Time perception · interval timing

How does the mind keep track of time?

Without looking at a clock, you can tell roughly when a minute has passed, and you get better at it with practice. In the model I developed with Hedderik van Rijn, the mind has an internal clock whose pulses get further and further apart. This page lets you run that clock, see why it makes our time sense proportional, and watch it learn from feedback.

Step 1 · The clock

A pacemaker that slows down as it ticks

The clock starts with pulses about 11 milliseconds apart. After every pulse, the wait for the next one is multiplied by a fixed factor (1.1 in the standard model) and disturbed by a little noise. The marks below are the pulses of one run over 10 seconds. A plain clock with equal intervals would need a very large counter for long durations; this one only needs about twice as many pulses to cover ten times as much time.

Growth per pulse ×1.10

Because the intervals grow, the pulse count grows only like the logarithm of elapsed time. That compresses long durations, and it is what makes the clock's errors proportional to the interval being timed.

Step 2 · Estimating an interval

Longer intervals are less precise, in proportion

Suppose the model has learned how many pulses belong to a target interval, and now has to produce that interval again. Noise in the pulses makes each estimate a little different. The histogram shows 2,000 estimates; the bars underneath show how the spread grows with the interval. In people, the spread of time estimates grows in proportion to the interval (a pattern known as the scalar property of timing); here it comes out of the clock itself.

Target interval 5 s Pulse noise 1.5%

Step 3 · Learning

Feedback tunes the clock's reference

The clock itself does not change. What is learned is the memory of how many pulses go with an interval. After each trial the model stores the pulse count that actually occurred during the true interval, and the next estimate is based on the average of what has been stored. Start from a wrong memory and the estimates drift to the target within a few trials, as people's do. Here the target is 5 seconds.

estimates in this runaverage of 200 runstrue interval

A deliberately simplified version of the model: Gaussian noise, a plain average over stored memories, and no interaction with other tasks. The full model is described in the paper below.

Why it matters

Time is one more mental resource

In the full model the clock is read by the same rule system that runs everything else, so timing interacts with what else the mind is doing, and the clock appears as another resource in threaded cognition. The model was designed as a module for ACT-R but can be adapted to any cognitive architecture; the paper below describes how clock, attention and learning work together.

References

Taatgen, N. A., van Rijn, H., & Anderson, J. (2007). An integrated theory of prospective time interval estimation: The role of cognition, attention, and learning. Psychological Review, 114(3), 577–598.