S-curves are life.

Imagine being presented with a pile of 500 jigsaw puzzle pieces without the box. At first, you will have no idea what image the pieces constitute. After finding a few pairs of pieces that fit, you still will not have any idea what the final image will be. At this early point, each additional piece will not significantly change your uncertainty about the image. Paradoxically, at the other end of the spectrum, when the puzzle is mostly complete, the addition of each of the final pieces will also not materially change your understanding of the puzzle image (because you already have a good idea of what it is).

In between the extremes, however, there is a magical zone in which each new piece placed into the puzzle significantly improves your understanding of the puzzle image by eliminating some possibilities and reinforcing others. In this zone, it is as if the insights were suddenly falling out of a super-saturated suspension, with each new piece now seemingly worth more than the first several dozen pieces combined. In helping you correctly guess the puzzle's image, the value of incremental pieces follows an S-curve: low at first, growing quickly in the middle, then declining again toward the end.

Most things in life follow this S-curve pattern: how long it takes concrete to harden, how much food to eat, how much fertilizer the lawn needs, how much exercise to get, how much light enables easy reading, how many friends to invite for a dinner party, how long a vacation should be, how big a house to build, how much water to drink daily, and so forth.

The magic is in the middle.