[rcthompson]

What about more abstract tasks that could be solved by visualization, such as "What is the shape of the graph of y = x^2" or "Given any shape made out of six squares, is it possible to fold it into a cube?" Would you be able to solve these kinds of questions mentally, and if so, how?

As an example, for the cube question, I would generally solve it by visualizing the shape starting out flat and then getting folded 90 degrees inward at each crease until it either forms a complete cube, in which case the answer is yes, or two of the squares are forces to overlap each other, in which case the answer is no. To be clear, I'm not imagining any person's hands actually performing the act of folding, I'm just visualizing the abstract shape floating an otherwise featureless void, folding of its own accord. In fact, here's a video that more or less shows what I would visualize: https://vimeo.com/64926672