There must have been a time when you saw an illusion and went, “Oh! Oh my God! Oh f**k”.
Welcome, to another round of the same. We call it the Muller-Lyer illusion.
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff3784f77-646e-4c57-b08e-b94dce25325c_1200x538.png)
You saw the image and your intuition made an impression that the arrow is shorter while the fork is longer as compared to the plain middle line. You readily accepted the interpretation generated by your brain. Yet, it is wrong. All three figures are of equal length.
You know what’s fascinating? You are aware of the correct answer now but still your mind sees the same. You need to put an effort into interpreting all three figures as having similar lengths.
If you think you can no longer perceive the illusion, try and beat this:
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb7661dab-817c-40e7-9e6e-699cc4565581_500x500.gif)
Or this:
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05a86c34-5b8c-402d-a65e-5846fbc3a3b6_777x338.gif)
What’s more, this illusion isn’t just limited to abstract images. It is cleverly exploited by cloth manufacturers to make your legs look longer when they want to. Consider the following image, for example:
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1022a4f4-29c0-4b99-b4c1-2461f133caaf_1200x674.png)
High-cut bathing suits employ the Muller-Lyer illusion to create a false perception of long legs.
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F88bdb92b-5935-41f2-a1a9-a6c270e8042a_1200x1287.jpeg)
There has to be a reason for our mind to get swayed by this trick. How could a few lines here and there steer the cerebral orchestra out of symphony? What is the sorcery behind this?
The answer lies in The Linear-Perspective Hypothesis. Big words, huh? We will deal with this concept a tad bit later. Before that, let’s learn a few more things, like, what a linear-perspective drawing is.
When a 3D image is projected onto a plane as a 2D image, giving a perception of depth nonetheless, it is known as a linear-perspective drawing.
Wikipedia defines it as, “….an approximate representation, generally on a flat surface, of an image as it is seen by the eye.”
Whenever we observe such a drawing, our mind views the 2D drawing as if it were in a 3D space because that’s where our vision has evolved. The mind assumes that whatever light strikes on the retina has bounced off a 3D object. The discovery of papyrus in Egypt has been a secret to the human gene pool ever since.
Consider the following image, for example:
This is essentially a linear-perspective drawing that our brain interprets immediately as a road going into the distance away from the viewer.
It happens because our visual system obeys the Law of Projective Geometry, which states that the apparent size of the objects in the image varies inversely with the distance portrayed in the scene, like the trees in this case. The furthest tree is shown smaller than the nearest tree but you immediately recognize that it is because the former is far away in a 3D setting, which means that the actual size of all three trees is the same.
Now let’s see a violation of the law of projective geometry.
The size of the trees does not change with the portrayed distance in this image. This creates an illusion that the tree furthest down the road is taller than the nearest one. However, if you measure the three trees with a ruler, you will find they are exact copies of each other. Your brain knows that in a 3D setting, the furthest tree should appear smaller than the nearest one if they are roughly of the same size. When this isn’t the case, it means that they are not of equal sizes, which is where the illusion lies.
This is called the Ponzo illusion and can be better visualized with the following gif:
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff3236d64-b19b-43e2-86bc-c67e428a9566_225x166.gif)
Note how the top yellow line looks longer than the bottom one even when they are exactly similar.
Now that we are familiar with linear-perspective drawings and the law of projective geometry, let’s look at the explanation of the Muller-Lyer illusion.
The Linear-Perspective Hypothesis
See the image below.
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437c8f6b-47de-4ec2-924c-3eb6959bbe31_1200x538.png)
We can see two walls meeting each other at a corner projected towards the viewer, i.e., in front of the plane of paper. The walls recede away from the viewer. Now, since the corner projects in front of the plane, the line representing the corner is perceived to be closer to the observer. This creates an impression that since a line appears to be of this size when it is nearer to the observer, it must be shorter than a line of the same apparent size located in the plane of the paper (Law of Projective Geometry).
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fec54078d-8d9f-4eac-b9d2-5ef2f90840d3_1200x538.png)
Here, we see two walls meeting each other at a corner projected away from the viewer, i.e., behind the plane of paper. The walls appear to be coming towards the viewer.
Now, since the corner projects behind the plane, the line representing the corner is perceived to be far away from the observer. This creates an impression that since a line appears to be of this size when it is away from the observer, it must be longer than a line of the same apparent size located in the plane of the paper.
Coming to the point, the linear-perspective hypothesis states that in the Muller-Lyer illusion, the arrow and the fork are interpreted by our brain as linear-perspective drawings of right-angled corners projecting toward the observer (convex corner) and away from the observer (concave corner), respectively.
If you remove the bricks in both the wall corners displayed above, you will notice that they look similar to the arrow and the fork in the Muller-Lyer illusion.
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9cf3d0fc-cef1-4832-b7f6-79b4768d6fb7_1200x538.png)
You may have guessed by now why our brain gets deceived like this. It is because we live in a civilization surrounded by rectangular buildings. Our brain tries and sees everything as if it’s in our environment, which mainly consists of buildings having walls meeting each other.
![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F003b9617-f145-47af-b30e-7b8ae159ba9b_1200x1600.jpeg)
This is supported by a study conducted in the early 20th century on the indigenous people of the Murray Islands in Australia. The majority of them were found to be immune to the Muller-Lyer illusion.
“Reality is merely an illusion, albeit a very persistent one.”
— Albert Einstein
TheUnknownDoktor
References:
Kubovy, Michael. (1986). The Psychology of Perspective and Renaissance Art. 10.2307/2540419.
Thanks for the article. Made my day :)