There is physics. Then there is psychology. And never the twain shall meet?

No, quite to the contrary: The nature of the relationship between the physical world and its psychological representation is among the most studied—and understood—of all mental phenomena. For more than 150 years, psychophysicists have been studying the mapping between physical quantities, such as weight or brightness, and their perceived psychological magnitudes.

Many robust psychophysical regularities have been discovered. Perhaps most famous among them is Weber’s Law, which holds that the change in a stimulus that will be just noticeable is a constant ratio of the original stimulus.

Put simply, if it takes 5g to tell the difference between a weight of 100g and a heavier one, then it will take 50g to tell that something is heavier than 1kg. The constant fraction of .05 (5/100 or 50/1000) is known as the Weber fraction or Weber ratio. Weber’s Law holds across a wide range of stimulus dimensions and magnitudes, with a few known exceptions such as stimuli at extreme magnitudes.

A recent paper in the Psychonomic Bulletin & Review by Simon Grondin, Vincent Laflamme, and Giovanna Mioni reported another boundary condition for Weber’s Law. Their paper addressed time perception; that is, people’s ability to differentiate two time intervals from another. Suppose you encounter a quiet interval between two tones that lasts ½ second, and then another one of variable duration—how much longer does the second interval have to be for you to be certain it’s longer than the first one?

It turns out that the answer to this question varies intriguingly with the absolute duration of the first interval. In a nutshell, Grondin and colleagues showed that intervals longer than 1.2 s are processed differently from shorter intervals—a finding that has considerable theoretical relevance.

Their experimental procedure was charmingly simple: People were instructed to count silently from 1 to a target number (such as 16 or 31), using a pre-determined “beat.” The beat was either reasonably fast (.8 s per count) or slow (1.6 s). The question of interest is how closely people were able to stick to the beat, as measured by the total duration of their counting up to the target number. The Weber ratio can be computed from those durations using some straightforward arithmetic.

The main result is shown in the figure below:

The interpretation of the figure is quite straightforward: as the interval between counts increases—that is, as the “beat” slows—people’s timing becomes less well calibrated. The Weber ratio is not constant but increases with duration, especially once the intervals exceed 1.2s.

It is important to note that the figure above plots ratios, not absolute magnitudes. So for the example from the outset involving weights, the hypothetical Weber ratio of .05 would be represented in a flat line (at .05) in this graph—even though that .05 might involve different absolute numbers depending on the weight in question (e.g., 5g for 100g, 50g for 1kg, and so on).

Clearly, the timing data cannot be captured by a flat line and hence Weber’s Law does not hold.

What are the implications of this result?

Grondin and colleagues argue that their data may reflect some capacity limit on short-term memory. It is well know that human short-term memory is capacity-limited in terms of how much information can be held in memory at the same time over brief periods. We already know that people can hold somewhere between 3 and 9 items of information—such as the final words of sentences they read out aloud—in memory at once. Intriguingly, knowledge of that “working memory capacity” explains fully half of the variation in people’s IQ.

Grondin and colleagues suggest that their data may point to a similar “maximal duration” of short-term timing processes in memory. They speculate that “What is sometimes simply attributed to inattention may rather be due to an inherent temporal capacity. For instance, people with attention deficit hyperactivity disorder (ADHD) might indeed have a time-related problem.” Perhaps people who suffer from ADHD might just lose track of their timing when the pace of events is too slow.

It appears that advertising professionals are aware of the importance of pace. Have you ever counted the number of distinct shots in a 30-second TV commercial? Some experts suggest there are 25-30 shots in a nationally televised commercial, putting each shot right within the “maximal duration” window identified by Grondin and colleagues.