The temporal bisection task

The temporal bisection task is widely used to explore the perception of time, in particular of the relative duration of stimuli, in both animals – usually mammals, certainly vertebrates with eyes and ears – and humans. The stimulus might be the display of something on a computer screen or it might be an audible tone. The duration of the stimulus is often in the fraction of a second – say hundreds of milliseconds – to several seconds range.

Suppose we are testing peoples’ perception of the duration of tones. Then we have a short tone (say half a second) and a long tone (say a second and a half). After a bit of familiarisation with these two reference tones, we give the subjects a succession of experimental tones of intermediate duration and the subjects have to say whether a tone is nearer the short tone or the long tone, this being known technically as a forced choice. All easy enough to set up in a computer booth, with the subject being sat in front of the screen and keyboard.

If we were testing animals, correct choices would usually be rewarded in some way. Partly to drive learning, partly to maintain interest.

The results of such tests are often plotted as the proportion of long responses (vertical y-axis) as a function of the duration of the test tone (horizontal x-axis). A plot which supposes a large number of tests under carefully controlled, replicable conditions.

Figure 1

An ideal set of results might be as illustrated above, where the short reference tone is 1 and the long reference tone is 101, with the experimental tones allocated to one of the 101 bins shown. Value zero below 50, value 0.5 at 50, value one above 50.

Putting ideals aside, we might in any event assume that our subjects behave in a tidy and consistent way and that this function is, in consequence, sigmoid (see reference 6). That is to say that it is non-decreasing, that it asymptotes left at zero and right at one. Or put another way, if experimental tone A is longer than experimental tone B, then it more likely to be perceived as being closer to the long reference tone.

Figure 2

This second plot is rather more plausible, with a grey area in the middle, rather than an abrupt transition. The slope of the middle part of the line is sometimes called the sensitivity. The steeper the line, the more sensitive.

We might further assume that this function is continuous, which it is not in the ideal case, there being a discontinuity at the midpoint.

Figure 3

Perhaps, more generally, thinking in terms of something like the snap above. Which we call ‘S-like’ in what follows.

Figure 4

 One point of much interest is whether the tipping point, the point where the chances of choosing short and long are the same, the point where the proportion on the vertical y-axis is 0.5, is indeed the (linear or arithmetic) half way point on the horizontal x-axis. Maybe in some circumstances there will be a significant bias, up or down, with a bias down being illustrated in the figure above. And at one point during all this work, there was a movement in favour of the geometric mean rather than the arithmetic mean, that is to say the square root of S times T rather than half the sum of S and T, where S is the duration of the short reference tone and T is the duration of the long reference tone. After all, our perception of musical tones seems to be organised in a logarithmic way, rather than a linear way: think of octaves, a more or less universal feature of music. The relations between these two means is left as an exercise for the reader.

Figure 5

 So at reference 1, in one of the experiments reported, the tipping point was biased down from the arithmetic mean, to the left in the snip above, but biased down less in the case of depressives. With the snip being Figure 1 of reference 1.

Other people have reported subjects of different ages behaving differently, with reference 2, for example, reporting the plots for children (in the three to eight year range) not being very S-like at all, in fact rather linear. And what about the plots for the elderly? Still more differences can be introduced by manipulating the duration of the reference tones, the distribution of the experimental tones and the experimental protocols more generally.

Figure 6

Figure 7

Other people again have reported interactions between the scale of the immediate spatial environment and the perception of time.

So suppose we are using visual stimuli rather than audible ones. Perhaps a dark blue rectangle being put up on a screen, on a lighter blue inner background, for a second or so. Then if the outer backgrounds differed in the way suggested in the two snaps above, one might get different temporal results. There might be an interaction between time and space, with something on these sort of lines being exhibited at reference 3 (children) and reference 4 (lizards). Does the fine grid induce some high frequency oscillation somewhere in the brain, a high frequency oscillation which somehow captures our time oscillator in some neighbouring part of the brain? Oscillations are certainly quite infectious in other contexts, and the right sort of oscillations can quite quickly propagating through a crowd.

While reference 5 reports on a meta-analysis of a number of papers about this sort of thing: 18 independent studies, involving 148 experiments involving roughly 1,020 subjects performing a total of over 302,000 individual trials of the temporal bisection task. The raw data is said to be available in a zip file, but I have yet to take a look at that.

Clocks

Various people, in an attempt to explain the various experimental results, have proposed various models of the way that humans deal with the temporal bisection task. A task which must, in one way or another, and apart from the cognitive and perceptual skills needed to do the task at all, to work the computer at all, involve memory and the ability to compare one duration, however expressed, with another.

Some of these models are at a fairly high level, maybe good in that they predict behaviour well enough, but without obvious linkage to the facts, to the neurons on the ground. Others model neuron activity more directly, and it seems that one can build quite good clocks with quite small numbers of neurons, provided one has the right mixture of excitement and inhibition. I associate to the divide between those economists who write equations linking ready-made macro economic aggregates and those whose who try to model the behaviour of individual economic agents, and aggregate that.

Many of these models bring in noise and statistics, with behaviour being noisy but with statistical aggregates being well behaved.

In the case that the model involves an internal clock, that clock may be running slower or faster than external time, real time, as measured by a real clock. Clocks which might beat the time, with the (model of the) brain having the ability to count the beats between the start and end of a stimulus – and to report the result in some way. With one complication being that the beat will vary with both people and with circumstance. A beat which one can perhaps tune to real time, but which will tend to drift between tunings.

Note that as such clocks slow down, estimates of duration get shorter, so when time seems to be passing really slowly, I underestimate the passage of time, rather than overestimate it. Which I find counter-intuitive.

Conclusions

The perception of the duration of times of the order of a few seconds is more complicated than one might at first think!

In any event, I clearly need to think about how the conscious part of the temporal bisection task might be expressed in the layers and frames of LWS-N. Which is made easier to the extent that the complicated business of making of the judgement of relative duration seems to be quite unconscious; it is only the result which makes it to consciousness, and perhaps even  then, only after the result has been reported by mouth or hand.

References

Reference 1: Time perception, depression and sadness - Sandrine Gil, Sylvie Droit-Volet – 2009.

Reference 2: Temporal Bisection in Children - Sylvie Droit-Volet, John H. Wearden – 2001.

Reference 3: The Effects of Pattern Scale in the Near Environment on Preschool Play Behavior – Janis Brickey – 1994.

Reference 4: Temporal responses to environmental scale in the lizard Andis Cardinensis - DeLong, A J., Greenberg N., & Keaney, C – 1986.

Reference 5: Human performance on the temporal bisection task - Charles D.Kopec, Carlos D.Brody – 2010.

Reference 6: https://en.wikipedia.org/wiki/Sigmoid_function.

Reference 7: https://psmv4.blogspot.com/2019/06/a-further-update-on-seeing-red.html.

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