Circling and squaring. Dichotomous? Not totally. Squaring is growing, taking an input and forcing it to rapidly grow. From a straight path, you can form a big diamond, which is just a familiar polygon standing on a point.
But if you start with a small input, squaring will shrink it. You can go on shrinking until it’s just honing on on nothing at all, as if it was spiralling towards its origin.
But both squaring and circling sport a common trait. It’s not that both do similar things; it’s that you can think of both as abstractions. 2-D forms, impossibly thin and insubstantial, but our 3-D world can’t hurt it. Our bias, our assumptions, our not knowing what “famous” should signify…nothing can touch such functions.
But though squaring allows things to grow, circling is only skirting around. Not growing, not shrinking, just turning. And though you turn, you cannot go in.