Much prior research has investigated how humans understand time using body-based contrasts like front/back and left/right. It has recently come to light, however, that some communities instead understand time using environment-based contrasts. Here, we present the richest portrait yet of one such case: the topographic system used by the Yupno of Papua New Guinea, in which the past is construed as downhill and the future as uphill. We first survey topographic concepts in Yupno language and culture, showing how they constitute a privileged resource for communicating about space. Next, we survey time concepts in Yupno, focusing on how topographic concepts are used to construe past, present, and future. We then illustrate how this topographic understanding of time comes to life in the words, hands, and minds of Yupno speakers. Drawing on informal interviews, we offer a view of the topographic system that goes beyond a community-level summary, and offers a glimpse of its individual-level and moment-to-moment texture. Finally, we step back to account for how this topographic understanding of time is embedded within a rich cognitive ecology of linguistic, cultural, gestural, and architectural practices. We close by discussing an elusive question: Why is the future uphill?