On 2016 Apr 05, Lydia Maniatis commented:

With respect to illusion and the theoretical explanation, Tyler addresses only one relevant factor, even though, as I explain in my article (and perhaps more clearly in a related chapter in the Oxford Compendium of Visual Illusions (in press for the past few years)), that factor is not enough to explain this new variant. He states that "Figure 3 also includes a verification that the primary illusion is not due to the orientation [of the] parallelogram of the top surfaces. The upper figure is a block-rotated version of the right- hand block with its surface parallelogram aligned with that of the left-hand block, showing that the illusion persists even in the aligned orientation. This result verifies that the illusion is due to the perspective context of the other two sides."

In fact, the illusion persists but also changes, a fact that as I have analyzed in detail implies that orientation as well as the 2D structure ("perspective context" is a meaningless term - try defining it) of the figure and its consequent 3D interpretation are implicated in the effect.

Another aspect of the original illusion that Tyler refers to as paradoxical are the apparent downward slopes of the tabletops, one left, one right. It isn't paradoxical. In the case, for example, in which the sideview of the structure is on the left, the horizontals must be receding from us to some degree. Receding lines rise in the visual field. In order to reconcile the fact that a line that is horizontal on the retinal is receding in space, we must also infer that it is downward sloping in space. When the left side is visible, the downward slope will be to the right, and vice versa.

On 2016 Apr 01, Lydia Maniatis commented:

The illusion presented in Figure 3 (without citation) was presented by me here:

http://illusionoftheyear.com/2009/05/another-turn-a-variant-on-the-shepard-tabletop-illusion/

reported on here: https://www.newscientist.com/round-up/best-new-visual-illusions/

and discussed theoretically here: http://www.ncbi.nlm.nih.gov/pubmed/21125946

Also, Tyler suggests he has discovered a new effect - “a paradoxical distortion of the length of the rear legs [i.e. the back legs appear shorter than the front legs] and proposes that an “interpretation in terms of surfaces can account for the difference in treatment of the filled-in versus open forms in the Chinese painting from more than 1000 years ago.”

However, he has overlooked the fact that we are in effect dealing with a case of the Muller-Lyer illusion, and that this therefore represents a confound with respect to the alternative explanation offered.

On 2016 Apr 01, Lydia Maniatis commented:

The illusion presented in Figure 3 (without citation) was presented by me here:

http://illusionoftheyear.com/2009/05/another-turn-a-variant-on-the-shepard-tabletop-illusion/

reported on here: https://www.newscientist.com/round-up/best-new-visual-illusions/

and discussed theoretically here: http://www.ncbi.nlm.nih.gov/pubmed/21125946

Also, Tyler suggests he has discovered a new effect - “a paradoxical distortion of the length of the rear legs [i.e. the back legs appear shorter than the front legs] and proposes that an “interpretation in terms of surfaces can account for the difference in treatment of the filled-in versus open forms in the Chinese painting from more than 1000 years ago.”

However, he has overlooked the fact that we are in effect dealing with a case of the Muller-Lyer illusion, and that this therefore represents a confound with respect to the alternative explanation offered.

On 2016 Apr 05, Lydia Maniatis commented:

With respect to illusion and the theoretical explanation, Tyler addresses only one relevant factor, even though, as I explain in my article (and perhaps more clearly in a related chapter in the Oxford Compendium of Visual Illusions (in press for the past few years)), that factor is not enough to explain this new variant. He states that "Figure 3 also includes a verification that the primary illusion is not due to the orientation [of the] parallelogram of the top surfaces. The upper figure is a block-rotated version of the right- hand block with its surface parallelogram aligned with that of the left-hand block, showing that the illusion persists even in the aligned orientation. This result verifies that the illusion is due to the perspective context of the other two sides."

In fact, the illusion persists but also changes, a fact that as I have analyzed in detail implies that orientation as well as the 2D structure ("perspective context" is a meaningless term - try defining it) of the figure and its consequent 3D interpretation are implicated in the effect.

Another aspect of the original illusion that Tyler refers to as paradoxical are the apparent downward slopes of the tabletops, one left, one right. It isn't paradoxical. In the case, for example, in which the sideview of the structure is on the left, the horizontals must be receding from us to some degree. Receding lines rise in the visual field. In order to reconcile the fact that a line that is horizontal on the retinal is receding in space, we must also infer that it is downward sloping in space. When the left side is visible, the downward slope will be to the right, and vice versa.