Humans spatialize time. This occurs within individual minds and also in larger, shared cultural systems like language. Understanding the origins of space-time mappings requires analyses at multiple levels, from initial individual biases to cultural evolution. Here we present a laboratory experiment that simulates the cultural emergence of space-time mappings. Dyads had to communicate about temporal concepts using only a novel, spatial signaling device. Over the course of their interactions, participants rapidly established semiotic systems that mapped systematically between time and space. These semiotic systems exhibited a number of similarities, but also striking idiosyncrasies. By foregrounding the interaction of mechanisms that operate on disparate timescales, laboratory experiments can shed light on the commonalities and variety found in space-time mappings in languages around the world.