The fourth dimension is, simply, something beyond our comprehension. Or maybe, everything. As a mathematical possibility, the fourth dimension begins with Euclid's Fifth Postulate, which outlines the following proof:
According to this model, there are only three dimensions of linear direction: variations of up, right, and forward. In other words, height, length, and width. But even with all the practicality of Euclid's model, the concept cannot be mathematically proven, opening the doorway to another fourth direction. This is the possibility laid out by Einstein's Theory of Relativity, which positions space as a curved, non-linear phenomenon. In other words, there may be not only a fourth, but many 'directions' we can't readily conceptualize.
That is the question. In many ways, it's in a direction we can't even point to. Still, the possibilities and implications are so staggering that the pursuit of the fourth dimension is not an endeavor to be dismissed. Some have defined the elusive fourth direction as time, but even though time is a direction of sorts, time is more of a function of the fourth dimension as opposed to its definition. Because of the nature of a 'new space', we may be able to see it only as a time-based phenomenon.
But even viewing the fourth dimension as time-based only gives us a limited perspective. As Euclid's failed model shows, science can only go so far to explore this undiscovered country -- there must be other ways to get there.
As an unknown, unsignifiable quantity, the fourth dimension emerges as not only an impetus for, but as an exercise and test for art. As ideas about the fourth dimension begin to form in the early half of the century, the parallel movements in Modernist art and literature cannot be consigned to mutually-exclusive spaces. Within this context, Modernist art and literature can be looked at for their own definitions of what this fourth dimension might look like, signify, be.