Taming The Infinite/ Chapter 16/ The fourth dimension.
"The advantage of high dimensional geometry is that it brings human visual abilities to bear on problems that are not initially visual at all. Because our brains are adept at visual thinking, this formulation can often lead to unexpected insights, not easily attainable through other methods. Mathematical concepts that have no direct connection to the real world often have deeper, indirect connections. It is those hidden links that make mathematics so useful."
That quote above really summarizes the meaning of this chapter, in the utility of imaginary worlds. I mention this previously on the last chapter, chapter 15 that is, but in this chapter the argument is made much more evident by weighing contributors such as Einstein that needed to imagine, truly imagine, new worlds, and then deduct it with mathematics.