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?

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.

Read the rest of this entry »

Does Big Ben look like it’s leaning over more in the right hand image than in the left hand one?  It can take a double-take to spot that the two pictures are identical. I find it a fantastically strong illusion.

It’s a demo of a new illusion found by Frederick Kingdom and colleagues (you’ll need to scroll down that link to get to their bit – look out for an even more than usual Leaning Tower of Pisa). Their discovery is a new version of the size-constancy illusion.   This is my second demonstration of it – a few posts back I used a picture of a historic streetlamp. But here’s an example that looks stronger to me, with a better known subject. 

There’s something amiss with this dagger, for sure. For a start, the blade’s a bit short. More important, you can’t be sure just from the picture where the blade is pointing. That’s because one and the same perspective view can arise from more than one three-dimensional configuration, out there in the world.  This dagger is particularly hard to interpret.  It could be pointing downwards, with one edge of the blade longer than the other, like the blade in the top left pair of little images, of the dagger seen head on and from the side. Or the edges of the blade could be the same lengths, so we must have a steep perspective view of it leaning sideways, as in the top right hand pair of views. Look at the big image for a few moments, and I think you’ll be able to see it both ways.

Both configurations present exactly the same view in perspective, and both are about equally likely. (Well, maybe equally unlikely with this dagger would be nearer the mark). It’s a variant on an illusion which presents another clash of improbable alternatives – but one that tricks us into going for what may seem the least likely choice.  We could call it the wonky flower box illusion.

Do the flower boxes in this scene look like they’re rectangular, if seen from above, but sloping downwards? But what if they stick straight ahead out from wall, like well-behaved flower boxes should, but are trapezoid, seen from above, (as diagrammed to the right)? Trouble is, once again the perspective view will be the same either way. What’s curious is that in this case, most observers opt for the downward sloping view of rectangular boxes, unlikely though that would be in the real world.  Trapezoid plan boxes just seem too unlikely. It’s a version of the preference for right angles that leads us to accept incredible distortions of size in the Ames Room illusion.  If technical stuff is for you, here’s a serious analysis of the window box effect (though with balconies rather than window boxes doing the weird sloping stuff).  And if you just can’t get enough of that sort of thing, here’s a report of the same illusion in a church (also a bit on the technical side).

Only joking, but the right hand picture does seem to show this old lamp near me leaning over more than it does in the left hand picture.  But now check out the two pictures.  They’re identical!  It’s an illusion only recently reported by Frederick Kingdom and colleagues in McGill University (scroll down that link for their bit).  It’s yet another demonstration of the strength of the size-constancy effect.  (See my earlier posts on the wonky window and paradoxical size-constancy).  What’s remarkable about the McGill report is that it shows size-constancy coming into play even across the gap between two clearly separate pictures. I guess it means that at an early stage in trying to make sense of the visual scene, the brain just accepts the consistent depth cues in the two pictures as signalling that they are both part of one spatial scheme.

As Kingdom and colleagues demonstrated, the effect also works horizontally.  Here’s a demo:

This time the platform looks pretty much the same in the two pictures (as it is – the pictures are of course once again identical). But rails to the right, seen at a more oblique angle, seem to point a bit more towards vertical in the right hand image than in the left hand one.

Here’s a rather subtle effect. It’s a competition underway, when the Zollner illusion is seen embedded in a staircase. In the staircase lower left, where two of the long lines are either side of the outside edge of a step (in other words like lines a and b here, on the sides of a convex step), the lines seem to get further apart with distance, as they would in a normal presentation of the Zollner illusion. But wherever on that lower left stair the lines are like b and c here, either side of the inner edge of a step, (so on a concave step), they tend to look much more parallel. In a normal version of the illusion, as below, the equivalent long lines appear to get closer together to the right.

Want to know more?

Read the rest of this entry »

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.

Read the rest of this entry »

Size constancy is the term for our tendency to see distant objects as larger than they are. So the far end of a shape with parallel sides looks wider than the near end. (See the earlier post on The Wonky Window). It seems to be such a basic feature of vision that it can give rise to amazing effects.  In the photo, first note note that the “sculpture” is impossible! All four blocks are receding from us, so they could only connect up in real space as a bendy snake. Instead they join up in an impossible, ever-receding, endless loop.  (See the earlier post on M.C.Escher’s Waterfall for how that kind of impossible figure works). Here the endless loop leads to a paradox, thanks to size constancy. The distant end of each block seems wider than the near end, and yet at the same time seems to be exactly the same size as the apparently smaller, near end of the next block. Measure the sides of the blocks and you’ll find them parallel. It’s one of many demonstrations that perceptual space is not always geometrically consistent, (or it can be non-Euclidean, as the specialists put it).

I located my impossible sculpture in a deeply receding space because that makes the effect just a bit stronger.

Update January 2010: How could I have overlooked this?  The stripes I’ve added to these blocks will be enhancing the effect of divergence by adding the chevron illusion to the size-constancy effect.  The chevron illusion was first reported 500 years ago, by French writer Montaigne, as related in Jaques Ninio’s book on illusions, page 15.  The chevron effect is a special case of the illusion later re-discovered a bit over a century ago as the Zollner illusion.  Some specialists would say both effects depend on the brain’s attempts to make sense of figures as shapes in space.  I suspect that’s true of the size-constancy effect, but that the chevron effect is 2D, pattern driven.  That seems supported by the observation that whilst in the picture above the chevron and size-constancy effects are acting in consort, they can also oppose one another, reducing the effect of divergence.

Read on for more on size-constancy.

Read the rest of this entry »

Size-constancy effects make distant objects, especially in pictures, look larger. So in the table above, the back edge looks wider than the front edge. In fact, the sides of the table are strictly parallel. The fact that they don’t get closer together with distance, as we expect them to following the rules of perspective, produces a specially strong size constancy effect.

Read the rest of this entry »