On another run, the participant may be asked to carry out a different task and instead distinguish subtly different lengths of the the vertical line. Again, this would require sensory+motivational stored contexts that were very close to one another but now separated by a small difference in length. Now consider what happens when the participant is in the middle of a run of the vernier task but the experiment throws in a 'catch' trial in which the stimulus is vertical (i.e. the vernier shift is zero on this trial) but the length is slightly greater than normal and, in fact, is longer to the extent that this would be considered a relatively 'easy' trial if the participant's task had been to detect a length change. It is quite likely that the participant would not notice any change in length of the line on this trail and would instead perceive the line to have a small vernier shift to the left or right depending on the noise in this trial. One way to describe this behaviour is to say that the participant was attending to the vernier shift in the stimulus rather than length on this trial. Another is the say that the sensory+motivational context on this catch trial falls within a region that does not raise any alarms about the stimulus having changed ('usual length line') but it falls to one side of the boundary between 'left' and 'right' vernier shift contexts. If the task had been different (a length-discrimination task), the sensory+motivational context would have been in a quite different part of sensory+motivational space with a different set of boundaries and then the same stimulus would have been recognised as an unusually long line and a catch trial of an 'easy' vernier shift might have been ignored. Of course, if the cue (such as length) on the catch trial is large enough then the participant will notice. This corresponds to the flanking Voronoi cell in the diagram either side of the 'usual length line' stored context.
The important point in this example is that there is a one-to-one relationship between (i) the different perceptions attributed to the participant See Discussion, (ii) the Voronoi cell in which the sensory+motivational context falls and (iii) in this case (being a forced-choice experiment), the button the participant presses. The argument here, which no doubt will be disputed, is that this one-to-one relationship is sufficient to explain the participant's perception.
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[add figure of cells for vernier shift and length for different tasks]