Topology has a concept that most strategists never encounter: the difference between a 'metric space' and a 'topological space.' A metric space tells you how far apart two things are. A topological space tells you only which things are *near* each other — without any notion of exact distance. William James, the pragmatist psychologist, made a structurally identical observation about human thought: we don't store knowledge in measured units, we store it in neighborhoods. What feels 'close' to an idea determines what comparisons we make, what solutions we reach for, what we fail to even consider. The mental model you're using right now is not just a framework — it's a topology. It determines the neighborhood structure of your problem space. Two product failures that look 'far apart' by one topology (one was a positioning problem, one was a technical one) might be immediate neighbors in another (both happened at the moment the team lost the user's voice). The practical implication is uncomfortable: when you're stuck, the issue often isn't that you lack information — it's that your current topology has placed the solution in the wrong neighborhood, somewhere your thinking simply doesn't travel. Reorganize which things you treat as adjacent, and the path often appears without any new data at all.

Pick a problem you've been circling for two weeks. What two things have you been treating as unrelated that might actually belong in the same neighborhood?

Drawing from Mathematical Topology / Philosophy of Mind — William James (The Principles of Psychology, 1890)