Category Archives: The Poggendorff Illusion

Poggendorff Switch

If the way I see this animation is how most people do, the strength of the Poggendorff illusion can depend on our patterns of fixation when looking at it.  Adding distracting dots to the figure can attract the eye either obliquely along the parallels or at right angles across them.  To my eye, when the oblique track between the acute angles in the figure is labelled with flashing blobs, the strength of the illusion is reduced.  When the track at right angles across the parallels is labelled, effect is maximised.  The effect doesn’t change instantly for me, but settles down after each track has flashed two or three times.  I get the same effect if I switch fixations every second or so between equivalent blobs in still Poggendorff figures. The effect is strongest, as below, when the blobs are in the acute angles when the parallels are vertical, and across parallels when the parallels are horizontal.  So in the figure below, the illusion is not far off equal strength for me in the bottom pair of figures, but looks maybe a bit stronger at top left, and has almost vanished at top right.

If you’d like more on this, plus some additional demos, check out my site devoted to the Poggendorff illusion.

Back-yard Poggendorff

This is another demo to see whether it’s true, as has often been claimed, that the Poggendorff illusion is much weaker when it’s seen in three dimensions.  To my eye, it’s not true:  in this lash-up of bits and pieces in my back yard, the illusion is still strong.  The long rod is straight as it passes behind the plank, but for me it looks just as decidedly misaligned either side of it when seen in 3D as when seen as a 2D photo.

To see the effect in three-dimensions, you’ll have to know how to view stereo picture pairs without a viewer, in what’s called “cross-eyed” mode.  If you don’t yet know that trick, you’ll find a tutorial at

But best to give it a miss if you have any problems with your eyes (apart from just being short sighted or colour blind, like I am) – or if viewing stereo pictures like these turns out to make you feel strange or queezy

Many theorists have suggested that the Poggendorff illusion arises because we try to impose an inappropriate 3D interpretation on a 2D figure, which is the usual form in which the illusion is presented. It’s a very reasonable theory that might work in various ways, but as it happens, I just don’t think it’s true.


When we see the figure presented as a stereo image, as at the head of this post, so the theory goes, the illusion should vanish.

For more detail, see our earlier post on the Poggendorff illusion and depth processing:

There’s another 3-D demo towards the end of that, but with the rod behind the plank in a plane parallel to that of the plank – in other words, not receding from us diagonally into the distance, like the rod in my back yard demo.  In this post, I wanted to check that the receding rod made no difference, and to my eye, it doesn’t, and nor does changing the orientation of the plank. The Poggendorff misalignment does look less in the lower pair, but that’s just because the plank that gets in the way in the lower images is at an angle where it looks much thinner.  It’s well-known that the illusion gets stronger as the gap between the rod segments gets wider.

However, all this does not rule out a role for depth processing in the illusion.  Qin Wang and Masanori Idesawa have shown that when the illusion is presented in 3D with the test arms in front of the inducing parallel, illusion vanishes.  That’s a real challenge for the 2D theories.

Competition and the Poggendorff and Muller-Lyer Illusions


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, thanks to the Poggendorff illusion, 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?

Subtle misjudgments of horizontal and vertical

The Walker Shank, Tolanski and related figures

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.

Dotty Poggy? Or Dotty Me?

Dotty variants on the Poggendorff illusion

Upper left is the classic Poggendorff figure:  the oblique lines are objectively aligned, but the upper one appears shifted just a bit to the left. There are lots of variants on this illusion. For example, about forty years ago, researcher Stanley Coren showed that the effect persists, weakly, when the configuration is reduced to dots, as at upper middle. And top right is another variant, the Poggendorff-Without-Parallels: the misalignment effect persists, weakly, in two objectively aligned segments even without the long parallel inducing lines. Most researchers have found that this last effect is greatest when the test arms are at an angle of around 22 degrees from vertical. An analogous affect shows up when they are rotated the same amount form horizontal.

To my eye, the Poggendorff-Without-Parallels effect even appears when the little test line segments are reduced just to dots, as shown lower left. Imagine joining up each of the three pairs of dots with the isolated dot, so that we end up with three triangles. If we then drop a vertical line from the isolated dot to the middle pair of dots, it will pass through the mid-point in between them, as diagrammed in yellow to the right.  So the middle triangle of dots has sides of equal length, or is equilateral, as the geometers call it, and that’s just how it looks.  No surprises so far.  But now here’s the interesting bit. The two other triangles of dots, rotated respectively clockwise and anti-clockwise from vertical, remain objectively equilateral, but that’s not how I see them.  For me they now look more like right-angles triangles, as diagrammed with yellow lines to the right.  The effect suggests a shift in apparent position of the right hand pair of dots, (rotated anti-clockwise about 22 degrees from vertical), just about equivalent to the shift we seem to see in the Poggendorff-Without-Parallels, shown above it at top right.  There’s an equivalent shift for me in the pair of dots rotated around 22 degrees from horizontal.

It would be really useful to have comments on whether that works for you, or whether for you the rotated dot arrays still present equilateral triangle arrangements.  Illusions like these often do look different to different observers, and it’s also all to easy, once you have a theory about what’s going on, to see things the way your theory says they should look.

11 June 2012:  This is a revision of the original post.  It included a 3D demo of the dotty effect, but with triangles of dots that turned out not to be truly equilateral….  Woops.

Subtle Bent Line Illusions

Bent line illusions
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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Poggendorff versus Mueller-Lyer


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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Padoxical illusions

morinaga's illusion

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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The Poggendorff Illusion and depth processing

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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