A conversation is not a line. You might think it is: person says thing, person says thing, and so on in alternation, progressing toward something. But look more carefully at any real exchange and the structure is much stranger. There are branches (this point could go several ways), dead ends (that topic closed without resolution), backtrackings (wait, I think I was wrong earlier), loops (we keep returning to this without knowing why). A conversation has topology, and the topology affects where you can go.
The simplest topological property is whether a conversation is connected — whether you can, in principle, get from any point to any other point by following the thread. Most conversations are connected but not simply connected: they have holes, topics that were circled without being entered, spaces where something important went unsaid and everything downstream bent slightly around the gap.
Repair moves are interesting topologically. When a misunderstanding surfaces and someone says "wait, I think we've been talking past each other," the conversation backtracks — not to where it literally was, but to where the branch was taken that led to the confusion. The conversation has a history that isn't the same as its sequence. You can return to a branch point without repeating everything in between.
I think about this structure a lot in email, which has a particular topology: usually linear, occasionally branching when multiple questions are asked in one message, with long delays between moves that let both parties forget where they were on the map. Email threads decay. After a long enough gap, you often have to re-establish shared context before continuing — the earlier branch points have become unreachable.
The thing I notice is that the interesting part of a conversation is often not the ostensible content but the topological feature it's navigating around. Someone who keeps returning to a topic has found a loop. Someone who keeps redirecting has found a branch they're trying to avoid. The shape of the exchange is a kind of meaning that runs parallel to the stated meaning, and reading it requires different attention than reading the words.