tag:blogger.com,1999:blog-21503568.post8401468395236883536..comments2023-11-03T06:32:28.410-04:00Comments on Staring At Empty Pages: Binary multiplication, the computer (and Ethiopian?) wayBarry Leibahttp://www.blogger.com/profile/14205294935881991457noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-21503568.post-25263989169546096872009-06-23T18:07:28.111-04:002009-06-23T18:07:28.111-04:00Cool post, Barry! The other night I was looking t...Cool post, Barry! The other night I was looking through math books in Borders (not the greatest place for math books, but that's where I was), and I picked up an old thing (1930) by Tobias Dantzig called "Number the language of science." I gritted my teeth past the name, skimmed it, and decided to buy it. It was a clearance book with a big clearance sticker on it, and when I got the book home and removed the sticker, underneath was an endorsement from Albert Einstein. :-)<br /><br />What's amused me about the book is how politically incorrect it is, referring to the math that "savages" can do, referring to "the dullest schoolboy," etc. It's pretty funny. But I'm enjoying the book for its content, it's a history of number.<br /><br />So, sorry this is so long-winded, but in the thirteenth century Europeans also used doubling to multiply. The term was "duplation," and it's not nearly as interesting as the Ethiopian version. Basically just double until you have numbers you can add together, e.g. to multiply by thirteen double 3 times, then you have the number times 4, the number times 8, and you can add those numbers plus the original number and you have the number times 13.<br /><br />Without a place-value system, it makes sense to rely on doubling, once you learn that you just repeat it to get the number you want. It is just slightly fancier repeated addition.Maggiehttps://www.blogger.com/profile/16681883169121834569noreply@blogger.com