Optical Illusions

As we are learning thanks to this blog and its entries, geometry is present in many aspects, practically all of our life and for this reason, I would like to talk about optical illusions, those images that play with our mind and transmit very different emotions, well, they have always caught my attention when I have seen them but I have never stopped to think about the geometric shapes they contain.

So what is an optical illusion? The most technical definition is a deceptive mental image caused by a false perception of reality due to the erroneous interpretation of the data perceived by the senses, also called optical game like the one we can see below, are the circles moving?

We can distinguish two types of optical games, those that transmit a sensation of movement due to their layout, or those that make us doubt about measurements and magnitudes, both being a very interesting way to enter the world of geometry by being curious about how these games work.

Most of these images are based on geometric figures to create these illusions, hence the entry in this blog, therefore, we can see the importance of this branch of mathematics in making us think and reflect on the present, on what we see and why we see it, thus expanding our abstract thinking, this so difficult to achieve.

Let's focus on the kind of optical illusions that make us doubt measures, magnitudes and perspectives. There is a very peculiar staircase, known as the "Penrose staircase", also known as the "infinite staircase" or "impossible staircase". It is an optical illusion described by the English mathematicians Lionel Penrose and his son Roger Penrose along with other impossible objects in an article published in 1958.

This staircase is a two-dimensional representation of stairs that change their direction 90 degrees four times while giving the impression that they go up or down at the same time, in either direction. In its strict version of 4 stairs joined together its 3D construction is impossible, the optical illusion of Penrose's image is based on cheating the perspective.

Even this optical illusion created by the mathematician has been taken to the cinema as we can see in the film Inception and its infinite staircase, explaining that structures that are normally impossible can be created within the world of lucid dreams. I leave here the fragment of the film where it appears.

Having learned more about geometry in optical illusions, would you be able to answer whether vertical lines are parallel?