… That little narrative is an example of the mathematician’s art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it’s fascinating, it’s fun, and it’s free!
I fake fake to have a fake life. Does that make me a real horse? Buy now for $777, wooden saddle sold separately. Real horseshoes not included. Imaginary ones – neither.
Don Quixote is not an imaginary person; he is as real as Alexander the Great.
… This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.
On the other hand, once you have made your choices then your new creations do what they do, whether you like it or not. This is the amazing thing about making imaginary patterns: they talk back!
Reality and fantasy are not two separate spheres but one whole. They are like a world’s atmospherereality behaving as a low front, fantasy a high front. Each remains somewhat distinguishable and yet they swirl and join, affecting and manipulating the other. One cannot perceive where reality ends and fantasy begins, but life would grow stagnant and die without the influence of both.