# What Kind of Thing is an Information Variable? The (Annoying) Case of Tau

By Andrew D Wilson @PsychScientists
The central contribution of the ecological approach is the idea of ecological information. Information variables are higher order relations that remain invariant over time as the elements of the pattern change. These relations are the kind of thing that can specify a dynamical property of the environment and support direct perception of that environment.

This is all a little abstract. One nice, simple example is the variable tau which specifies time-to-contact (TTC). TTC is an important property of objects approaching you that, if perceived, would support you intercepting or avoiding the object. Tau is one variable that specifies TTC and therefore might get used by organisms to perceive TTC.

This post will use tau as an example of information because it's straight forward and has lots of the relevant key features. However, tau is a pain in the ass because organisms typically don't actually use it - it's too limited in it's scope to be the best information. People discussing this fact sometimes says it reveals a weakness in the ecological approach. It doesn't; it just reveals a weakness in tau (and the error ecological psychologists made getting as excited as they did about it as an exemplar). It highlights a lot of useful issues, though, so I thought it was still worth the post.

The computational strategy for figuring out time-to-contact is an algorithm that needs estimates of the distance and speed of the moving object. Distance divided by speed is time (e.g. metres divided by metres per second = seconds). Time needs to be derived in this approach; it's not available in the stimulus, whereas distance and speed can be. You process those elements in a way described by the equation 'time = distance/speed' and output time-to-contact.

The informational strategy is to look for kinematic patterns in the optic array that specify time-to-contact. This pattern does not have to be identical to TTC, just specific to it. Picking up that pattern is then equivalent to perceiving TTC, with no processing required.

One such pattern is that described by the variable tau. It was actually first described by physicist Fred Hoyle in his book 'The Black Cloud'. A huge cloud is approaching Earth and scientists want to know when it will arrive; one realises that to figure this out, all they needed was the ratio of the image size to the image expansion rate (gained from images taken at different times). Assuming a constant velocity, this ratio is equal to time-to-contact.

Optically, tau is the inverse of the rate of expansion (change in angular size) of the projection of the approaching object in the optic array. If you simply arrange your measurement system so that it works in a way described by this mathematical description, you can perceive time-to-contact by detecting tau.

Key points:

• tau is not composed of either distance or speed, as the physics based analysis would assume.
• tau is not computed, it is detected. It is a ratio, but this is just a description of the relevant relation that must be detected. The relation does not have to be created by the organism, the relation has already been implemented by the lawful projection of the approaching object into the light. A 'smart' mechanism can be built that is sensitive to the pattern described by the ratio rather than either of the components. Psychophysically, this has been demonstrated by showing thresholds for tau are lower than thresholds for either of the elements in the mathematical description (Regan & Hamstra, 1993).
• tau specifies time-to-contact but is not identical to it. This is important because it reminds us to keep the world variable (the thing to be perceived) and the information variable (the thing that enables that perception) separate in our analysis.
• tau is a temporal variable. which is actually exactly what the organism needs access to. Knowing how far away an object is or how fast it's moving doesn't tell you anything you need to know in order to control your actions with respect to that object. An organism can use time information to control when to initiate interception/avoidance behaviours.

Figure 1. Diving gannets have to retract their wings at the last possible minute to balance the risks of uncontrolled flight vs impact on the water

Lee & Reddish (1981) discuss a nice example of the last point, the diving gannet (see some videos here and here to get a sense of how high stakes this behavior is). Gannets are birds that dive from great heights at great speeds into the ocean to catch fish. To control their flight they have to have their wings extended for as long as possible; to avoid having those wings ripped off as they enter the water, they need to fold them in in time. Lee & Reddish measured the timing of this wing retraction behavior and found the gannets retract their wings at a constant time-to-contact, rather than at a constant distance from the water. They also found evidence that tau was the information controlling that behavior. This allows them to account for variations in speed that would affect how long it would take them to cross a set distance, and the critical value of TTC is related to how long it takes them to fold their wings.

Weaknesses of tauTau is an optical variable and it does specify time to contact. However, it only does so if the speed is relatively constant and the object is a sphere, among other problems (Tresilian, 1999). Most interception events involve accelerating, non-spherical participants (predators speeding up, rocks accelerating under gravity, etc). Organisms therefore tend not to use tau to perceive time-to-contact because of this limitation; with experience they learn that using it to stand in for TTC only works some of the time and this makes it not that useful.This is not a flaw in the ecological, information approach. Turvey, Shaw, Reed and Mace (1981) spelled out the law based account of how an information variable might be able to specify a world variable. One key fact about laws is that they have a finite scope. That is, they only hold for a limited set of conditions. Many of the laws of physics hold for huge proportions of the universe, but there are well known examples where even these laws 'break down', e.g. in a black hole. The ecological laws that govern how dynamical variables are projected into light also have a scope. Their scope tends to be less universal but are often sufficently wide that they cover life on Earth. The law that makes tau specify time-to-contact just happens to have quite a limited scope, and this means it's not the kind of thing that's useful in a sufficiently large number of occasions to get used by many organisms. This is a weakness of tau as information, but it's a nice example of the general principle of scope.

Summary

Tau is a nice example of the kind of thing information is, but because of it's limited scope it's not an information variable organisms typically rely in. It demonstrates all of the key points about information and specification and scope, and it will always remain a useful example.Further ReadingLee, D. N., & Reddish, P. E. (1981). Plummeting gannets: a paradigm of ecological optics. Nature, 293(5830), 293-294.
Regan, D., & Hamstra, S. J. (1993). Dissociation of discrimination thresholds for time to contact and for rate of angular expansion. Vision Research, 33(4), 447-462.Tresilian, J. R. (1999). Visually timed action: time-out for ‘tau’?. Trends in Cognitive Sciences, 3(8), 301-310.