A Geometric Mind

By Impronta – Own work, CC BY-SA 3.0, https://commons.wikimedia.org

I challenge you to describe the following images in terms of simple geometric shapes: shapes such as rectangles and circles, and flat surfaces called planes.

If you see one of those shapes in the image, then mentally note it.

You may not be able to completely define the image with those simple shapes, but at least note those parts of the image where you can see a plane, or a rectangle, or a circle.

The shapes are not likely to be seen dead on; they may be seen at an oblique angle.

Color is an interesting variable in the images, but it is not the primary focus of this exercise. The ability to use geometrical shapes is the point of this post.

The first such shape is Figure 1.

Copyright John R. Clarke.


The next shape is Figure 2. Do you see a lighted plane on the left partially obscured by an extruded rectangle, otherwise known as a rectangular prism or cuboid?



Figure 3. Yet another image, somewhat similar to Figure 2:



And a fourth image, Figure 4.

Copyright John R. Clarke.


Now, lets try some variations on the theme.


















The four images immediately above are identical to the first four images, but by seeing them in this order you may detect that there are only two unique images.

The images on the right are simply the images on the left rotated 180°; that is, they are turned upside down.

And yet most people identify an entirely different geometry, depending on which way the images are rotated.

So, seeing is believing …

… or is it?

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I do not know if this visual phenomenon has a name or not: I accidentally discovered it when looking at images to post on a laboratory wall. One figure looked unfamiliar; I was confused by it, until I happened to rotate it.

As the French say, voila. It was an optical illusion caused by our brain’s tendency to look for familiar shapes in unfamiliar and potentially confusing images.

There is a literature on the illusions of inverted images where images have been digitally manipulated (sometimes called the Thatcher Effect), but the images above have not been altered in any way.






Killer Optical Illusions — Size Does Matter

A discrepancy between what you see and what you expect to see can prove fatal.

In graduate school at Florida State University I drove a motorcycle between Tallahassee, FL and my home in Thomasville, GA almost every day of the week, an 80-mile roundtrip. I seldom took the heavily traveled direct route. One alternative route took me through the boonies along a road that apparently rarely saw a motorcycle. One summer day, somewhere between Miccosukee and Metcalf I approached a ramshackle, rusting tin-roofed house, and out of the yard came bounding a dog which apparently lived for the excitement of chasing cars.

As bikes go, a Honda CL 350 was not a large bike. It was a combination road/trail bike called a Scrambler. It was smaller than even a 500 cc Honda, and much smaller than a car. That disparity in size caused the charging dog to misjudge his distance from me. He was falling prey to an optical illusion: objects that are smaller than you anticipate seem farther away than they actually are.

As a pilot, and knowing something about firearm marksmanship, I can admire in retrospect the animal’s uncanny ability to properly lead and zero in on a fast moving target. He was on a collision course with my 346 lb bike traveling at highway speed. Of course, when intercepting hard steel with something as fragile as a skull, it is not a good idea to complete the interception.

I well remember the image of that dog, mouth open, tongue lolling happily to the side of his maw, seeming to relish the chase of a moving vehicle. And then in an instant his expression changed when he realized that he was actually going to catch a moving vehicle.

I don’t think he had thought through the consequences of completing his intended attack.

He applied his brakes —- front legs fully and stiffly extended, toes digging into the asphalt. But he was too late; his momentum carried him headfirst into the mid-section of the bike as our paths crossed.

His car chasing days were over.

We humans might smugly think we are not so easily confused by an optical illusion based on expected sizes and shapes. After all, we are highly intelligent creatures. But we would be wrong in our smugness.

There is a new airport in the Florida Panhandle built in the middle of millions of slash pine acres. It was a land donation designed to assist the land owners with developing sylvan land into valuable real estate. Unfortunately the real estate crash has stymied development around the airport, so an aircraft flying at night into the field which boasts a long 10,000 foot runway, sees only blackness around the airport. What results is the so-called black-hole illusion.

The black-hole illusion applies to unusually long runways lit up at night and surrounded by impenetrable blackness. The runway at ECP (Panama City) is about twice as long as the usual runways used by general aviation aircraft, and at 10,000 feet is far longer than the runway at the previous Panama City airport (PFN). The almost overpowering visual illusion is that you are closer to the runway than you actually are, and that you are considerably higher than you are in reality. On final approach the unwary pilot gets the impression that he is too high, and must push the nose of the aircraft down. In fact, nothing could be further from the truth. A pilot has to be on his game to resist the potentially deadly optical illusion.

In a black-hole situation, it is critical to fly by the aircraft instruments, with the altimeter being one of the most important. When in the grips of the black-hole illusion I find it very easy to fly the “pattern”, the rectangular visual approach that eventually leads you to the runway, at too low of an altitude. Now I am aware of the trap, but I still have to concentrate on the instruments and ignore the visual cues from the humongous runway. I also find new pilots flying my aircraft into the field for the first time falling into the same trap. Looks can be very deceiving.

A simulated black hole approach to a runway. Orbiter imagery from Guleit.com

Boeing engineers found through their night approach research that during a black hole approach flown solely by reference to the view out the windscreen, pilots will have an almost overwhelming urge to fly too low as they approach the airport. The result of such action is likely to be impact with the ground two to three miles from the runway. Details of that discussion, relying heavily on geometry, are aptly given in the following aviation news item from 2000. http://www.avweb.com/news/airman/182402-1.html.

Airline transport pilots using autopilots to fly an Instrument Landing System guided approach to the runway seldom have to worry about visual illusions. But even they can be fatally fooled when going visual. There have been at least two commercial crashes caused by the black-hole optical illusion; Alitalia Flight 4128and VASP Flight 168. (For more details, click on the Alitalia and VASP links.)

A depiction of a black hole feeding on stars and gas.

As we learn about astronomical black holes, we realize they destroy all things in their grip. However, much closer to home are personally destructive phenomena that result from nothing more than visual trickery, a vicious mental confusion between actual and perceived sizes of airport runways, and as it turns out, even between motorcycles and cars.