The Fourth Dimension in Art

(From Last Time)

We've seen the fourth dimension supported by mathematics and speculated about in literature.

Key Points So Far:

  • We can't picture the fourth dimension, nor can we truly picture a four dimensional object, but that doesn't mean they don't exist.

  • Flatland helps us imagine what it might be like for a four dimension being to view our three dimensional world, using the analog of a 3D being visiting a 2D world.

  • We still need help picturing this though - so why not ask an artist?

Back to Picasso

On Tuesday, we saw that Picasso really is a talented artist that chose to work in a style that many would accuse of being simple.

In fact, his work fell into many different styles over his lifetime, from realism to abstraction.

Picasso's Old Guitarist, 1904

A New Style for Picasso

Some of his more well known styles are his Blue Period and African Movement. But many of his most famous works are categorized as "Cubism", and he is credited with being a founder of the style.

He was joined by other revolutionary artists, including Marcel Duchamp, Jean Metzinger, Andre Derain, and Georges Braque.

But what is cubism, and how did it start?
Picasso's Femme Assise, 1909


This painting, Les Demoiselles d’Avignon was completed by Picasso in 1907, and is often considered the "first" painting of the Cubism style. There are still some signs of his African Movement, but the full concept of Cubism has not yet been developed.

So far, it just means that the subjects are "angular" and geometric.


However, the original Cubism style was not as radically new or different as Picasso was hoping for.

Maurice Princet, 1875-1973

Princet was a French accountant and actuary (good with numbers).

Despite being on the fringe of mathematics, he was an avid reader of journal articles on fourth dimension and non-Euclidean geometries.

This is a page from a book he was reading on the subject, by Esprit Jouffret.

Maurice Princet, 1875-1973

Princet was introduced to Picasso by his girlfriend, Alice.

He told Picasso what he was reading about, and even gave him that book by Jouffret.

Princet explained how from the fourth dimension, we could see all aspects of our 3D universe at once: inside, outside, underneath, and on top.

Maurice Princet, 1875-1973

Completely irrelevant gossip:

Princet's girlfriend knew Picasso because she was having an affair with him. Still, Picasso was a witness at Alice and Maurice's wedding, where he commented "Why should they marry simply in order to divorce?".

Just a few months later, Picasso introduced Alice to another artist in his group, Andre Derain, with the intention of interfering with her marriage. She divorced Princet 6 months after their wedding.
Derain's portrait of Alice

Maurice Princet, 1875-1973

The only artist to stay in touch with Princet was Jean Metzinger, who had this to say about him:

"Princet joined us often. Although quite young, thanks to his knowledge of mathematics he had an important job in an insurance company. But, beyond his profession, it was as an artist that he conceptualized mathematics, as an aesthetician that he invoked \(n\)-dimensional continuums. He loved to get the artists interested in the new views on space that had been opened up by Schlegel and some others. He succeeded at that."


Cubism grew from Picasso and his contemporaries' attempts to capture the concept of the fourth dimension.

Specifically, what our 3D universe might look like from the perspective of a four dimensional being.

We are not just seeing a woman in this painting, but her front, back, sides, and even insides.


Georges Braque began experimenting with Cubism in 1909, and was inspired by Picasso's attempts to capture the concept of the fourth dimension.
Braque, Bottle and Fishes, 1910


Jean Metzinger is often credited with establishing the mathematical "rules" of Cubism, perfecting the approach by depicting 3D objects from multiple views.

This work was purchased by physicist Niels Bohr as "inspiration".

Metzinger, La Femme au Cheval, 1910


In the later years of the Cubism period, Picasso even glued objects to the canvas, attempting to utilize the third dimension in his portrayal of the view from the fourth, rather than relying on a flat 2D projection.

Picasso's Glass and Bottle of Suze, 1912


Marcel Duchamp took a different approach, and used the idea of time as the fourth dimension in his work. His attempted to capture the "phases" of his subjects, in both appearance and motion.

Duchamp, Sad Young Man on a Train, 1912


Duchamp's ideas began to drift toward another developing movement in art, known as Futurism.

This was one of his last paintings during the Cubist period.

Duchamp, Nude Descending a Staircase No 2, 1912

Étienne-Jules Marey

Duchamp brought a new idea to Cubism, but not one that hadn't appeared before in the world of art.

In the mid 1880's, Étienne-Jules Marey used his "chronograph gun" to capture multiple still images of an object in motion (up to 12 per second), and layered those images together.

Étienne-Jules Marey

Étienne-Jules Marey

Étienne-Jules Marey

Étienne-Jules Marey