# Changes

When is a dependency graph cyclic or acyclic? Circular dependencies are kind of weird in the sense that if we increase the resolution of concept space, it seems like we can always get the graph to a point where it's no longer circular. Superficially, we might say $X$ and $Y$ depend on each other, but actually, if you break them down, $X$ has parts $X'$ and $X''$, and (1) $Y$ depends on $X'$ and (2) $X''$ depends on $Y$, so at this finer resolution, the dependency has no cycle (the graph looks like $X' \rightarrow Y \rightarrow X''$), but if you look at the original graph with nodes $Y$ and $X=\{X', X''\}$, then it looks like there's a cycle. Is there a counterexample to this?