2021-01-02 - times tables

when i was in primary school, there was a time i was tasked with memorizing (!) a matrix of 10×10 (not so) random values, with their exact positions – aka: times table. no way – it never worked for me this way. memorizing (i.e. hardcoding into brain) that much stuff was out of the question. but i still need to pass an oral exam out of it… so… why not just multiply it fast enough, so that no1 will notice¹⁾? and so i did. yes – i never learned times table. over time i did remember some random elements of it, but vast majority i was just multiplying on the fly. to do so i developed some simplifying algorithms, like:

• multiplying N*5 is N*10/2
• multiplying N*9 is N*10-N
• etc…

the 2nd “rule” was a bit exceptional for me, as it was just an observation at that point. when i've noticed this property i was happy as it knocked out a full line of multiplications with it. i was even happier when sometime later i came up with a formal proof of it. after all 9==10-1, thus N*9 is N*(10-1) which in turn is N*10-N. generally simple stuff, but having barely 2-digits of age it was like discovering what dark matter is. i think it was one of those rare moments in education, when given a (yet another) really brain-dead task turned out to be a positive thing – overall fun and insightful process. and btw: why it was not presented as such a task in a first place?

anyway – somewhere last month, while listening to a podcast of unnecessary detail, namely the tables episode, i learned that Steve Mould did exactly the same when tasked with memorizing times table. it was comforting there are more ppl who utterly hate / can't memorize stuff if it is not well understood first. high five! :D