"nach" can mean "to" and "after". Today, we'll explore the common core of this, and explore the various uses of "nach", both alone and as a prefix.
nach, nachmachen, nachlaufen, nachlassen, nachgehen, nach
The core idea of the root (according to English sources) was:
German sources have the meaning for focused on motion and describe it as
twitching with the foot, unrest
In German, it shifted toward a sense of tracking (by foot) and then kept going toward the sense of perceiving.
English doesn’t have many relatives – spur, spoor, spurn.
They haven’t shifted their meaning as much, so they’re still somewhat close to ankle or to a broad sense of twitching.