Whatever we learn has a purpose and whatever we do affects everything and everyone else, if even in the tiniest way. Why, when a housefly flaps his wings, a breeze goes round the world; when a speck of dust falls to the ground, the entire planet weighs a little more; and when you stamp your foot, the earth moves slightly off its course. Whenever you laugh, gladness spreads like the ripples in a pond; and whenever you're sad, no one anywhere can be really happy. And it's much the same thing with knowledge, for whenever you learn something new, the whole world becomes that much richer.
Expectations is the place you must always go to before you get to where you're going. Of course, some people never go beyond Expectations, but my job is to hurry them along whether they like it or not.
And remember, also, added the Princess of Sweet Rhyme, that many places you would like to see are just off the map and many things you want to know are just out of sight or a little beyond your reach. But someday you'll reach them all, for what you learn today, for no reason at all, will help you discover all the wonderful secrets of tomorrow.
... for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where-but just because you can never reach it doesn't mean that it's not worth looking for.
Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless.
You must never feel badly about making mistakes, explained Reason quietly, as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons.