Stimuli and results from
Experiment 1. (A) Isotropic visual feedback stimuli. They were isotropic Gaussian blobs with
σblur = 4° × 4° and 24° × 24°. (B) Just-noticeable differences (JNDs) in the visual localization experiment as a function of
σblur. Visual discrimination thresholds increased monotonically from 0.4° to 2.4° as
σblur was increased from 4° to 24°.
y = 0.16*
x − 0.085,
R2 = 0.9821. (C) Average adaptation profiles for isotropic feedback stimulus. On the first trial, subjects had no information about the size and the direction of the step, so initial errors were roughly equal to the step. Subjects gradually adjusted their visuomotor mapping estimate, X ^
t, so that the observed errors approached zero. Light blue represents the data when
σblur = 24° × 24° and green represents the data when
σblur = 4° × 4°. The upper panel plots horizontal error (in degrees) against trial number and the lower panel vertical error (also in degrees) against trial number across trials. One degree corresponds to ∼2.5 mm on the tablet, so the shift of 8.2 deg corresponds to ∼2 cm on the tablet. The line segments represent the data, and the smooth curves are the averages of the best-fitting exponentials (
Equation 6). Exponentials and power laws, each with two free parameters, were fit to all individual subject data (exponential:
Et = (
b +
C)
e− λ( t − 1) +
b; power:
Et = (
b +
C)
t− λ +
b). Exponentials provided a better fit 78% of the time (
p < 1.7*10
−27; sign test,
n = 384 (24 subjects × 8 conditions [4° × 4°, 8° × 8°, 12° × 12°, 16° × 16°, 20° × 20°, 24° × 24°, 24° × 4°, and 4° × 24°] × 2 dimensions [
x, y])). (D) Histogram of all vertical and horizontal adaptation rates for subjects in which
σblur was 4° (green) or 24° (light blue) in the respective direction. The histogram includes data from conditions with 4° × 4°, 4° × 24°, 24° × 4°, and 24° × 24° feedback. Rates were significantly slower in the large blur condition (
t test,
p < .0001;
n = 96). (E) Average time constants as a function of average visual JND for each condition of the experiment. Exponential fits were performed along the diagonal (
C = 8.2°). This includes the two conditions with anisotropic blobs plotted in
Figure 4 and four additional conditions with isotropic blobs (8° × 8°, 12° × 12°, 16° × 16°, and 20° × 20°). Stimuli and data from these conditions are shown in
Figure 1d and
Supplementary Figure 1. Error bars indicate one standard deviation. The thick black line (actually a curve) shows the predicted change of adaptation rate with feedback uncertainty for σ ^
x = 0.08°. The thin black lines are the 95% confidence intervals (
R2 = 0.61). As σ ^
x changes, the
y-intercept of the Kalman filter prediction changes, but the slope is effectively unchanged.