J, L, and arrow keys for 3D rotations W, A, S, D, Q, E for 4D rotations G, V, B, N and T, 5 for 3D translations R, Y for 4D translations A fourth spatial dimension is a direction perpendicular to up-down, left-right, and forward-backward. Visualizing the fourth dimension is impossible because our brains are wired to perceive only three. However, we can conceptualize it through analogy. Just as a 2D being living on a flat plane would perceive 3D objects as slices of that object, we perceive 4D objects in a similar way. When we manipulate the fourth dimension, we’re essentially exploring different 3D “slices” of the tesseract, revealing different perspectives and configurations. For example, imagine a tesseract, which is a four-dimensional analogue of a cube. In the same way a cube is made of squares, a tesseract is made of cubes. The lines along the fourth dimension (the w-edges) within a tesseract may appear to deviate from parallelism when viewed from a three-dimensional perspective. However, in reality, these lines are always parallel and run along the fourth dimension in the fourth-dimensional space. Our perception of non-parallelism arises because we, as three-dimensional beings, can only observe the tesseract one three-dimensional “slice” at a time. Each slice presents a different perspective of the tesseract, just like viewing a cross-section of an object from various angles. To better understand this concept, consider slicing through a cube. Depending on the angle of the cut, the resulting cross-sections may appear as squares, rectangles, or even trapezoids or triangles. Similarly, when we observe the tesseract from different viewpoints, the lines along the fourth dimension may seem to converge or diverge, giving the illusion of non-parallelism. However, if we could perceive the tesseract in its entirety, from a four-dimensional viewpoint, we would recognize that these lines remain consistently parallel throughout. It’s our limited three-dimensional perspective that creates the illusion of varying alignments.
