digit of the multiplier Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n. >mediation and duplation of 69 · 21 21 69 * 10 138 5 276 * 2 552 1 1104 * Am I mistaken in reading this as RPN? You put the operator to the side of the operands rather than the middle. Slightly unorthodox to put the op on the right, but still obvious in meaning. Your English is obviously perfect, but you have a very idiosyncratic way of writing math that I've never seen before. For example you wrote "from the 01950s". I've never seen anyone use a 5 digit year format, and rarely if ever have I seen anyone include a leading zero in a number at all. Its not bad or wrong, I just don't know what this style is except possibly a type foreign accent?
  - kragen 4y ago
    > Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n. 2 log₂ 10. a multiplier m with 5 digits has a log₂ between 13.29 and 16.61, 3.32 per digit; you need log₂ m halving operations and log₂ m doubling operations. so 6.64 is an upper bound but it's usually pretty close. in the example there, it would have led you to expect 13.28 halving and n-digit doubling operations, when the reality was 8 halving and doubling operations, of which three were n+1-digit doublings n is the number of digits of the multiplicand, so it holds just as well for small or large n, except in the sense that n can be a bad estimate for how many digits you need in the doublings when it's small > Am I mistaken in reading this as RPN? yes; those asterisks mark the rows where the mediation column was odd, as i explained below in 'now we add the starred duplation column items where the mediated multiplicand was odd'. they do not denote multiplication or any other operation on the two numbers to their left. you are surely not the only person who misinterpreted this, and i apologize for the lack of clarity
t-3 4y ago
When I was in school (90s-00s, MI public school), we didn't have to memorize times tables at all. They taught us a bunch of different methods in succession and told us to use whichever we found easiest.
- kragen 4y ago
  which methods did you learn
  - t-3 4y ago
    Honestly, I didn't learn them at the time so I couldn't tell you. I was good enough at mental math that I never had to use any (and stubborn to the point that I refused to show work that was done in my head, and so got horrible grades for correct answers). It's only as an adult that I've become interested in learning algorithms and gained any appreciation for mathematics.

kragen 4y 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?

IIAOPSW 4y ago
>6.64 halving and n-digit doubling operations per digit of the multiplier Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n. >mediation and duplation of 69 · 21 21 69 * 10 138 5 276 * 2 552 1 1104 * Am I mistaken in reading this as RPN? You put the operator to the side of the operands rather than the middle. Slightly unorthodox to put the op on the right, but still obvious in meaning. Your English is obviously perfect, but you have a very idiosyncratic way of writing math that I've never seen before. For example you wrote "from the 01950s". I've never seen anyone use a 5 digit year format, and rarely if ever have I seen anyone include a leading zero in a number at all. Its not bad or wrong, I just don't know what this style is except possibly a type foreign accent?
- kragen 4y ago
  > Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n. 2 log₂ 10. a multiplier m with 5 digits has a log₂ between 13.29 and 16.61, 3.32 per digit; you need log₂ m halving operations and log₂ m doubling operations. so 6.64 is an upper bound but it's usually pretty close. in the example there, it would have led you to expect 13.28 halving and n-digit doubling operations, when the reality was 8 halving and doubling operations, of which three were n+1-digit doublings n is the number of digits of the multiplicand, so it holds just as well for small or large n, except in the sense that n can be a bad estimate for how many digits you need in the doublings when it's small > Am I mistaken in reading this as RPN? yes; those asterisks mark the rows where the mediation column was odd, as i explained below in 'now we add the starred duplation column items where the mediated multiplicand was odd'. they do not denote multiplication or any other operation on the two numbers to their left. you are surely not the only person who misinterpreted this, and i apologize for the lack of clarity

t-3 4y ago

When I was in school (90s-00s, MI public school), we didn't have to memorize times tables at all. They taught us a bunch of different methods in succession and told us to use whichever we found easiest.

kragen 4y ago
which methods did you learn
- t-3 4y ago
  Honestly, I didn't learn them at the time so I couldn't tell you. I was good enough at mental math that I never had to use any (and stubborn to the point that I refused to show work that was done in my head, and so got horrible grades for correct answers). It's only as an adult that I've become interested in learning algorithms and gained any appreciation for mathematics.