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.