This is so neat! I must have glossed over this when I read the Republic years back. I think there's no way Plato would have mentioned them being divided by the same proportion if he wasn't aware of an interesting result from it.
It's very easy to miss the divided line given where it's located and how brief and impressionistic it is. The Republic is so complex and it gets more complex the more you interrogate it—like a living organism indeed.
That's a good point about the proportions. If Plato just wanted to establish vague relations, he didn't have to do it so specifically! The divided line seems weird once you notice it, then it seems weird that you didn't notice it right away, given how weird it is. There are a LOT of things like that in Plato's writing.
This is so neat! I must have glossed over this when I read the Republic years back. I think there's no way Plato would have mentioned them being divided by the same proportion if he wasn't aware of an interesting result from it.
It's very easy to miss the divided line given where it's located and how brief and impressionistic it is. The Republic is so complex and it gets more complex the more you interrogate it—like a living organism indeed.
That's a good point about the proportions. If Plato just wanted to establish vague relations, he didn't have to do it so specifically! The divided line seems weird once you notice it, then it seems weird that you didn't notice it right away, given how weird it is. There are a LOT of things like that in Plato's writing.
2500 years on and we're still finding easter eggs!