Plane Books

“A plane in mathematics is not merely a flat surface but a flat surface of infinite thinness and size. Trivial? Not to us. When I say plane, I'm not thinking of a tabletop or sheet of glass or a piece of paper. You might point to any one of these objects; but all of them are precisely that: objects. They exist in the world. And because they do, they are defined by their breadth and reach. To a mathematician, a tabletop is no more a plane than a slice of rum cake is. In the world we know, in fact, the only thing that can actually be called a plane--or a portion of one, anyhow--is a shadow.
You see?
Words fail us. Even the world fails us.
Are there not a thousand forms of sorrow? Is the sorrow of death the same as the sorrow of knowing the pain in a child's future? What about the melancholy of music? Is it the same as the melancholy of a summer dusk? Is the loss I was feeling for my father the same I would have felt for a man better-fit to the world who might have thrown a baseball with me or taken me out in the mornings to fish? Both we call grief. I don't think we have words for our feeling any more than we have words for our thoughts. I don't even believe that we actually do the things we call thinking and feeling. We do something, but it is only out of crudeness that we call it thinking; and when we do the other thing, we call it feeling. But I can tell you, if you asked Archimedes ... or Brahmagupta ... or Hilbert ... when they'd first known that they'd solved their great problem, I suspect they'd all say they had a feeling.”
― Ethan Canin, A Doubter's Almanac