The mathematician's sense of tension is intimately related to his sense of beauty, and is what makes mathematics worthwhile doing. - Douglas Hofstadter

By the time we emerge from childhood, we have acquired a reflex-level intuition for where most of our everyday world’s loci of unpredictability lie, and the more unpredictable end of this spectrum simultaneously beckons to us and frightens us. We’re pulled by but fearful of risk-taking. That is the nature of life.

Thus our categories keep us well informed at all times, allowing us to bypass the need for direct observation. If we didn’t constantly extrapolate our knowledge into new situations — if we refrained from making inferences — then we would be conceptually blind. We would be unable to think or act, doomed to permanent uncertainty and to eternal groping in the dark. In short, in order to perceive the world around us, we depend just as much on categorization through analogy as we do on our eyes or our ears.

"It is an inherent property of intelligence that it can jump out of the task
which it is performing, and survey what it has done; it is always looking for,
and often finding, patterns. Now I said that an intelligence canjump out of
its task, but that does not mean that it always will. However, a little prompt-
ing will often suffice. For example, a human being who is reading a book
may grow sleepy. Instead of continuing to read until the book is finished,
he is just as likely to put the book aside and turn off the light. He has
stepped "out of the system" and yet it seems the most natural thing in the
world to us. Or, suppose person A is watching television when person B
comes in the room, and shows evident displeasure with the situation.
Person A may think he understands the problem, and try to remedy it by
exiting the present system (that television program), and flipping the chan-
nel knob, looking for a better show. Person B may have a more radical
concept of what it is to "exit the system"-namely to turn the television off!
Of course, there are cases where only a rare individual will have the vision
to perceive a system which governs many peoples' lives, a system which had
never before even been recognized as a system; then such people often
devote their lives to convincing other people that the system really is there,
and that it ought to be exited from!"