The fourth dimension is a hypothetical spatial dimension, distinct from the time dimension. The concept was introduced in the 19th century, and mathematicians have since developed a foundation for four-dimensional geometry. The fourth dimension is represented by an additional axis, called the w axis, and movements along this dimension are referred to as ana and kata. Visualizing the fourth dimension can be difficult, but drawing multiple cubes and connecting their vertices can help to understand the concept.
The fourth dimension is generally understood to refer to a hypothetical fourth spatial dimension, added to the standard three dimensions. It should not be confused with the space-time view, which adds a fourth dimension of time to the universe. The space in which this dimension exists is referred to as 4-dimensional Euclidean space.
Beginning in the early part of the 19th century, people began to consider the possibilities of a fourth dimension of space. Mobius, for example, understood that, in this dimension, a three-dimensional object could be picked up and rotated to its mirror image. The most common form of this, the four-dimensional cube or tesseract, is generally used as a visual representation of it. Later in the century, Riemann established the foundation for true four-dimensional geometry, upon which later mathematicians would build.
In the three-dimensional world, people may regard all space as existing in three planes. All things can move along three different axes: altitude, latitude and longitude. Altitude would cover up and down movement, latitude north and south or back and forth movement, and longitude east and west or left and right movement. Each pair of directions is at right angles to the others, and is therefore said to be mutually orthogonal.
In the fourth dimension, these same three axes continue to exist. To them, however, is added another axis entirely. While the three common axes are usually referred to as the x, y and z axes, the fourth falls on the w axis. The directions along which objects move in that dimension are usually called ana and kata. These terms were coined by Charles Hinton, a British mathematician and science fiction author, who was particularly interested in the idea. He also coined the term “tesseract” to describe the four-dimensional cube.
Understanding the fourth dimension in practical terms can be quite difficult. After all, if someone said to take five steps forward, six steps left and two steps up, she would know how to move and where she would end up in relation to where she started. If, on the other hand, a person were told to move even nine ana steps, or five kata steps, he would have no concrete way of understanding this, or of visualizing where he would place her.
There is a good tool for understanding how to visualize this dimension, however, and that is by first looking at how the third dimension is drawn. After all, a piece of paper is a two-dimensional object, roughly speaking, and therefore can’t really convey a three-dimensional object, like a cube. However, drawing a cube, and representing three-dimensional space in two dimensions, turns out to be surprisingly easy. What you do is simply draw two sets of two-dimensional cubes, or squares, and then connect them with diagonal lines connecting the vertices. To draw a tesseract, or hypercube, a similar procedure can be followed, drawing multiple cubes and also connecting their vertices.
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