Full Tour: Visual Illusions on Campus

1: Bathroom Tile Illusion

The bathroom tile creating this illusion can be found in the Men’s room on the 4th floor of Old Minor (same floor as Minor 489). And yes, ladies it can also be found in the Women’s room on the 3rd floor.

The light tan tiles are squares, but notice that each tan pair appears to have a wasp waist (that is, their sides don’t appear to be parallel). The inward bend is most obvious on tiles near, but not on the point of fixation.

We don’t know the explanation for this illusion, but it’s related to Fraser’s Spiral and the Café Wall Illusion.

2: The Shadow-Fan Illusion

This illusion can only be seen in the morning (roughly 8-10 am) on a sunny day. Go south from Minor Hall toward Bancroft Avenue. Pass Wurster Hall on your left. Kroeber Hall is approaching on your right.

You’re walking toward Café Strada, a local cappuccino hang-out. You approach vertical rods stuck in the sidewalk. Stop on the Minor Hall side of the rods at a distance of ~10 feet.

Notice the shadows created by the rods. Do they appear to be parallel to one another? Or do they appear to fan out (left ones to the left and right ones to the right)? Most people report that they fan out. They’re actually parallel.

To prove that, you can measure them, but it’s simpler to note that the shadows are created by the sun light, which because the sun is essentially infinitely far away, has parallel rays and therefore creates parallel shadows.

3: The Sinking Tower Illusion

Go to the east (upper) side of the Haas School of Business. Position yourself so you can see Sather Tower (the Campanile) through the archway.

Now walk slowly toward the archway keeping the tower centered in the arch. You’ll notice that the tower seems to sink as you walk forward. The most likely explanation is the following.

The brain estimates the distance from you to the arch and from you to the tower. The tower is quite large and quite distant, so the brain actually under-estimates its distance (and its size, but that’s not important to the explanation).

Suppose, for example, that the ratio of actual distances (tower/arch) is 20 (a pretty good approximation), but that the ratio of perceived distances is 5 (another pretty good approximation).

Given the assumed ratio of 5, when you step forward, the top of the tower should rise in your visual field at 1/5 the rate as the top of the arch (from the geometry). It doesn’t rise that fast, so the brain concludes (erroneously) that the tower is sinking.

This illusion is related to the well-known size-distance illusion. It works better during earthquakes. There is an interesting variant of this illusion, which we will call the Growing Tower Illusion.

After positioning yourself to see the Sinking Tower Illusion, walk slowly backward in a straight line away from the archway. Keep the archway centered in the arch as you did when walking forward.

You will notice that the tower seems to grow as you move farther away. Also notice the difference on how the tower grows and shrinks.

Upon moving forward, the tower shrank in increments and upon moving backward, the tower grows at a more constant rate. The explanation for the Growing Tower Illusion is the basically the same as explanation for the Sinking Tower Illusion.

When you move backward, the image of the tower goes higher in the archway. The distance to the tower is great, so we don’t take its distance into account properly. As a result we see the tower appear to rise.

4: Inverted Tower Illusion

Hold your hand up (as the nerd who took the photograph has done) such that you can’t see the parts above the clocks. Do the illuminated and shaded sides of the tower look equally bright? That is, do the reflectances of the bricks on the two sides appear equal? Most people see the reflectances as similar.

Now see if you can through conscious effort get the vertex of the tower to flip perceptually. What we mean is this. The vertex is obviously convex, but you may be able to imagine it as concave. If you can get it to flip like that, what happens to the apparent brightnesses of the left and right sides of the tower? Doesn’t the right side (if it is the shaded side) now look darker?

The explanation for this illusion concerns the way in which the brain takes the known position of the light source (in this case the sun) into account when estimating the reflectance of a surface. This illusion was first described by Ernst Mach, the Austrian physicist and philosopher.

For more information on Sather Tower and its history, refer to:
Brief History
UC History Digital Archives

5: The Elliptical Tree

Stand on the other side of the path from that sign. Look downhill at the dead, grayish tree. It’s important that you don’t move your head while viewing the tree. The main trunk is bifurcated.

Look at the left half of the tree and make a judgment (while not moving the head!) of the 3d shape of the cluster of branches. Does it appear spherical in shape (that is as deep as it is wide) or ellipsoidal (less deep than it is wide). Most people report that it looks ellipsoidal.

Now walk downhill to the left of the tree and notice that the branch cluster is really spherical, not ellipsoidal.

This illusion is probably the consequence of impoverished depth information. It’s relatively easy to estimate the width of the branch cluster, but it’s difficult to estimate the depth. Because you weren’t moving your head, motion parallax doesn’t provide a useful cue to the depth. Because you were standing pretty far away, binocular disparity doesn’t provide a useful cue to the depth either.

The branches are all different sizes, so the relative sizes they create on your retina are also not a very useful cue to the depth. The brain appears to have what statisticians call a Bayesian prior (basically an expectation) that objects we see are more likely to be flat than they are to be spherical. When we make the depth information weaker, the prior affects our perception of the 3D shape.

6: Falling Tower Illusion

Before long you will notice that the tower appears to fall toward you, with a constant angular velocity. To prevent the tower from crushing you, close your eyes.

This infamous illusion has bewildered the brightest minds on the Berkeley campus for decades. That’s probably why they put the “NL” parking places near this location. Can you guess what the “NL” stands for? Think Stockholm.

For a better look without risk, please visit: The Campanile Movie

7: Elliptical Trunk Illusion

You should be able to see a lamp post behind the tree on the left and a tall building (Evans Hall) behind the tree on the right. Look with one eye while holding the head still at the trunk of the tree. It might take 15 seconds or so of looking.

What is the apparent 3d shape of the trunk? Does it look cylindrical or does it look flatter than a cylinder (an elliptical cross section)?

Most people report that it appears elliptical. If you see that, open the closed eye and move your head and you’ll see that the shape becomes more cylindrical.

The explanation for this illusion is the same as #4. It works on this tree trunk because the texture of the bark doesn’t provide a good cue to its actual shape.

8: Compressed Fence Illusion

Now look down the fence as it extends westward (downhill). Compare the apparent width of the 1st segment of the fence (the distance between the posts) and the 10th segment. Do they appear equal in width or does the 10th look considerably narrower? Most people report that the 10th appears narrower.

This illusion occurs because we tend to under-estimate long distances. We estimate the distance from the 1st to the 2nd post accurately because they are at short range. We under-estimate the distance from the 9th to the 10th post because of the tendency to under-estimate relative distances at long distances.

This is a well-known phenomenon called “depth compression.” You can experience this quite strikingly when hiking outdoors. Large distant mountains appear much closer than they actually are.

9, 10, & 11: Three Visual Effects from One Spot

The first effect concerns the cables on the Golden Gate Bridge. The horizontal cables are 35 inches in diameter and you can see them easily from Barrows Hall on a clear day. They are 12 miles away, so what visual angle do they subtend at the retina? The answer is approximately 10 seconds of arc! On a very clear day (and with your specs on), you can also see the vertical cables. They subtend only 2 seconds of arc. To give you some insight on these numbers, an individual foveal photoreceptor subtends about 30 seconds of arc. Thus, a person with good acuity can see features whose width is a fraction of the diameter of a single photoreceptor. (Contributed by Ahna Girshick and Stan Klein.)

The second effect concerns the apparent orientation of the water of the Bay. As one looks out toward the Bridge, most people report that the Bay appears pitched up (as if the water would flow toward Berkeley). It’s not a tsunami. Rather it’s the consequence of the sloping terrain of Berkeley as it meets the Bay. Our brains assume that the flat terrain of Berkeley is horizontal (perpendicular to gravity). The Bay is pitched relative to that terrain, so the brain sees the water as pitched. (Contributed by Cliff Schor and Dhanraj Vishwanath.)

The third effect concerns the pier off the Berkeley Marina. You can see the pier toward the right side of the above photograph. What fraction of the distance to Alcatraz (the island to the left of the Golden Gate Bridge) does the end of the pier appear to be? Most people report that it’s more than half the distance. It’s actually approximately 1/3. This is another example of the compression of perceived distance. Very distant objects (like Alcatraz) appear to be closer than they really are. The curvature of the earth might contribute to this illusion as well. (Contributed by Marty Banks.)

12: The Apparent Beauty Illusion

Yes, it was apparently designed by the faculty of the School of Architecture. They seem to have wanted to emphasize concrete, the modern building material. Lots and lots of concrete.

And just to make sure you can see all the concrete, it’s not painted. In case you think the interior is different, look for yourself. (Brings back fond memories of Khrushchev’s Moscow.)

You’re probably thinking that the building must be pretty darn strong with all that concrete. Think again. Wurster Hall was found to be unsafe in earthquakes after the 1989 Loma Prieta Quake, so it is now being retro-fitted.

Anyway, you’re asking, “What’s the illusion here?” Well, most people report, despite the good intentions of the Architecture faculty, that this building is not beautiful. That indeed it’s real ugly. Probably the Architecture faculty wanted to inspire future generations of architects by building their self-esteem: “These guys get paid for this stuff? I could do a whole lot better.”