The nuances of the word ‘complexity’

One of the most popular ways to explain the difference between risk and uncertainty is the example of the coin:

Imagine you flip a coin 100 times. If the coin was perfectly balanced the final tally would read: 50x head, 50x tails. However, since coins are not perfect, in real life you’re more likely to get something like a 48/52 distribution. Your lack of knowledge about coin imperfections is the uncertainty you need to consider.

When one thinks about politics/economics upon this example one imagines that uncertainty is essentially the result of lack of information and complication. Many, many, many, coins with unknown imbalances being flipped at once make for a lot of uncertainty.

This has a fun language parallel, as recently pointed out by a student of mine. In English, the dictionary meanings of the words complication and complexity is almost the same:

Complication: a circumstance that complicates something; a difficulty.

Complexity: The state or quality of being intricate or complicated.

In German, however, the words imply a very different type of situation. Complicated is used for something with many parts. Complex is reserved for things that are uncertain on top of being complicated. A Swiss watch: complicated but certain. Many coins with unknown imbalances flipping at once: complicated and uncertain.

Can both these situations be described as complex? In English, yes. In German, apparently, not.