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.
I love soap bubbles, so following our earlier series of pictures that are not illusions but soap bubble fantasies, here’s an incident involving the statues on the Pont Alexandre III in Paris (at least I think it’s that bridge ….). If you want to view some more bubble pictures, there’s a whole category of soap bubble pictures, and it includes one post on how I (and others) take photos of soap bubbles and films.
This is a version of an illusion discovered by Jacques Ninio. Imagine that the coloured rectangles are real translucent plastic sheets, different in colour but identical in size. They are shown in correct perspective, as they would appear if both were sloping away from us at the same angle. However, the nearer one appears to slope much more than the further one. Ninio shows the effect with a diagram of arches in his book The Science of Illusions, p. 27 and fig 3-7. He explains it as an example of the way that we sometimes seem to compress visual space with distance, so that for example a flight of stairs seen head on looks steeper the further we are from it. It’s a reminder of the way that visual space is far from geometrically regular. The distortions of space must have evolved because they are advantageous in everyday vision. But in the unusual arrangements presented in some optical illusions objects can appear distorted, as in this illusion and in size-constancy effects. With those, space and objects seem to expand with distance, rather than contract as in this illusion.
Like the effects in many illusions, it is the unlikeliness of this configuration of inclined planes that makes it a challenge for the strategies we normally find reliable in making visual sense of the world. When planes in our field of view are seen in a more usual configuration, aligned with gravitational vertical, we have no problem in correctly judging their inclination in space, even if the planes are inclined in relation to our field of view. Try this picture of some more imaginary planes, this time in the cathedral of Sees, in France.
For another case where the brain struggles with sloping planes, see the post on the wonky dagger and balconies illusions. In those illusions, puzzling sloping planes are shown, but not, as here, at different distances. Instead, the slope in those cases is ambiguous.
This wonderful ornamental canoe prow represents some fabulous creature, looking to the right. Prows like this appeared on boats used in a cycle of trade around the Trobriand and nearby Islands in the Western Pacific, called the Kula trade. The wonderfully ornamented canoes were only a small part of the story of this cycle of trading, but an intriguing one: the idea was to contrive a canoe so visually baffling that as your fleet of canoes approached the beach, it left your trading partners too bemused to compete in bartering. (For a more detailed account, if you fancy a bit of fairly heavyweight anthropology, there’s a fascinating essay by Alfred Gell called The Technology of Enchantment, in a book on art and anthropology from 1992).
The canoe prow is in the museum in Liverpool, UK, but to see a whole canoe go to the museum in Adelaide, Australia. It doesn’t have quite such a splendid, baffling prow, but it does show what these fabulous boats were like.
If you’d like to know out why these canoe prows remind me of paper marbling, read on.
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.
To view this illusion, you’ll need the knack of viewing 3D picture pairs without special spectacles, or a viewer – that is, by viewing them cross-eyed. If you haven’t got that trick, and want to try, start with one of our earlier posts on 3D.
If you do have the knack of viewing 3D pictures cross-eyed OK, what you should see in this demo is that, when the room space appears in 3D, the pendulum seems to be swinging in a circle. It’s MEANT to be a web-based demo of a famous pendulum effect you can fairly easily rig up in real life. It’s called Pulfrich’s pendulum, after researcher Carl Pulfrich, who published it in 1922. Here’s how it should work in real life.
You hang up a pendulum, say two meters long, but so that it can only swing from side to side – it must not be free to swing backwards and forwards at all. (Details below on a low-tech way of doing that). You place a reference object under the pendulum, (I use a candle stick), so that the swinging pendulum just misses it, right at the mid-point of the swing. Then you view the swinging pendulum head on, but with a dark filter over one eye. All being well, you should see a really vivid illusion: the pendulum appears to swing not just from side to side, but in a circle. So it seems to swing alternately in front of, and then behind, the centre point marked by the reference object.
The effect, in a real life demo, seems to arise because the brain takes longer to process the filtered, darker signal coming via one eye. The position of the pendulum at each moment therefore appears slightly different in each eye. The effect mimics the signal that would reach the brain if the distance of the pendulum from the eye was varying cyclically. The brain therefore infers that the pendulum is most probably swinging in a circle.
So why is my on-screen version here a fake? Read on to find out.
