hamnox comments on Truly Part Of You - Less Wrong
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I make it a habit to learn as little as possible by rote, and just derive what I need when I need it.
Do realize that you're trading efficiency (as in speed of access in normal use) for that space saving in your brain. Memorizing stuff allows you to move on and save your mental deducing cycles for really new stuff.
Back when I was memorizing the multiplication tables, I noticed that
9 x N = 10 x (N-1) + (9 - (N-1))
That is, 9 x 8 = 70 + 2
So, I never memorized the 9's the same way I did all the other single digit multiplications. To this day I'm slightly slower doing math with the digit 9. The space/effort saving was worth it when I was 8 years old, but definitely not today.
I learned my nines like that too, except I think the teacher showed us that trick. Of the things I learned personally... My tricks were more about avoiding the numbers I didn't like than being efficient.
I could only ever remember how to add 8 to a number by adding ten and then subtracting two. I learned my 8 times tables by doubling the 4th multiple, and 7 by subtracting the base number from that. I suppose I only ever really memorized 2-6 and 12.