What's the difference between 平行 and 並行?

Question

They both seem to mean "parallel". In my プログレッシブ dictionary, it seems to point to the former being the more mathematical sense of the definition (two co-planar, non-intersecting lines), while the latter indicates a more metaphorical definition (doing things at the same time, parallel computing, etc.).

However, my 大辞泉 has the following:

平行：「並行（へいこう）②」に同じ。（並行② is the metaphorical definition)

So which is it? Are they distinct like プログレッシブ says, or does 平行 encompass 並行 like 大辞泉 says?

Answer 1

平行 can mean the same thing as 並行 in the second sense (物事が同時に行われる), so it does not encompass 並行 completely. For example, 電車と並行して走る should not use 平行 (although don't be surprised if you see the two mixed up). However, just look at the characters, the 並 of 並行 can be seen in words like 並ぶ while the 平 of 平行 can be seen in words like 平面. So, in general, 平行 is primarily used in the mathematical sense while 並行 is used to just mean "do two things at once" or "line up and proceed together" like in 英語とフランス語を並行して勉強する . Also, notice that parallel in the computing sense is 並列, not 並行, which would be concurrent computing.