In case it helps stimulate discussion, here are some comments that have been made about the results reported in the paper.

The results can be criticised on grounds of novelty and generality...
"Novelty because Glennerster et al. already showed in 2006 that objects whose parallax alone puts them 4 times farther or closer seem to be at the same distance. This is a clear sign that spatial relations are extremely perturbed by the dissociation between static depth cues and parallax. In this context, the new finding hardly seems surprising. Generality because the comparison has to be performed across the environment size change to demonstrate intransitivity, and therefore seems to depend on the dissociation between static and parallax cues. Thus, intransitivity is not demonstrated under ordinary circumstances."

As we point out in the paper, intransitivity could not be demonstrated under 'ordinary circumstances'. Both models we discuss would predict correct performance in this case. This comment fails to address the issue of the participant's perception. Participants are not aware of any difference between the trials in which the room remains stable ('ordinary circumstances') and those in which it changes size. The generality we appeal to applies to the perception of a stable room and the representation of it that the participant generates (under all conditions). The novelty of this paper lies in the rigorous demonstration of intransitivity. Some readers of earlier papers on the expanding room had assumed that a distorted representation might explain participant's biases.

Below is a thoughtful criticism. It suggests that the perceptual coordinates of an object (eg square C) might vary depending on whether it was viewed as a comparison or a reference object, even though the viewing conditions during the interval in which it was visible were identical.

"..the important point is that you are testing people's perceptions. Here the fact that participants did not notice the change in size of the room is important. However, I do wonder if the fact that, despite this, observers were using the information that they were ignoring (in not noticing that the room had expanded) complicates the interpretation of the results. Adopting the terminology from the authors' previous publication (Svarverud et al, 2010) we can consider two sources of information about the relative distance of the targets, physical and texture-based. When the room expands, these provide very different answers. This might be important because results are presented in terms of physical distances, whereas relative depth judgements combine physical and texture-based information, with weightings that depend on the viewing conditions. Specifically, the weightings depend on whether objects are near the wall, or the centre of the room, which gives rise to the differences in biases reported. This might be a concern because relative weightings could change between Row I and Row II. Although C is in both cases near the wall, in row I A is in the centre of the room, which might affect weightings even in the other interval. Could it then be that the perceived distance of C in row II is different from the perceived distance of C in row I? Not if all cues provide unbiased information, but it is a possibility if there are any biases, and if the weights change between conditions. If so, then it might not follow that Aref and Dc1 have the same apparent distance. The way I have phrased this suggests an interpretation in terms of biases away from the ground truth. The important issue for this example however is, can we be sure that the apparent distance of C is the same in rows I and II?"

A good test of this hypothesis would be to include some trials in the stable room (row I) in which the reference and comparison location were swapped round, with the reference near the wall and the comparison near the middle of the room. If the comment above is correct, ie that the perceived distance of C in interval 1 of row II differs from the perceived distance of C in interval 2 of row I, then there should be a bias in these 'swapped' trials large enough to account for the results we observe in D_C. I must say that I would eat my hat if that could be shown, but it is an ingenious criticism.

I suspect that the commentator means something a bit different. One could imagine that after both interval 1 and 2 are over, taking all things into consideration, you go back and assign coordinates to the objects in both intervals. This really must be ruled out of court. Aside from being impossible to distinguish from the pairwise comparison model we describe, it has little justification for being part of a 3D reconstruction model with coordinates attached to objects. The first interval and the ISI were quite long (at least 3s). It is not reasonable to assume that the brain waits around till a bit later to decide what coordinate to assign to the objects in the room in the first interval.

The comment continues:
"There may be other ways to frame these concerns, with different examples, but the underlying worry is that the relative and absolute information are inconsistent, and differently weighted depending on viewing conditions. It is not then straightforward to go from physical distance to perceptual distance. To my mind these worries need to be pitted against the phenomenal stability, since these other sources of information do influence perceived distance, which is the perceptual attribute under consideration."

It is quite hard to appreciate the force of this last comment. "Not straightforward" for whom? The viewer finds the task indistinguishably easy to carry out the task on trials with or without an expansion, so the brain must produce a perceived distance in each case. The onus should be on people who think that the brain produces a single set of coordinates for the objects to say what these coordinates are (even if some coordinates have a larger variance than others). The attempt above to suggest that there is not a single set of coordinates for the objects (eg object C) is another possible route but I don't find it convincing.


Two less thoughtful comments:
"The critical finding is that although participants can make quite accurate judgments in a stable room, they are biased in their relative distance judgments when the room expands between intervals. That in itself is not surprising and this is not that distinct from what the authors have demonstrated previously. The case in this paper is based upon the difference between conditions II and III where different reference locations were used. Much of the paper then hinges on comparing the difference, but I regret that I didn't find this particularly convincing. In both cases the bias is monotonic, there is no "reversal of the effect" and the demonstration that participants make larger errors (in the same direction) in one condition vs another doesn't really have the impact to radically change our thinking about visual space. So when I got to the discussion I really wasn't swayed that this [is an important finding]. There isn't really a new (predictive) model for how humans generate their estimates."

and

"Anyone who has read some of the literature on distance perception knows that it is kind of a mess and that distance perception is generally far from veridical. What this study shows is that an object is not perceived to be at the same distance when the virtual room expands, unbeknownst to the subject. Given that the expanding room changes the distribution of binocular disparities and motion parallax in the scene surrounding the object, why is it surprising that the perceived distance of the object changes (given that we already know that the perceived distance of an object is not simply determined by it's disparity and motion parallax)? We already know from many studies that perceived distance is often inaccurate and can depend on various context effects. To me, this study is essentially just demonstrating a context effect on distance perception. In addition, one could consider how priors might come into play. Let's say, just for illustration, that subjects have a prior to perceive an object near the center of the room. If the room then expands 4-fold, the prior will pull the object toward a larger distance away from the subject. I'm not saying that this happens, per se, only that there can be many factors at play here. Thus, while this study is another demonstration that distance perception is unreliable, it really fails to teach us any new mechanisms or laws that govern how and why distance perception is inaccurate. Sure, intransitivity sounds cool. But, in reality, the prior probability that the room you are in will expand suddenly by 4-fold is essentially zero. So it would make sense that the visual system would be willing to tolerate intransitivity as a consequence of faulty distance perception under such conditions. "

Both comments simply note that the results can be predicted from earlier findings (particularly those on the expanding room) without engaging in the debate about whether a 3D reconstruction model could account for the data.