Tool-based culture is not unique to humans, but cumulative technological culture is. The social intelligence hypothesis suggests that this phenomenon is fundamentally based on uniquely human sociocognitive skills (e.g., shared intentionality). An alternative hypothesis is that cumulative technological culture also crucially depends on physical intelligence, which may reflect fluid and crystallized aspects of intelligence and enables people to understand and improve the tools made by predecessors. By using a tool-making-based microsociety paradigm, we demonstrate that physical intelligence is a stronger predictor of cumulative technological performance than social intelligence. Moreover, learners' physical intelligence is critical not only in observational learning but also when learners interact verbally with teachers. Finally, we show that cumulative performance is only slightly influenced by teachers' physical and social intelligence. In sum, human technological culture needs ``great engineers'' to evolve regardless of the proportion of ``great pedagogues.'' Social intelligence might play a more limited role than commonly assumed, perhaps in tool-use/making situations in which teachers and learners have to share symbolic representations.