Behind the canvases of the Renaissance masters, a rigorous geometric construction. By "inventing" perspective, Italian artists create the illusion of depth... and revolutionize the representation of the world.
The Ideal City, preserved in the city of Urbino, Italy, and made between 1480 and 1490 by an anonymous painter, is a perfect demonstration of perspective. Aided by the geometric straightness of the buildings and the floor slabs, the viewer's view inevitably leads to the vanishing point hidden behind the central temple.
This article is taken from the "Indispensables" of Sciences et Avenir n°202, dedicated to the theme of "infinity", on sale in newsstands from July to September 2020.
Giotto, Vinci, Michelangelo, Fra Angelico… Renaissance painters offered us new perspectives! By inventing, from the 15th century, a way of representing the world in three dimensions on a flat surface, infinity has become perceptible in paintings which, while offering an unprecedented poetic vision, come as close as possible to reality. . What a long way since the Egyptian characters, drawn flat and in profile! Their awkwardness takes on a form of charm for our eye formed by geometric perspective, unknown to artists of the time.
In the West, it was in Greece and Rome that people began to experiment with representation in three dimensions. The painter Agatharcos (5th century BC) is said to have mentioned, in his treatise on scenic painting, the notion of vanishing lines from a single focal center, introducing the illusion of distance into painting. . But in the Middle Ages, painters cared more about storytelling than realism. The size of the characters is determined by their social position:a lord will be shown taller than his vassal...
The revolution will come from Florence, during this period which begins the Renaissance:the Quattrocento. "Italian cities, rivals, snap up the best scientists and the most talented artists , recalls Pierre Curie, curator of the Jacquemart-André museum in Paris. And starting with Giotto, the Italians seek to get closer to human vision."
This article is taken from the "Indispensables" of Sciences et Avenir n°202, dedicated to the theme of "infinity", on sale in newsstands from July to September 2020.
Giotto, Vinci, Michelangelo, Fra Angelico… Renaissance painters offered us new perspectives! By inventing, from the 15 e century, a way of representing the world in three dimensions on a flat surface, infinity has become perceptible in paintings which, while offering an unprecedented poetic vision, come as close as possible to reality. What a long way since the Egyptian characters, drawn flat and in profile! Their awkwardness takes on a form of charm for our eye formed by geometric perspective, unknown to artists of the time.
In the West, it was in Greece and Rome that people began to experiment with representation in three dimensions. The painter Agatharcos (5 e century BC) would thus have mentioned, in his treatise devoted to scenic painting, the notion of vanishing lines issuing from a single focal centre, introducing the illusion of distance into painting. But in the Middle Ages, painters cared more about storytelling than realism. The size of the characters is determined by their social position:a lord will be shown taller than his vassal...
The revolution will come from Florence, during this period which begins the Renaissance:the Quattrocento. "Italian cities, rivals, snap up the best scientists and the most talented artists , recalls Pierre Curie, curator of the Jacquemart-André museum in Paris. And starting with Giotto, the Italians seek to get closer to human vision."
"The success of the perspective is linked to an operation of reconquest of political power by the Medici, in sobriety", precise in his Stories of painting Daniel Arasse, the famous art historian who died in 2003. When Cosimo de' Medici came to power in the Tuscan city in 1434, he took the opposite view from his rivals, the Strozzi, who commissioned Gothic paintings all in gilding and reliefs. A great patron, he provided artists with an ideal framework for expressing themselves and inventing a new technique, linear perspective, which Daniel Aarasse defines as follows:"a perfectly arbitrary monofocal system of representation which supposes a motionless spectator at a certain distance , looking with a single eye, and not with the movement of two eyes that would sweep the field. This geometrization of space and time is the fundamental innovation of perspective."
A ray from the eye to the calf
Filippo Brunelleschi, architect of the dome of Florence, established the principles around 1420, with a process allowing a building to be represented on a plan while respecting the ratios of proportion. Leon Battista Alberti codified it in 1435. At the same time philosopher, painter, architect, mathematician, he wrote the first scientific study on perspective. It supposes to determine the point of observation of the spectator and the dimensions of the painting. Linear perspective is based on a central point placed on a horizon line towards which converge all the parallels that seem to meet beyond the painting, suggesting an infinite depth:the vanishing lines. Alberti finds a method of constructing the apparent decay of the tiles from the floor as they recede into the painting. One of the principles consists in drawing oblique lines starting from the eye of the spectator or the painter. Each time they cross a vanishing line, the square formed is smaller. These projective methods, theorized in geometry at the beginning of the 17 e century, will renew the discipline:the geometry of concrete figures will become the geometry of abstract space. "Linear perspective is the one that comes closest to the work of the eye, which is only a tool. It is the brain that makes us understand the information it transmits, and that interprets it according to a cultural system", says Pierre Curie.
The artists then seek first to reproduce reality, do not yet speak of vanishing point (point at infinity):Alberti calls it ray of the eye. This can be placed anywhere in the table. Thus Antonello of Messina, in his Saint Sebastian, places it at the level of the character's calf, which makes it appear like a giant, with a cinematic close-up effect!
Techniques other than Alberti's create the illusion of depth. Aerial perspective relies on the difference in sharpness and contrast, with shapes becoming more blurred the farther away the subject is. The sfumato , which approaches it, softens the contours of the distant. Far from the Tuscan cities, the Japanese developed the cavalier perspective, where the receding lines are parallel - a method still used for technical drawing.
Italian artists, for their part, once the rules had been mastered, would never stop trying to free themselves from them. Their Annunciations often include an element that breaks the geometric rigor, escapes perspective, just as, in the religious thought of the time, the Incarnation escapes Man. Leonardo da Vinci, in his Last Supper , builds a ceiling of perfect perspective. But the table, too big in relation to the space, gives the apostles a heightened effect of presence.
In a few decades, the Albertian system conquered Europe, where it imposed itself in the representation of reality for five centuries. The first, the cubist painters, shattered forms and volumes and freed themselves from realism. Until the world of 3D put perspective back in the foreground, offering us emotions no doubt as powerful as those experienced by Renaissance spectators.
Penrose's Impossible Staircase
It can be climbed indefinitely… Such is the paradox of the staircase represented by the Dutch artist M.C. Escher in his lithograph Ascending and Descending 1960). How do flights of stairs condemn you to always return to the starting point? To understand it, you have to consider the impossible figure that inspired the designer, imagined by the British psychiatrist Lionel Penrose. He designed the two-dimensional representation of a staircase made up of four flights turning at right angles. On this drawing, it is impossible to identify a high point or a low point. Conversely , the 3D model has steps progressing continuously from bottom to top, but the latter do not join the former, leaving an empty space. It is the play of perspectives that creates the illusion, from a given angle. An illusion that is based on the shortcuts operated by our brain during the tenth of a second necessary for the information to reach it from the eye and during which it selects, among an infinity of interpretations, the most plausible. For example, in the absence of additional information, two close lines touch, like, on the model, those of the "departure" and the "arrival". But if Escher's games of perspective are so destabilizing, it is also because our brain can produce a coherent perception of each detail of the drawing, but not of its wholeness.