I was expecting (or hoping) that the pictorial versions would somehow illuminate why these various identities hold. But they seem to be just an alternative set of symbols.
I wonder why numerals are used to represent 2 and 3 in some places, but stacked boxes are used in others?
The idea appears to be that artists find the use of colors easier to memorize / mentally manipulate compared to letters for variable identifiers. I'm not an artist, so I'm curious if others find this to be true.
Actually as both artist and mathematician, the first thing I had to do is 'translate' her visualization into something I could relate to my visualization on a given subject. Hmmm--- that is not really clear; I suppose what I mean is that we all 'see' things differently, the trick is to line things up! BTW, I didn't really notice the colors, so for me at least they made little difference...
When I imagine mathematical operations like these, I sometimes imagine numbers moving around, distorting, and fading in and out in a way representative of the calculation. For instance, “x^2 * x” would show the x on the right moving onto the x on the left, and the 2 fading down to be replaced by a 3 fading in, like an odometer. I’d like to some day create a Flash animation of some calculation showing those movements.
I wonder why numerals are used to represent 2 and 3 in some places, but stacked boxes are used in others?
The idea appears to be that artists find the use of colors easier to memorize / mentally manipulate compared to letters for variable identifiers. I'm not an artist, so I'm curious if others find this to be true.