The Fourth Dimension can refer to time as another dimension, along with length, width, and depth. This idea of time as a fourth dimension is usually attributed to the "Theory of Special Relativity" proposed in 1905 by the German physicist Albert Einstein (1879-1955). However, the idea that time is a dimension goes back to the nineteenth century, as we see in the novel The Time Machine (1895) by British author H.G. Wells (1866-1946), wherein a scientist invents a machine that lets him travel to different eras, including the future. The Cubists may not have known about Einstein's theory, but were aware of the popular idea of time travel. They also understood Non-Euclidean geometry, which the artists Albert Gleizes and Jean Metzinger discussed in their book Cubism (1912). There they mention the German mathematician Georg Riemann (1826-1866) who developed the hypercube.
Simultaneity in Cubism was one way to illustrate the artists' understanding of the Fourth Dimension. In this sense, the Fourth Dimension concerns how two kinds of perception work together as we interact with objects or people in space. That is, to know things in real time, we must bring our memories from past time into the present. For example, when we sit down, we don't look at the chair as we lower ourselves on to it. We assume the chair will still be there when our bottoms hit the seat.
Another definition for "the Fourth Dimension" is the very act of perceiving (consciousness) or feeling (sensation). Artists and writers often think of the fourth dimension as the life of the mind.