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?
I’ve been wanting to do a new version of my earlier post of The Twisted Stairs. That’s partly because the way I placed the figures in the original posting, they got in a bit the way of seeing the twist in the lateral flights of stairs. I reckon you can see the twist effect better now, as they transform from stairs seen from below (at the top by the balcony), to stairs seen from above (down at floor level). I wanted to see if I could get it right, because this is an impossible stair effect that maestro M.C.Escher never used. Sometimes his staircases as a whole can be seen either as from above or from below, but they don’t twist from one viewpoint to the other half way up. As I mentioned in the earlier post, I reckon that’s because the twist effect depends on fudging the perspective, and Escher didn’t do fudge. His perspective is almost always miraculously lucid.
Another reason for a new version is that I wanted to produce a high resolution version, suitable for giant 35 x 23 inch posters. As ever, you are welcome to use downloads of the image here for any private purposes, but if you wanted to think about buying a framed print, or giant poster, here’s where to take a look.
There are more technical details on the original post. I borrowed the figures for this new version from Durer, Pieter Brueghel the elder, and Hogarth.
You’re welcome to download and use for private purposes any of the imagery on the site, except for a very few pictures where I indicate that third party copyright might apply. But if you’d like a giant, 35 x 23 inch poster, full of illusions, you can buy it (along with loads of illusions on bags, T-shirts etc.) from www.Cafepress.co.uk/optoct. I was delighted when I saw the quality of the poster. Each of the illusions is identified with a discreet caption line, so that you’d be able to follow them up on this or other sites. And of course, lots of these illusions are brand new versions, often with an extra twist of some kind.
Illusions make brilliant gifts.
You’ll also find a poster of the whole of my optical illusion cartoon story. If you’d like to preview that, read on.
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.
This is a brilliant illusion discovered by Baingio Pinna of the University of Sassari in Italy. The circles appear to spiral and intersect, but are in fact an orderly set of concentric circles. The illusion is due to the way the orientation of the squares alternates from circle to circle, and that contrast alternates from square to square within each circle. The illusion is related to the movement illusions of Akiyoshi Kitaoka and to twisted cord illusions.
What’s going on is suggested by this next version, with the edges enhanced, plus a bit of blurring.
This image approximates (with false colour) the data transmitted within the brain once the image has been filtered by cell systems early in the visual pathway, including centre-surround cell assemblies (a bit technical, that link). The role of these is to enhance edges, so that bright edges are now emphasised by dark fringes and vice versa. Note that between the little stacks of alternating light and dark fringes, along the line of the circles, the dark fringes of bright squares align with the dark edges of adjacent squares and vice versa. The scale and spacing of the squares is just right to get that alignment, and as a result the effect enhances the inward turning, spiralling effect due to the orientation of the squares. The fringes combine to give an effect a little like interfering waves. The illusion seems to be bamboozling processes that are usually superbly effective at filtering out the key information about edges and their orientation in the visual field.
However, showing that centre-surround cell outputs could be enhancing the inward turning character of the lines forming the large circles doesn’t explain why the brain integrates the local effects into the perception that the large circles as a whole are spiralling inwards. I guess that’s because, to a much greater extent than we realise, we infer global configurations from what we see just in the central, foveal area of the field of view. That also seems to be the case with impossible 3 dimensional shapes, as in the impossible tribar.
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.
This is a third look at the Shepard’s tables illusion. If you didn’t see the earlier posts, you might like to get up to speed on the illusion by scrolling down two posts to an animated demo. The two pairs of table-tops in these views are absolutely identical, and within each pair the two lozenge shapes are identical except that one is seen short end on, and the other wide side on. However, they don’t look identical. Most dramatically, the lower table in the left hand image looks much longer and thinner than the upper table. But we don’t see that stretch into depth in the identical pair of table-tops in the right hand image. They look quite different, just because the tables are shown tipped over.
The stretch-into-depth of the lower table in the left hand image is a kind of size-constancy effect. But the tables also show a more familiar kind of size constancy effect. Check out the blue lines in the left hand image (left edge of the upper table and alignment of the bottom of the table legs). Those blue lines are parallel, but to my eye they look as if they get wider apart with distance.
In the left hand image, to my eye, only the blue lines show apparent divergence with distance. The horizontal edges (yellow) and the vertical table legs (red edges) stay parallel for me. But in the right hand picture, just tipping the tables over makes all three pairs of coloured edges appear to diverge with distance. The effect may not be very strong. It’s easier to see in bigger versions of the pictures, so I’ll add those in in what follows, where I want to pose a question: are the differences between the table-tops as seen upright and tipped over only to do with how we see pictures, or are they a clue to how we see more generally?
The previous post presented an animation of Shepard’s Tables. If you didn’t see that, you might want to check it out first (scroll down to the previous post) to get the basics of the illusion. This new version of the illusion, with nested tables, follows the pattern: all eight of the lozenge shaped table-tops are identical in shape, but the more that a lozenge is seen with its long edge parallel to the line of sight, the more it looks long and thin as it stretches into the distance. The more it’s seen short edge parallel to the line of sight, the more it looks wide and stumpy.
Describing the illusion that way may explain a puzzling variant of Shepard’s Tables, recently reported by Lydia Maniatis, as mentioned in the previous post. As the problem appears in these nested tables, at B the edges of the table-tops that are horizontal on the screen must be receding into depth, and yet they don’t show the dramatic illusion of a stretch into depth that we see in the edges receding into distance at A. Why not?
Isn’t it a question of perspective? At A the horizontal table edges are represented as if seen head on, parallel to the image plane – the plane at right angles to our line of sight. The table edges that are oblique on the screen at A must therefore be extending into depth in the most extreme way, parallel to the line of sight and at right angles to the image plane. Seen like that, depth effects are maximised. At B, no edges are aligned with the image plane, and all the edges, even the ones that are horizontal on the screen, are receding at 45 degrees to the line of sight. That’s a much less extreme recession into depth. So although the table edges that are objectively horizontal on the screen at B are receding, they don’t show as much illusory stretch into depth as the receding edges in A.
Lydia Maniatis observation raises a general point that’s really interesting – the way that appearances can depend on what we mean by “up”.
This is an animation of Shepard’s Tables, an illusion first published by Roger Shepard as Turning the Tables, (see his wonderful book Mind Sights, 1990, pages 48 and 127-8). The left hand lozenge-shaped table top seems to get longer and thinner as it rotates, but it’s an illusion. It remains identical to the right hand table-top, except for rotation. The table-tops look even more different as the legs appear. The illusion is an example of size-constancy expansion – the illusory expansion of space with apparent distance. The receding edges of the tables are seen as if stretched into depth. Earlier posts on size-constancy showed how objects can appear wider with distance. That shows up with Shepard’s tables too, in the way that the oblique edges of the tables seem to get a bit wider apart with distance. The stretch into depth is more striking.
Recently Lydia Maniatis pointed out a puzzling aspect of the illusion, in her prize-winning entry for the Illusion of the Year Competition. Here’s a version of her figure.
All three table tops are identical, but the middle one looks different from the one on the left, though it’s not even rotated. Instead the vertical axis of the figure is shown at an angle to gravitational vertical. That means that the blue edges are no longer aligned with the frontal plane of the image, as to the left, even though they are horizontal on the page, but must be receding into distance. And yet we don’t see the dramatic stretch into depth that appears with oblique edges that recede into distance. Why not? Try looking at the middle block with your head leaning over to the left, so that the short edges are aligned with your head, and therefore with the vertical axis of your field of view. Now (for me) the blue edges do stretch into depth, though not as much as in the right hand image viewed normally.
What do you think is going on? I’ll take a shot at an explanation in a post in a couple of days.
If you can see this illusion, you may be amazed to discover it’s not an animation. Most people will see waving movement, yet the pattern of lozenges is not really moving at all. But about 5% of people just don’t see this kind of illusion, and if that’s you, it doesn’t mean anything’s wrong. If you do see the movement, it won’t be wherever in the pattern you focus, but in the periphery of your field of view. However, the effect is also very sensitive to size. I see it vividly with the screen about 15 inches (36 cms) from my eyes, and the image 8 inches (21.5 cms) wide on the screen, but I think you’ll get an even better effect by clicking on the image, if a bigger version then comes up on your system.
It’s a kind of illusion only discovered in the last few years. Lots of discoveries about it have been made by Japanese researcher Akiyoshi Kitaoka, and on his site (amongst scores of other stunning illusions) you’ll find his masterpiece in this line, his famous rotating snakes illusion.
