Nonlinear visuomotor transformations: Locus and modularity

Abstract

Participants in two experiments moved a mouse-like device to the right to move a cursor on a computer screen to a target position. The cursor was invisible during motion but reappeared at the end of each movement. The relationship between the amplitudes of the cursor movement and the mouse movement was exponential in Experiment 1 and logarithmic in Experiment 2 for two groups of participants, while it was linear for the control groups in both experiments. The results of both experiments indicate that participants adjusted well to the external transformation by developing an internal model that approximated the inverse of the external transformation. We introduce a method to determine the locus of the internal model. It indicates that the internal model works at a processing level that either preceded specification of movement amplitude, or had become part of movement amplitude specification. Limited awareness of the nonlinear mouse–cursor relationship and the fact that a working-memory task had little effect on performance suggest that the internal model is modular and not dependent on high-level cognitive processes.

We would like to thank Petra Wallmeyer, Barbara Herbst, Matthias Manka, Dirk Knol, and Wolfhard Klein for assistance in running and analysing the experiments, and Dirk Jäger, Matthias Manka, and Andreas Volgmann for writing and modifying the experimental software. Also, the first author wishes to thank Martina Rieger for the fruitful discussions on these matters during his stay at the Max Planck Institute for Human Cognitive and Brain Sciences, in Leipzig, Germany.

Notes

¹ We speak of amplitudes rather than of positions as there are indications that with display-based movements, these movements are generally specified in terms of amplitudes (e.g., Heuer & Sangals, 1998).

² We used A _C = (A _H − 220)² + 130 for A _H > 230.

³ Linear extrapolation involved A _C = S(A _H − 230) + 230 for A _H > 230 mm. One of these involved slope S being based on the theoretical slope between the 180- and 230-mm amplitudes, S = (230 – 93.7)/50, and the other the theoretical slope S between the 130- and 230-mm amplitudes, S = (230 – 62.2)/100. The third-power extrapolation involved A _C = (A _H – 220)³ – 770 for A _H > 230 mm.

⁴ (a) In the data analyses, we used the time between onset of the (second) amplitude signal and actual onset of the movement, which we call target–response interval or TRI. SOA and TRI are identical when the movement starts exactly at onset of the fourth tone (i.e., the go signal). (b) For our simulation we assume a linear change over SOA as we have no reason to assume a more complex curve. However, to emphasize that this change may well have another form, we drew a nonlinear amplitude change in Figure 1 (upper right frame).