| Abstract: | Poisson processes—random pacemakers driving accurate counters—are common models for timers. Such clocks get relatively more accurate the faster they go. This is not true of real clocks, where the relative error is approximately constant, an example of Weber's law known as scalar timing. This distinction was the core problem motivating Gibbon's Scalar Expectancy Theory. Since worse pacemakers cannot generate scalar timing, the necessary variance must be found elsewhere. This article reviews three failure modes of counters and shows that any one (or all together) provides a mechanism for scalar timing. Unique microdeviations from proportional timing in real data provide signatures of underlying machinery. This paper assays the maps between these signatures and those of stochastic counters, finding family resemblances that range from kissing cousins to clones. |
