Before we end this article, let's use the principle: The smaller portion of the visual field an object occupies, the smaller the object appears to be, and vice versa, to explain two more illusions. The first one is called the Occlusion illusion, in which a figure bounded by an occluding edge looks larger than the same figure not bounded by an occluder, as shown in the figure

on the left below. The most acceptable explanation, like all the other size illusion figures, is that it is caused by perspective. The gray bar seems to be in front of a solid black circle; hence the semicircle we can see is behind the gray bar and it must be farther away from the viewer in comparison to the semicircle which is not blocked by anything. According to the perspective hypothesis the faraway object looks larger than a nearer object of the same retinal size. The distance and perspective are the factors that we have already dismissed as contributing to the size illusions with reasons listed above. If the above principle is correct, all we need to do is to expand the visual field (or the sub-visual field to be specific) to decrease the portion of the semicircle in the visual field in order to make it appear smaller. I think that I have achieved the expected result by lengthening the gray bar to make the semicircle appear smaller, as shown in the figure on the right below. Lengthening the gray vertical bar for the occlusion illusion is the equivalent of widening the road for the lower red bar for the famous Ponzo illusion picture on the right. As a result, the sub-visual field around the objects has been expanded. At this point, someone might ask why the semicircle that is not occluded by anything looks small; in fact it looks even smaller than the semicircle occluded by the lengthened bar. I think that it looks smaller because our brain treats the whole page, from the top to the bottom, on the left side of the semicircle is blocking it. Thus, we have a much larger sub-visual field for the unbounded semicircle so that it appears to be much smaller according to the principle. As a matter of fact, this understanding of the unbounded semicircle gave me the idea of lengthening the vertical gray bar to expand the visual field in the first place.

As I said earlier, I am going to use the principle: The smaller portion of the visual field an object occupies, the smaller the object appears to be, and vice versa, to explain the illusion. The upper figure and the lower figure must be enclosed in a differently sized sub-visual fields. As shown in the diagram on the left below, both the upper figure and the lower figure are enclosed in the extended curve lines of the upper figure's curved sides. I also tried to extend the curved sides of the lower figure; but the extended curve lines of the lower figure do not have any illusory effect on the figures. Therefore, I have only kept the extended curve lines from the upper figure. Now let's look at the diagram on the right below. I have separated the two figures with their surrounding extended lines. Thus, the figures are inside their separate sub-visual fields. I have placed the lower figure on top and the upper figure at bottom in the diagram on the right below, in an attempt to eliminate the effect of a longer side facing a shorter side as in the original illusion. As predicted by the principle, the top figure looks bigger because it is in a smaller visual field than the bottom figure. Some readers might not buy my explanation of the Jastrow illusion and might think that it is far-fetched. The only way I can convince them is to urge them to take a look at the magnitudes of the size difference between the two figures in the diagram on the right below and compare with the magnitudes of the size difference in the original illusion figure. The explanation should be deemed credible if there is a close match between them. It is up to you to decide.

I have used the principle that the smaller portion of the visual field an object occupies, the smaller the object appears to be, and vice versa to explain some of the size illusions which are depicted usually by the 2-D drawings or pictures. You can also test this principle in the real world. Join your two hands with curved fingers to make a large tube; then view an object through this hand tube with one eye and the other eye closed. Pay close attention to the edges of the hand tube while viewing the object, and you will find that the object appears smaller than before. Now make a smaller tube by cupping one hand and view the same object through this cupped hand. You will find that the object appears to become larger than when viewed through the larger hand tube. Thus, the sub-visual field volumes created by our own hands in the real world can make the real objects appear larger or smaller following the above principle.

I have discussed some of the most important size illusions in this article, and we have gained a quite different outlook from the conventional wisdom. Some of the issues are far-reaching and could be even fundamental to our understanding of the perception, our mind, and perhaps the world. Also, some of these issues are very complicated, with which you probably feel that I haven't dealt thoroughly. You are right that it is impossible for an article of this length to discuss all these important issues adequately. Therefore, I am going to further discuss these issues in the next articles. Finally, all the discussions will lead us to the most important size illusion, the Moon illusion. This article is just the beginning. We have a long way to go!

The Delboeuf, Ponzo and More Illusions

Other Size Illusions

References

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