In the US, an adult on average spends two hours and 51 minutes on their smartphone every day. That is eight minutes longer than Andrei Tarkovsky's film Stalker. We're not interested in telling you put your phone down and start paying attention to the real world. Instead, we want to investigate the kind of experience we have whilst staring at these tiny screens and the digital platforms that inhabit them. We are interested in calling this something other than smartphone addiction. We are interested in calling it cinema. Digital Tarkovsky is an extended poetic exploration of how our experiences of visual entertainment and time itself are changing in the era of the smartphone and near-constant connection. The essay applies the 'slow' cinematic art of Andrei Tarkovsky to our interaction with the digital, visual reality of screens and interfaces. Digital Tarkovsky is a way of tracing what cinema, storytelling and time mean in our platform-based world.