Evaluation of quantitative theories of timing.

Bell (1999) compared two math models of timing. One is scalar timing theory. The other is the newer multiple-time-scale theory. The paper used logic, not new data, to judge which model fits known facts.

Scalar timing explains most timing facts, but leaves gaps. Multiple-time-scale theory could fill those gaps, yet no one has tested it with real data. The author calls for experiments before picking a winner.

Malone (1999) disagrees. That same year, J argued multiple-time-scale theory is too vague to test. Both papers talk about the same models, but J rejects the new theory while M keeps the door open.

Webb et al. (1999) sides with M. They also favor multiple-time-scale ideas, showing the field was split in 1999.

Staddon et al. (2002) later built a tuned-trace model, a cousin of multiple-time-scale theory. This extends M’s view by giving the theory more detail.

If you write protocols that depend on precise timing, like fixed-interval DRL or token release, you need to know the rules that govern how learners “feel” time. M warns that scalar rules may fail in some conditions. Track response patterns that don’t fit scalar predictions; they may be the place where newer timing models help you adjust schedules or cues.