Proffitt, Stefanucci, Banton, and Epstein (2003) reported a set of studies showing that the perceived distance to a target is influenced by the effort required to walk to its location. Hutchison and Loomis (H&L) reported an experiment that failed to find a significant influence of effort on indices of apparent distance. There were numerous important differences between the design and methods of H&L's study and those of Proffitt et al. Moreover, there are important theoretical reasons to believe that these differences were responsible for the different results. The theoretical motivation of H&L's studies was also brought into question.

While acknowledging that their design and methods were different from the original Proffitt, Stefanucci, Banton, and Epstein (2003) study, Hutchison and Loomis (H&L) continue to argue that their findings qualify our account of energetic influences on distance perception. This reply provides a brief and focused discussion of the methodological differences between their study and ours and why these differences were likely responsible for the different results. It is also argued that the measures employed by H&L are assessments of apparent location, not apparent distance.

Emmert's law and the size-distance invariance hypothesis have been said to be formally equivalent, provided that Emmert's law means that the perceived size of an afterimage is proportional to the perceived distance of the projected surface of the afterimage. However, there have been very few studies that have attempted to verify this formal equivalence empirically. We measured both the perceived size and distance of afterimages and real objects with the same proximal size. Nineteen participants projected afterimages of 1 deg in visual angle on the wall located at distances of 1 to 23 meters from the participants. They also observed real objects, disc-shaped and made from a sheet of Styrofoam board, with the same proximal size as that of the afterimages, which were located at the same physical distances as those of the wall on which the afterimages were projected. Each participant reproduced the apparent sizes of the afterimages and real objects using the reproduction method and estimated the apparent distances using the magnitude estimation method. When the mean apparent sizes of the afterimages and real objects, represented as a function of apparent distance, were fitted to a linear function, the slopes for the afterimages and real objects did not differ significantly. These results are interpreted as evidence for the formal equivalence of Emmert's law and the size-distance invariance hypothesis.

In a series of recent studies, Proffitt and his colleagues have reported that the perceived distance to a target is influenced by the energy expenditure associated with any action, such as walking or throwing, for spanning the distance to the target. In particular, Proffitt, Stefanucci, Banton, and Epstein (2003) reported that wearing a heavy backpack caused verbal reports of distance to increase. We conducted a study to determine whether three responses dependent on perceived distance (verbal report of distance, blind walking, and estimates of object size) are influenced by the backpack manipulation. In two experiments, one involving a between-participants design and the other involving a within-participants design, we found that none of the three responses were influenced by the wearing of a heavy backpack.