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.
