Time, an everyday yet fundamentally abstract domain, is conceptualized in terms of space throughout the world's cultures. Linguists and psychologists have presented evidence of a widespread pattern in which deictic time-past, present, and future-is construed along the front/back axis, a construal that is linear and ego-based. To investigate the universality of this pattern, we studied the construal of deictic time among the Yupno, an indigenous group from the mountains of Papua New Guinea, whose language makes extensive use of allocentric topographic (uphill/downhill) terms for describing spatial relations. We measured the pointing direction of Yupno speakers' gestures-produced naturally and without prompting-as they explained common expressions related to the past, present, and future. Results show that the Yupno spontaneously construe deictic time spatially in terms of allocentric topography: the past is construed as downhill, the present as co-located with the speaker, and the future as uphill. Moreover, the Yupno construal is not linear, but exhibits a particular geometry that appears to reflect the local terrain. The findings shed light on how, our universal human embodiment notwithstanding, linguistic, cultural, and environmental pressures come to shape abstract concepts.