Thanks =) The truth is, I often spend my time while I'm walking around coming up like little tricks like this--just mental shorthand to make some thought process or another faster. I also record which images/"gestures"/sounds/tastes/general associations come up over and over again when I'm solving problems, so that I can sort of translate a problem into mental structures, translate the mental abstractions into other mental abstractions, manipulate them as desired, and then pop back out with an answer.
The end result is that I can solve problems and come up with insights that would floor most other people, but I can never explain how I got there in any sort of sensible way. And, when thinking about how I feel in a given moment, if I'm moving anywhere beyond happy, sad, or angry, I end up with things like "tastes like carrot" or "feels like carrying a pumpkin" or "smells like walking on red cement in the summer at the age of eight past picnic tables."
I don't actually have synesthesia, but I spent about four years or so teaching my brain to pretend it had it, and now I use the resulting networks to my advantage.
how does the shape thing help? it seems like it'd be more confusing...
Because instead of saying:
I know six is two threes
I say
I know two triangles is two triangles.
It moves things from computation to identification. I also have hand gestures to keep me on track when I'm doing long computations: swipe down for derivatives, pull back for multiplication, two hands together for a dot product, flipping the hand over to take the inverse, squeeze two fingers together when something cancels out, shove sideways when moving a term from one side of an equation to another. I don't usually perform these hand gestures, but knowing which motion goes with whatever I'm supposed to be doing tends to make it a lot faster--because the motion encodes everything I know about the computation into a single idea, condensed and easily usable.