Since the mid-1990s, the mountain of Tindaya (Fuerteventura, Canary Islands, Spain) has been in limbo. Despite being listed as a Natural and Cultural Asset by virtue of its environmental singularity and indigenous engravings, the conservation plans have never been implemented. Instead, the state institutions designated it as the location for artist Eduardo Chillida’s Monument to Tolerance (a huge, bare cubic cave to be dug in its interior) – a controversial project that remains suspended, neither in construction nor abandoned. To complicate matters, the mountain also features three quarries, and speculation over the mining rights associated with them resulted in a long series of trials and appeals. Tindaya is therefore a site of truncated futures, fragments of which are still to be found in and around the mountain. This article works with these material traces as a way of activating the mountain’s role in a plurality of strategies of anticipation, from the economic and cultural superabundance ascribed to Chillida’s project by the state to the indigenous rituals and offerings that took place in the mountain. It is argued that Tindaya stands today as an unintended monument to the ruins of a modernity envisaged in the language of economic development and artistic abstraction, but also represents the possibility of enacting other, minoritarian futures, connected to the poorly understood indigenous lifeworlds attached to the mountain and its surroundings. The critique of the former is accompanied by the cultivation of the latter through an exercise in speculative ethnography.