The world is able to surprise us again and again. There are phenomena that cannot be rationally explained, for example, optical illusions or obscure geometric shapes. No matter how many people look at them, the mind cannot explain what is happening. How can there exist an endless staircase or triangle, in which all angles are 90º? Yes, maybe the father and son of Penrose are the authors of these brilliant ideas. But let's start from the beginning.
Impossible figures
The first figure came out by chance. Once in 1934, a 19-year-old high school student Oscar Ruthersvard openly missed a Latin grammar lesson. From nothing to do, he scribbled with a pencil in the textbook cubes that suddenly formed into a triangle. The drawing was unusual, because such geometric figures do not exist in three-dimensional space and perspective.
Oscar Ruthersward, becoming an artist, will draw another 2,500 such images that will attract attention and surprise people. From this moment, a new direction in art and science is launched, which breaks the notion of space and experiments with perspective.
Penrose, father and son
After several years in another country, another young man will publish an article in a psychological journal about the endless staircase. He did not suspect the existence of Oscar Ruthersward with his impossible figures. But brilliant ideas are in the air, waiting in the wings, and now, the drawing of the stairs from the magazine will become famous throughout the world, together with its authors Lionel and Roger Penrose.
Father and son: two brilliant people who have chosen to serve science as the goal of their lives. Lionel Penrose was a math geneticist. And his son, Roger Penrose, became a mathematician who became interested in physics. However, what is the genius of the idea? Why is she still admired?
Penrose Staircase
The peculiarity of the stairs is that it is closed on itself. As if the world of Lewis Carroll with his "Alice through the Looking Glass" became real. Moving in any direction, a person is at the starting point.
The wonders of the Penrose staircase do not end there: if you go clockwise, you will constantly go down, always appearing on the step from which you started. And vice versa, if you go counterclockwise, you will go up all the time and again be in the starting position. This movement with its infinity causes delight and bewilderment: how does this happen? What is the secret of the impossible staircase?
How is this possible?
As the authors themselves explained, the whole point is in the peculiarities of human perception and thinking.
All impossible figures, including the Penrose staircase, are images of three-dimensional figures on the two-dimensional space of a sheet of paper. The human brain tries to interpret images through the prism of its experience, but constantly encounters inconsistencies, which leads to confusion. The secret is simple: the figures are presented from only one angle.
There is no way to get around and look from the other side. This is all the beauty. It is as if you are sitting in the theater’s auditorium on the fifth row from the edge and you see the stage from a certain point. From this place, part of the scenery is hidden behind the scenes, but if you transfer to the center of the row, the vision will change.
Images of impossible figures are built on this effect. The name itself suggests that the real existence of a triangle in which all angles are 90 ° is impossible. But you can draw such a figure. Moreover, a sculpture of the impossible Penrose triangle appeared in 1999 in Perth, Australia. And here the fun begins: how does it exist that in principle cannot exist?
Illusion or reality
False perspective, especially thinking, a certain viewing angle - that's what Penrose's ingenious engineering is built on. The stairs and the triangle lose their integrity if you look at them from a different point of view. A figure seems closed only if you look at it from a certain position.
It turns out that the figure is considered impossible only in the drawing or from a certain point of view. This is because when a person looks with two eyes at one object, the brain receives two images of one object and focuses in one image. This means that the eyes, being at a certain distance from each other, perceive the object from different points. Due to this, gaps in the figures are visible, and therefore they lose their mystery.
In the photo behind the figure of an impossible triangle is a mirror. We look at the triangle, and it seems to be whole, but the mirror shows us the real picture. Also with the Penrose staircase. For it to exist in reality, a gap is needed in the right corner.
World of impossible figures
If you plunge into the world of impossible figures, then it amazes with its variety and fields of application. It turns out that on the features of the perception of our eyes, not only interesting, but also useful things are created. For example, camouflage hides a person, as if smearing him in space - this was suggested to us by nature, where the mass of animals has a protective color.
Designer Chris Duffy designed an impossible chair. For fans to make fun of the guests you can’t imagine better. It seems that the chair is standing on two front legs, which is basically unrealistic. The secret lies in the shadow of the stool, which is a solid base.
Not only fashion designers and decorators, but also psychologists use optical illusions with pleasure. The method of deception perception diagnoses many psychological problems. For example, Japanese psychiatrist Akiosha Kitaoka suggested using optical illusions to diagnose stress levels.
Impossible figures, blurring the line between illusion and reality, show our imperfect vision of the world. This is an important aspect for a person who wants to understand himself and others.