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So, we have the kanji 上・下 which can be read as either かみ・しも or うえ・した, and as I
understand it, those two are antonym pairs. But what are the differences
between the two?

The thesaurus isn't very helpful. For instance, it says, for うえ

> 何かとくらべて高い方の位置、場所。

and for かみ it says

> 位置が高いこと。また、ひと続きのものの初め。川では上流、和歌などでは前半をいう。

If I understand this correctly, this is saying that うえ is simply the place or
position above some reference level, while かみ is the state of _being_ above,
or the start of a series. But the dictionary entry for かみ goes on to give
definitions like

> 位置の高い所。

which bring it right back into the territory of うえ, or at least very close. It
almost looks like the distinction is supposed to be relative vs absolute, but
this just confuses me since, at least in my mind, above/below are inherently
relative.

**Question.** What are the differences between かみ・しも and うえ・した? Are there
minimal pairs illustrating these differences?
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meaning synonyms direction
Ups and downs: かみ・しも vs うえ・した
AFAIK, うえ・した is just "(on) top/above vs. (on) bottom/underneath".

かみ・しも is usually "upper vs. lower", meaning talking about different parts of
the same thing. The easiest example of this to remember is "upstream" vs.
"downstream" (川上【かわかみ】 vs. 川下【かわしも】) or "upwind" vs. "downwind" (風上【かざかみ】 vs.
風下【かざしも】). Also, more generically, 上手【かみて】 (upper part) and 下手【しもて】 (lower
part).

Other than these few examples, the only other ways I've seen かみ・しも used are
referencing place names (地名). An example in Osaka is
[[上新庄]{かみ・しん・じょう}](http://bit.ly/2sT3dpu) and
[[下新庄]{しも・しん・じょう}](http://bit.ly/2sHIZ2G) (upper and lower Shinjou). You can
see on the map that they are pretty even north-south-wise, so the 上 and 下
probably refer to their positioning along the Kanzaki river which empties into
Osaka Bay to the southwest. Another is [[桂]{かつら}](http://bit.ly/2sHptnf) and
[[上桂]{かみ・かつら}](http://bit.ly/2sHq7Bb) near 嵐山 in Kyoto. Also,
[[上京区]{かみ・ぎょう・く}](http://bit.ly/2M9nFeJ) and
[[下京区]{しも・ぎょう・く}](http://bit.ly/2Mbzm4C) districts in Kyoto.

**TANGENTIAL NOTE** : notice that `上手` and `下手` both have multiple readings
that mean different things.

### 上手

  * 上手【じょうず】（じょうず）／上手【うま】（うま）い → Skillful; clever; good at
  * 上手【かみて】（かみて） → the upper part; stage left
  * 上手【うわて】（うわて） → to be better than someone else at something; to "have the upper hand" (advantage); overhand (sumo throw / baseball pitch)

### 下手

  * 下手【へた】（へた） → lack of skill; poor; bad at
  * 下手【しもて】（しもて） → the lower part; stage right
  * 下手【したて】（したて） → take a lower position; being humble/modest; underhand grip (sumo / baseball)
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Your dictionary definition seems to be saying that:

>   * かみ, しも are used when the objects in question are lined up along a single
> dimension monotonically with respect to the height/degree in question.
>   * うえ, した are used when the objects are distributed within two or more
> dimension.
>

This matches with my intuition.
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