Dimensional analogy

Dimensional analogy is the comparison of the functions of extra spatial and temporal dimensions based on our understanding of the mathematics and physics of the universe we inhabit. Most commonly, 3D spaces are shown interacting with a 2 + 1 universe to illustrate how a 4D space may interact with lower dimensions. Because it is thought to be impossible for humans to literally picture the fourth dimension, the use of 3D slices and dimensional analogies is the only way it can be inagined as a visual space.

Flatland analogy
Hypothetical 2D universes are sometimes referred to as Flatlands, after a book of the same name published in the early 20th century. 3D shapes intersecting with the 2D space is a subject frequently touched on by Flatland analogy; in particular, the fact that 2D spaces would only be able to show a single slice of a 3D space at a time, just as a 3D space would only show a single slice of a 4D space.

In a Flatland world, inhabitants would only ever be aware of this single slice. They would struggle to understand any explanation that there is a direction that they cannot perceive. To the Flatlander, "up and down" would seem the same as "back and forth. This can be compared to an inhabitant of the 3D world being unable to distinguish "in and out" and "back and forth."

Analogy mediums
Dimensional analogy has been explored extensively in art, physics, mathematics, and modern mediums.

Physicists and mathematicians have long extrapolated rules of higher dimensions from those seen in lower dimensions. Indeed, because a higher dimensional space is not directly observable, most research on extradimensional spaces is based on the perceived rules of 3D apace. Some details of higher dimensions are easily determined by this method, such as the number of faces on an n-dimensional hypercube. Other generalizations of 3D observations lead to more inconclusive results, such as the kissing number of an n-dimensional hypersphere.

Artists in the western hemisphere became increasingly literate of research on extra dimensions in the form of both time and space. Shortly before the start of the 20th century, artists were attempting to capture the appearance of time as a spatial dimension in their work. Pieces painted after the turn of the century focused more on the novel concept of a fourth spatial dimension extending in a new direction. Salvador Dali's famous painting Crucifixion illustrates the trend of the time.

In the modern day, countless artists, writers, and other content creators have touched upon the topic. Game developers have explored 4D spaces, using 3D projections on a 2D screen to represent slices of extradimensional worlds.