The anticipation of imminent events is time-scale invariant.

Humans predict the timing of imminent events to generate fast and precise actions, decisions, and other behaviors. Such temporal anticipation is critical over wide timescales, and especially salient over the range from hundreds of milliseconds to a few seconds. Despite advances in our understanding of basic timing behavior and its underlying neural mechanisms, it remains an open question whether anticipation is stable across these short time scales. Recent work shows that the brain models the probability density function (PDF) of events across time, suggesting a canonical mechanism for temporal anticipation. Here, we investigate whether this computation holds when the event distribution covers different time spans. We show that, irrespective of the time span, anticipation, measured as reaction time, scales with the event distribution. This demonstrates that the key computation-the estimation of event probability density-is invariant across temporal scales. We further show that the precision of anticipation is also scale invariant which contradicts Weber's law. The results are established in vision and audition, suggesting that the core computations in temporal anticipation are independent of sensory modality. Perceptual systems exploit probability estimation over time independently of temporal scale to anticipate imminent events.