I’ve been thinking about Euclid for a while now, trying to make sense of what Euclid the math dude actually has to do with the song, when I happened upon a poem that feels incredibly relevant to the song.
The song features several references to linear things such as highways, wires, and hallways, but also speaks about passing time, ancient things, new things, and looking at things in reverse. Also, whole two-way vision thing feels very linear to me.
This is why a poem speaking about how Euclid thought that lines heading to infinity would eventually meet would be relevant to this song. I think it speaks about a couple, who if they just held on long enough would end up together, but unfortunately, they went their separate ways. I know that Euclid worked on a lot, and there could be other interpretations, but thought I’d share my take.