**7.1 A family of biases**

Our description is intentionally limited to 3D slant in manual reaching space because it is fairly clear that the underfoot haptic perception of ramp orientation, for example, follows a rather steeper function than the one for manually reachable surfaces (Hajnal et al., 2011). The shape of that function has only been explored over a limited range, however. Similarly, the bias function for the perceived orientation of palm boards (Bhalla & Proffitt, 1999) has been shown to differ (especially at steeper orientations) from the haptic perception of stable surfaces (Durgin, Li & Hajnal, 2010). There seems to be some continuity between the nearspace bias function and biases shown in hill perception, once distance is taken into account. That is, Li and Durgin (2010) argue that there is a perceptual gain of about 1.5 in the lower range of slants at all distances they tested, but a shift in the overall intercept. Durgin and Li (2011a) have argued that the 1.5 gain also applies to perceived gaze declination in the relevant range of declinations (i.e. out to about 45°).

With so many similar bias functions developed by recording verbal estimates of slant it is natural to wonder whether the bias might actually be in the numeric production system, but three important facts argue against this. First, non-numeric horizontal/vertical bisection tasks seem to provide converging evidence that a 3D slant or orientation of about 30° appears to be equidistant between horizontal and vertical. This is consistent with the gain of 1.5 for the low range of angles. Second, in the present study, the bias function was very similar in shape when a very different set of numbers was required to produce it as a result

Using real surfaces with a clearly-demarcated axis of haptic exploration, we sought to extend the bisection method used by Durgin, Li and Hajnal (2010) to the haptic domain. Our results are consistent with a close correspondence between visual and haptic spatial biases in the perception of orientation. The haptic results are also quite similar to the average perceived horizontal/vertical bisection point (31°) measured by Durgin and Li (2011a) for perceived gaze declination. In other words, across a variety of modalities (proprioception of gaze declination, visual perception of 3D surface orientation in depth and haptic perception of 3D surface orientation in depth) the perceived bisection point between horizontal and

**7. A descriptive model of the slant bias function for manual reaching space**  The main purpose of our present study has been to clear up an apparent discrepancy in the coding of near-space orientation. That is, for manual reaching space, there had seemed to be a discrepancy between the dynamic touch results of Hajnal et al. (2011) and the static haptic results of Durgin, Li and Hajnal (2010). The present results support the idea that the same bias exists for dynamic touch as has been found for visual slant perception and static haptic slant perception. The bias function found previously for the evaluation of visual slants and for haptic slants experienced by static contact has now been replicated for dynamic touch by fingertip. In combination with recent evidence that the proprioceptively-perceived orientation of a freely-extended hand shows a very similar bias function (Li & Durgin, submitted), the present results seem to point to a stable and systematic bias in the

Our description is intentionally limited to 3D slant in manual reaching space because it is fairly clear that the underfoot haptic perception of ramp orientation, for example, follows a rather steeper function than the one for manually reachable surfaces (Hajnal et al., 2011). The shape of that function has only been explored over a limited range, however. Similarly, the bias function for the perceived orientation of palm boards (Bhalla & Proffitt, 1999) has been shown to differ (especially at steeper orientations) from the haptic perception of stable surfaces (Durgin, Li & Hajnal, 2010). There seems to be some continuity between the nearspace bias function and biases shown in hill perception, once distance is taken into account. That is, Li and Durgin (2010) argue that there is a perceptual gain of about 1.5 in the lower range of slants at all distances they tested, but a shift in the overall intercept. Durgin and Li (2011a) have argued that the 1.5 gain also applies to perceived gaze declination in the

With so many similar bias functions developed by recording verbal estimates of slant it is natural to wonder whether the bias might actually be in the numeric production system, but three important facts argue against this. First, non-numeric horizontal/vertical bisection tasks seem to provide converging evidence that a 3D slant or orientation of about 30° appears to be equidistant between horizontal and vertical. This is consistent with the gain of 1.5 for the low range of angles. Second, in the present study, the bias function was very similar in shape when a very different set of numbers was required to produce it as a result

**6.3 Discussion** 

vertical is very close to 30° from horizontal.

perception of 3D orientation in reachable space.

relevant range of declinations (i.e. out to about 45°).

**7.1 A family of biases** 

of labelling vertical as 0°. Finally, the third important fact that argues against a purely numeric bias is that a very different bias function emerges when 2D orientation (of lines on a plane) is studied using similar numeric methods (Durgin and Li, 2011b). In this case, there is still a bias function that exaggerates deviations from horizontal, but absolute signed error peaks at 30° rather than at 60° as for the 3D function.
