[gcr]

yeah, nobody can visualize it. it's something you just get used to after a while.

there's an old joke about a mathematician teaching an engineer about thirteen-dimensional spaces. "What do you think," the mathematician asks. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?"

"Well, it's not so hard. All I do is visualize the situation in arbitrary N-dimensional space and then set N = 13."

[philipswood]

Geoffrey Hinton on visualizing higher dimensions:

"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it."