I’m fascinated by the Poggendorff illusion, and this is a new version of it. (Well, it is according to me.  Others would say it’s a different illusion). I’ve prepared it as an image that can be seen in 3D without a viewer, just to make it more vivid, but you don’t have to view it in 3D to see the effect.  (If you do want to view it in 3D, but don’t have the knack, visit this tutorial).

To see what it’s all about, first check out the figure below:

To the upper left is the classic Poggendorff figure:  the oblique lines are objectively aligned, but the right hand one appears shifted just a bit upwards.  About forty years ago, researcher Stanley Coren showed that the effect persists, weakly, when the configuration is reduced to dots, as at upper right.  But now look at the little array of three spheres to the left below.  I reckon this is a new kind of dot (or sphere) Poggendorff illusion.  Imagine joining up the centres of those three spheres, to make a long, thin triangle, pointing a bit up from horizontal.  Remembering we’re looking just at those three lower left spheres, what kind of triangle would you get?  To my eye, very nearly a right angle triangle.  But now look at the lower right three dots, making up a vertical triangle.  To me they present very much an equilateral triangle.  And yet the relative positions of the dots are identical in the two sets, just rotated to vertical at lower right. For the array lower left to look like a right angle, the target sphere must appear shifted upwards, just like the right hand oblique test line in the traditional, blue figure, immediately above.

It would be great to have comments on whether that works for you, or whether you see both lower arrays as equilateral triangle arrangements – illusions like these often do look different to different observers.

Now try viewing the array at the start of the post. It’s just a multiple version of the array of spheres lower left in the second figure. Check out just the three yellow spheres top right, for example.  If you see it how I see it, the position shifts we see here are like the ones we see in classic Poggendorff figures, but none of the explanations advanced for the misalignment seen in the Poggendorff illusion, including Stanley Coren’s dot version, can easily be applied to these new figures.

The explanations focus on the way we mis-judge the angles between the oblique and vertical lines, or the track between the angles. Other explanations assume that our brains attempt to interpret the line figure as an array in depth. Various spatial confusions might then be responsible for the illusion. (I discussed those in an earlier post). It remains conceivable that, even in my sphere figure, very early in the visual pathway we interpret the oblique transit between target and aiming spheres as receding in depth.  So we can’t be sure depth processing has no role in the illusion, even in that figure. But I think it’s more likely a 2D effect.

I wonder whether Poggendorff type misalignments may arise from a quite different process, a subtle conflict very early in the process of making sense of scenes, when we seek to extract an axial skeleton from what we see. I think our brains might do that as part of the contribution of vision to balance.  I have a whole rather specialised website devoted to that speculation.

With so many spheres in the figure at the head of the post, it could be objected that apparent displacements could creep in from accidental configurations of dots acting like the ones in Stanley Coren’s dot arrangement. But that can’t be the case when there are just three dots, in the second figure.  And that looks to me just like the effects in the 3D figure, so I don’t think that the shear number of spheres and shadows is making any difference.

There is a reason for all the spheres in the first figure.  It shows an added paradoxical effect.  Look just at the yellow spheres. The single sphere is at the focus of two pairs of aiming spheres, one upper right aiming downwards and the other middle right aiming upwards. The single target sphere appears at the same time shifted downwards from the upper aiming pair, and upwards from the lower one. That would only be possible if the gap between target and aiming spheres was seen as narrower than it is, but that doesn’t seem to happen. So the illusion is paradoxical. The paradox is repeated with all four single target spheres in the figure, and can also be achieved with full Poggendorff figures, as below: