<p>Forms of collective intelligence range from natural and artificial neural networks to swarm robotics and social insect colonies. One key axis for comparing such systems is the mobility of their individual units: systems like neural networks and wireless sensor networks typically rely on fixed topology and consistent neighbour relationships, whereas mobile robots or ants may encounter each other once and never meet again. Consequently, the core mechanisms that these systems use to compute and learn differ fundamentally between static and fluid topologies. This divide has limited the exchange of ideas across domains. This Perspective examines how mobile units achieve collective learning—through plasticity within individuals, transient formations and, notably, environmental modifications—and identifies analogous mechanisms in static networks. It then explores the advantages of mobility, showing how, for certain tasks, unit mobility can allow a collective system to achieve a given level of performance using many fewer units. An analogy between robot swarms performing a consensus task and convolutional neural networks classifying images illustrates how this principle can inform the design and use of smaller static networks, yielding resource savings. Conversely, temporary immobility or predictable movement patterns can enable mobile unit networks to perform more complex computations by leveraging the benefits of static topologies. Viewing each topology through the lens of the other may inspire advances in both domains, including novel network architectures and swarm algorithms.</p>