What's the semantic field of "nach"?

Question

I'm seeking an answer like Alain Pannetier's. Wiktionary lists nach with its many apparently unrelated meanings, as shown below. How are these seemingly unrelated meanings actually connected? Can someone unearth what the "base meaning" or Semantic Field is, and make them "glaringly obvious"?

Wiktionary's meanings appear to match those on Cambridge and Collins dictionaries.

Etymology

From Middle High German nāh, from Old High German nāh with preservation of word-final -h as -ch; thus pertaining to modern nah (“near”) (from Old High German inflected nāh-), from Proto-Germanic *nēhw. Cognate with Dutch na, English nigh.

1. after, past (later in time)
   \3. to, towards (with geographical names; see usage notes below)
   \4. according to; guided by
   \6. (with verbs of sensual perception) like (see usage notes below)
   \7. for (indicating desire for an object)

Answer 1

The semantic field would be nearness. The different senses are derived from a base meaning of ‘near’.

For the special temporal meaning of ‘after’, the contrast to «vor» is also important. Originally, the temporal «nach» as in «nach Sonnenuntergang» would have meant something like ‘near sunset’. Now, it means ‘near sunset, but contrasting to «vor»’, in other words, ‘after sunset’.

The spacial sense of ‘towards’ must have evolved from a resultative understanding. «Ich gehe nach Berlin» would have meant something like ‘I go with the result that I am near Berlin’, from which the meaning ‘towards’ is derived.

The other meanings show the concept of nearness more directly. When something is “according to” something else, then the two are ‘near’. When something is perceived “like” something else, then the two are ‘near’. When I desire “for” something, then I want to be ‘near’.