now, i have a feeling descartes would have loved one of my favorite toys, the etch a sketch. it's all about coordinates. with one of these knobs, i can control the lines that go back and forth, the horizontal direction. and with the other, i can control the up and down, the vertical dimension. we can make some pretty pictures with this toy, but our freedom of movement is limited to just these two independent dimensions, or parameters, we might call them. now of course, we don't move in a world of two dimensions like the etch a sketch. we're able to move not just side to side and back and forth, but up and down as well, so that we need three numbers to describe a point in our physical world. so suppose we had a three-dimensional etch a sketch. well, let's not suppose. i actually have one. come on, let's see it. here's my three-dimensional etch a sketch. now, with three knobs, i can draw vertically...horizontally, and with depth. this is so cool. i now have three independent parameters so that i have freedom of motion in three dimensions, just like in our everyday world. but in