Tau and Kappa effects in physical space: the case of audition

Abstract

The organization of spatio-temporal information in an auditory memory task was studied in two experiments. Stimuli consisted of four different configurations of eight sequentially presented beeps. In two configurations, the stimuli were space–time congruent, with (constant or variable) inter-stimulus distances corresponding to (constant or variable) inter-stimulus time intervals. In the other two configurations, the stimuli were space–time incongruent, with (constant or variable) inter-stimulus distances not corresponding to (variable or constant) inter-stimulus time intervals. After a learning phase consisting of 20 presentations of the target configuration, participants reproduced the spatial (Experiment 1) or temporal (Experiment 2) characteristics of the target 60 times in succession without re-examining the target configuration. Accuracy (with respect to the target) and variability (between responses) were found to evolve independently. In the incongruent space–time conditions, effects of variable inter-stimulus time intervals or distances on the reproduction of, respectively, constant distances (Tau effect) or constant time intervals (Kappa effect) were observed, while the reverse was not the case. Thus, dimensional interference occurred when the dimension to be ignored was variable. The results are discussed in the light of the distinction between properties of the stabilized mental image and the process of stabilization.

Appendices

Appendix 1

To replicate an invisible motion in the horizontal plane, software developed at the Movement and Perception Laboratory (Centre National de la Recherche Scientifique) uses the Inverse Distance Clamped Model, extended to guarantee that for distances below REFERENCE_DISTANCE, gain is clamped. This mode is equivalent to the IASIG I3DL2 (and DS3D) distance model.

$$\begin{aligned} {\text{dist}} =& {\text{max}}({\text{dist}},{\text{REFERENCE}}\_{\text{DISTANCE}}); \\ {\text{dist}} =& {\text{min}}({\text{dist}},{\text{MAX}}\_{\text{DISTANCE}}); \\ {\text{G}}\_{\text{dB}} =& {\text{GAIN}} - 20*\log 10(1 + {\text{ROLLOFF}}\_{\text{FACTOR}}*({\text{dist}} - {\text{REFERENCE}}\_{\text{DISTANCE}}) / {\text{REFERENCE}}\_{\text{DISTANCE}}); \\ {\text{G}}\_{\text{dB}} =& {\text{min}}({\text{G}}\_{\text{dB}},{\text{MAX}}\_{\text{GAIN}}); \\ {\text{G}}\_{\text{dB}} =& {\text{max}}({\text{G}}\_{\text{dB}},{\text{MIN}}\_{\text{GAIN}});\\ \end{aligned}$$

The Inverse Distance Clamped Model is an extension of the well-known OpenAL sound system.

OpenAL website: http://www.openal.org

Appendix 2

The correction of the gap between the first four and the last four dots was performed for each reproduced configuration. The positions of the dots are denoted p ₁, p ₂, ..., p ₈, while the distances between adjacent pairs of dots are denoted d ₁, d ₂, ... d ₇. Two standard deviations were computed. The first, SD1, was computed over all distances. The second, SD2, was computed over d ₁, d ₂, d ₃, d ₅, d ₆, and d ₇, i.e., with the size of the central gap removed from the calculation. The correction of the gap was accomplished by repositioning the dots so as to make SD2 approximately equal to SD1. To do so, we first computed M1, the mean of d ₁, d ₂, and d ₃, and M2, the mean of d ₅, d ₆, and d ₇. The new positions of the dots were computed as follows: p ₁=abs (p ₁−0.25 M1); p ₂=abs (p ₂−0.125 M1); p ₃=p ₃; p ₄=abs (p ₄+0.125 M1); p ₅=abs (p ₅−0.125 M2); p ₆=p ₆; p ₇=abs (p ₇+0.125 M2); and p ₈=abs (p ₈+0.25 M2).