I’ve not been posting much because I’ve been struggling with a mammoth revision of my technical site on the Poggendorff illusion.  But now that’s done, here’s a post on another Poggendorff puzzle.

In earlier posts I’ve shown examples of competition between illusions, and included a demo of a paradox when the Poggendorff and Muller-Lyer illusions go head to head.  Bottom left above I’ve shown that last demo again – not so pretty, but I think a clearer demo.  Thanks to the Muller-Lyer illusion the outward pointing arrowheads appear closer together than the inward pointing ones, when objectively the arrow points are identical distances apart (note the reference lines in the middle of the figure).  But at the same time, at the left end of the figure, the arms of the same arrowheads, objectively aligned, would have had to move further apart, not nearer, in order to produce the effect of misalignment that we see.  So the two illusions seem to coexist in total opposition to one another, without a qualm. I’ve repeated the arrowheads to the lower right, to show that, at least as I see it, their appearance is just the same as when embedded in the Poggendorff figure.

But then the top figures show that both these illusions can be inhibited, when set in competition with other illusions.  Top left the Poggendorff illusion is normal to the left, but cancelled to the right (or is it even reversed?) when the test arms are illusorily rotated by the addition of some Cafe Wall characteristics. And top right, there’s much less difference (again to my eye) between the illusorily lengthened and shortened elements of the Muller Lyer illusion when we see them in the context of a Ponzo illusion (a scene in apparent depth) than as we see them isolated below the Ponzo scene.  In the Ponzo scene, the size-constancy effect is increasing the size of the smaller Muller-Lyer element.

So why are the Poggendorff and Muller-Lyer illusions sometimes inhibited when set in competition with other illusions, when at other times they co-exist with rivals in glorious paradox?  Any ideas?

Here are a couple more variants of the Poggendorff illusion (mog, or moggy, by the way, is a term of endearment for a cat in UK English, but I’m not sure it’ll be familiar if your background is in American English). The symmetry axes of the dog and cat heads are objectively aligned, but to my eye appear displaced in much the way that the (objectively aligned) test line appears to be in classic versions of the illusion (as in pale blue, to the left).

I’ve added the blobs to the dog version, and the pigeons to the cat figure, because I have the impression that they make the illusion a little stronger. However, I haven’t tested that experimentally with these figures.  It’s also interesting to try deleting the images progressively, to see how much can be deleted before the illusion vanishes. Maybe there are conventional Poggendorff figure elements embedded in these figures in a way I haven’t realised.

For example, it’s well established that the illusion can arise when the usual line elements are reduced just to dots, (the dot version that might apply here is Stanley Coren’s – scroll down that link to view it). It would be possible to selectively erase the figures here until just dots were left. But reduced to dots the illusion is very weak, and here it looks quite robust to me.

I think it is the symmetry axes that are taking the place of the usual test lines here.  For me, that makes it that much more likely that the illusion arises because of two dimensional pattern elements.  (However, many specialists don’t agree, and attribute the illusion to attempts by the brain to interpret Poggendorff figures as arrays of lines in depth).

I have a special interest in this illusion, and you’ll find stacks more on it by clicking on the Poggendorff illusion category, in the categories list to the right.  I have ideas about what I think might be going on – but actually, I don’t rate them all that highly. Sometimes in science, when a problem resists progress for a very long time, (over a century in the case of this illusion), so that there are all sorts of ingenious competing explanations, it’s a sign that something is going on that nobody’s even begun to imagine.  I think that could well be the case with Poggendorff.

Back in 1987 James Walker and Matthew Shank in the university of Missouri were doing a study of the Bourdon illusion. In some figures they devised for comparisons in their study they noticed a new effect, quite unrelated to their study. The figure upper left is a version of their chance discovery. The centre line is objectively horizontal, but can seem to rise slightly to the right. Walker and Shank tried the effect experimentally, and found it was indeed seen by a majority, but not all of their observers.  (Note for techies:  For a PDF of their article, input 1987 as year, the authors’ names plus Bourdon and contours as keywords on the Psychonomic Society search site).

The effect seems related to the Tolanski illusion, lower left: the gaps in the sloping lines are exactly level with one another, but the right hand one looks a touch higher. Generally, our judgments of horizontal or vertical across empty space between lines with a pronounced slope seem to get just a little rotated in the direction of the slope. The effect is even stronger for me with curved lines (as bottom right) than with straight ones. I’ve even found it in informal experiments with a number of observers as upper right, when vertically positioned target dots appear rotated towards the slope of blurred or broken slanting edges in which they are embedded.

But in my version of the figure, upper left, we can also see the Poggendorff effect at work, (according to me at least). Look at the two outer, nearly horizontal arms. They are exactly aligned, but to my eye the right hand one looks higher than the left hand one. That’s just the result we would get if we deleted the middle three pairs of lines, to end up with opposed obtuse angles, in what is sometimes called an obtuse angle Poggendorff figure.

Do the Tolanski and Pogendorff illusions share a mechanism, or do we see in the top left figure both the rotation of the horizontal line, and the misalignment of the outer arms, arising by chance from different processes in the brain? We can’t yet be sure, but I reckon the same processes are most probably at work, and are to do with projecting orientation and alignment judgments across figures with powerfully competing axial emphasis. The Tolanski and Poggendorff figures present a sort of reciprocal pairing: with Tolanski figures judgments of vertical or horizontal are compromised in a figure with a dominant slant, whereas in classic versions of the Poggendorff illusion judgments of oblique alignment are rotated between vertical or horizontal lines.

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.

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Here are three rather subtle illusions, each showing bent lines. In Bourdon’s illusion, to the left, the straight left hand edge looks bent. In Humphrey’s figure, centre, the straight, loose line touching the corner of the cube looks bent. And in the figure to the right, the straight line interrupted by the corner looks bent. I don’t think we really understand any of these illusions, and they are not very dramatic, so you don’t see them often. When someone does puzzle them out, for sure they’ll be a key to subtle ways the brain works. There’s probably a different explanation for each. For example, both the left and middle figures show a bent line that is the backbone of two triangles meeting at a point, so you might think, hello hello, we’re getting somewhere. But then you notice that the lines bend in different directions in relation to the triangles each illusion.

If you like to tangle with the technicalities, there are learned studies of the Bourdon illusion and the corner figure, though unfortunately, you’ll only get an abstract of the articles on those links, unless you are in a university library where they subscribe to the journals. And you won’t find much on Humphrey’s figure anyway, it’s seriously obscure.

Here’s a bit more on the corner figure  ….

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This is a stereo picture-pair, but you can see what’s happening here without having to view the images in 3D if you prefer.  However,  if you’ve not got the knack, and would like to practice on this post, here’s how.  Hold up a pen about in the middle, between the two pictures, and about five inches from your eyes (careful!).  If you now try to focus on the tip of the pen, you’ll notice that the blurry image of the figure has doubled.  Now move the pen-tip away from your eyes, and notice that the two blurry middle images of the figure are beginning to overlap.  Once they overlap (probably when the pen-tip is something like ten inches away from your face), see if you can get them to overlap exactly, and then come into focus.  If that doesn’t work, try this great tutorial on another site. Or try our earlier post about stereo picture pairs.

If you’ve got it, you should see the parallel vertical bars and their attachments floating in front of a surface with their shadows thrown on it. You’ll see the same if you view the image normally, but not with the illusion of 3D.  So what’s going on?

It’s a much stronger version of some paradoxical effects I showed in an earlier post.  The tips of the arrowheads are all objectively exactly the same distance apart, as indicated by the horizontal lines aligned with them in between the vertical bars.  But that’s not how they appear if you look at the arrowheads:  the inward pointing arrows look much further apart than the outward pointing ones.  (That’s the Mueller-Lyer illusion).  But now check out the lower, coloured arrowheads.  The coloured arms that contact the vertical bars are objectively aligned, but appear not to be – the upper arm in each case seems shifted a bit upward, and the lower arm a bit downward.  (That’s the Poggendorff illusion).  For the arms to appear out of alignment like that, you’d imagine the arrowheads must move further apart.  But that’s exactly the opposite of what the Mueller-Lyer illusion is making them seem to do.

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This is Morinaga’s paradox – two illusions in one, but two illusions that contradict one another. First note the vertical alignment of the arrow points. Don’t the tips of the inward pointing arrowheads, top and bottom, appear to be located just a little further inwards than the tips of the middle, outward pointing arrowheads? That could only be right if the horizontal space between the tips of the (top and bottom) inward pointing arrowheads was slightly less than the space between the tips of the (middle) outward pointing ones. But that’s not how it looks. The inward pointing arrowheads look further apart than the outward pointing ones.

In reality both judgments, of vertical alignment and of the horizontal gaps, are illusions.  The tips of the arrows are perfectly aligned vertically, and the horizontal gaps between the three sets of arrowheads are all exactly the same. That last effect is a version of the Muller-Lyer illusion.  

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One of the most obstinately puzzling illusions is Poggendorff’s, in which a slanting line interrupted by a gap no longer looks aligned. For over a century specialists have been unable even to agree whether it arises from 2D properties of the image, or as a result of attempts by the brain to interpret the configuration as 3D. Papers written a hundred years ago treat the problem in very much the same terms as we do today. I’m betting on 2D (I argue for that on another, website devoted to the Poggendorff illusion). It’s not likely my speculations are spot on, and they may well not even be in the right direction. But read on here if you’d like to see demonstrations that show why I don’t think depth processing can be the answer.

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