Complex processes, the spread of ideas, the flow of influence, the contingency of historical events, unfold over networks. But understanding them requires more than static snapshots. This talk walks through a research thread connecting three related problems: how things diffuse through networks, how we trace plausible paths of influence under uncertain evidence, and how counterfactual reasoning reveals which claims are robust and which are accidents of circumstance. Drawing on work in digital art history, epidemiology, and simulation, the talk argues that visualization is not just a display layer. It is the reasoning environment itself, keeping complex dynamics interpretable and open to human judgment.