Semester 2 Lecture 7

As human beings we have a very particular architecture for perceiving the world. We have the commonly agreed five senses, although any of you who were in my reading group last semester might remember that some cultures say that there are 11 different senses. We also have a capacity for thought which means that we are able to imagine far more than we can actually perceive. We do this imagining in various ways – through images, stories, poems, philosophy but also through mathematics which is an abstract language for describing things that exist beyond what we can perceive.

You know that for a time people believed that the world was flat because it looks flat. Pythagoras, an ancient Greek mathematician had already proposed that the earth must be round in the 6th C BC, but that was not widely accepted until the 15^th C. We don’t perceive the world as curved, but we know it in our minds. Our experience of space in general is similar; the way that we perceive space is different from the way that science and technology tell us that space actually is. We are going to spend a few minutes talking about space and geometry for reasons that I hope will become clear in the second half of the lecture.

Geometry literally means the measure of the earth. It is a branch of mathematics developed by the Ancient Greeks, concerned with questions of shape, size, relative position of figures, and the properties of space. Euclid was of the most influential of the Ancient Greek geometers. He developed theories to describe the basis of physical space –the point, the line, the plane, right angles and parallel lines. In Euclid's time, there was no clear distinction between physical space, the kind of space that we experience around us what we might also call intuitive space, and geometrical space. Euclid’s descriptions of space using the point, the line and the plane produced a very ordered and regular space, harmonious, logical, predictable. It was this kind of space that was rediscovered in the Renaissance. In addition to using geometry to represent that space, as in one-point perspective, mathematicians and geometers used geometry to map and chart the surface of the planet.

 

In the late 18th and early 19th-century the concept of space as a logical, ordered, predictable entity underwent a radical transformation, based partly on the discovery that space over large distances is curved rather than straight. This is too complex mathematically for me to understand or explain properly, but to cut a long story short, one of Euclid’s ideas that parallel lines always run alongside each other without ever touching is a problem when space is curved. At the beginning of the 19th C two alternatives to Euclidean space were accepted; the first is called hyberbolic space, which is always expanding, and the send is called elliptical space which is always folding inwards. These are called non-Euclidean spaces, and they suggest the possible existence of multiple dimensional worlds and perspectives in which things might look very different.

At first this transformed idea of space was limited to the mathematics community, but gradually it filtered out into the culture at large, with significant effects on art in particular. For example, in 1884 Edwin Abbott wrote a satirical novel entitled Flatland. It is written from the point of view of a two-dimensional being and the complexities that arise when it encounters a third dimension. Although the book was really a social critique about the hierarchy of Victorian culture, it also contributed to the popular understanding of multiple dimensions.

This brings us to the work of the Post-Impressionist artist Paul Cezanne a French painter who strove to develop an ideal synthesis of naturalistic representation, personal expression, and abstract pictorial order. Although he was influenced by the Impressionists, Cezanne's work demonstrates a mastery of design, colour, composition and draftsmanship.

 

When he first arrived in Paris in the 1860’s, he studied traditional academic painting, with a traditional use of light and shade and muted colour. However, as soon as he was exposed to the work of the impressionists, everything changed. He met Camille Pissaro in 1872, who introduced him to the notion of plein-air painting, that is painting directly out of doors, and immediately Cezanne shifted from dark tones to bright hues and began to concentrate on scenes of farmland and rural villages. Under Pissarro's tutelage, and within a very short time, Cezanne developed his characteristic repetitive and exploratory brushstrokes, using planes of colour to build up complex forms. This was both a direct expression of the sensations of the observing eye and an abstraction from observed nature. He studied his subjects intently, often working very slowly over months or even years on a canvas, struggling to deal with the complexity of human visual perception.

In his still-life paintings from the mid-1870s, Cézanne rejected the contrasts of light and shadow of his earlier years and adopted the a refined system of color scales placed next to one another developed by the Impressionists. He became a master of building forms completely from color and creating scenes with distorted perspectival space.

Though he considered the study of nature essential to painting, he nevertheless opposed many aspects of the Impressionist aesthetic. He epitomized the reaction against it when he declared: ‘I wanted to make of Impressionism something solid and enduring, like the art in museums.’ He believed that colour and form were inseparable, so he tried to emphasize structure and solidity in his work, features he thought neglected by Impressionism.

 

Cézanne wanted to capture all the complexities that an eye observes, so his paintings are the result of prolonged meditation in front of nature, not of instantaneous recording of its fleeting effects.. He wanted to get to the point where "sight" was also "touch". He gave up classic artistic elements such as pictorial arrangements, single view perspectives, and outlines that enclosed color in an attempt to get a "lived perspective". By ignoring the laws of classical perspective, allowing each object to be independent within the space of the picture, his works represented an illogical space which the viewing public and critics found hard to accept. For many years his work was not well received critically, as it seemed clumsy and awkward. However, we can see this work in terms of non-Euclidean space and the breakdown of single-point perspective, or we can also look at it in terms of the cinematic, images that shift and change over time. Cèzanne believed that while he was painting, he was capturing a moment in time, that once passed, could not come back. The atmosphere surrounding what he was painting was a part of the sensational reality he was painting. Cèzanne claimed: "Art is a personal apperception, which I embody in sensations and which I ask the understanding to organize into a painting."

 

He would take hours sometimes to put down a single stroke because each stroke needed to contain "the air, the light, the object, the composition, the character, the outline, and the style" as he once said. A still life might have taken Cézanne one hundred working sessions while a portrait took him around one hundred and fifty sessions.

During the late 1870s and '80s Cezanne drifted away from the Impressionists and spent much of his time in his childhood home in the south of France. He inherited his father's wealth and became financially independent, but he remained quite isolated socially.

From 1882, Cézanne executed a substantial number of landscapes, concentrating on pictorial problems of creating depth. He used an organized system of layers to construct a series of horizontal planes, which build dimension and draw the viewer into the landscape.

Until the end of his life he received little public success and was repeatedly rejected by the Paris Salon. In 1895, however, Ambroise Vollard, a Paris art dealer, arranged a show of Cezanne's works and by the time of his death in 1906 he had attained the status of a legendary figure.

One of his most famous quotes is “to treat nature by means of the cylinder, the sphere, the cone, everything brought into proper perspective so each side of an object or a plane is directed toward a central point.” This quote is supposed to have been the basis for the title Cubism which was adopted by Braque and Picasso later.

The 20th century began with a veritable explosion of scientific and technological discoveries.  During its first decade alone, the telegraph was invented, airplanes made their first successful flights, Henry Ford started mass-producing automobiles, and Albert Einstein formulated his theories of relativity. This was a mathematical equation that proved that time and space are relative, not fixed, and even more than this, that time and space are continuations of each other. Although we experience time and space as separate things, Einstein demonstrated the existence of spacetime. Space, rather than being a big emptiness with some matter zooming around in it, is actually a complex fabric of distortions and vibrations.