โImagine you have a cube.
Notice some of its features. It clearly has 3 dimensions; length, width, and depth. It has 12 edges, each of equal length and perfectly at 90 degrees to each other.
Now look at its shadow. As you can see, its projection is only 2-dimensional, its edges are no longer equal in size, and its angles vary from acute to obtuse.
What weโve essentially done is scaled down a 3-dimensional object to a 2-dimensional object, and in doing so weโve lost/distorted some information about the object.
Since we are 3-dimensional beings, we are able to perceive and comprehend what a 3-dimensional object looks like, even if we interpret it from a 2-dimensional projection.
Similarly, we cannot comprehend what a 4-dimensional object actually looks like, but we can look at its shadow.
This is a hypercube, or at least our interpretation of its projection. In the fourth dimension, the hypercube would have all of its edges simultaneously equal length and at perfect right angle to each other. In order to scale it down to the 3rd dimension, we have to distort that information, similar to how we distorted information about the cubeโs 2-dimensional shadow, so its edges are no longer equal or at right angles.
Just as a cube is a very simple shape in our three dimensional world, a hypercube is one of the simplest four dimensional shapes. We can only imagine the extent of complexity in the fourth dimension.โ Austin Gariepy from Ametek Aerospace in response to โWhat would a 4D object look like to a human being?โ
Another response by โSilk Roadโ from The Science Space
โ
4D stands for four-dimensional, which means having four dimensions of space. We are used to living in a 3D world, where we can describe any point or object with three numbers: length, width, and height. For example, a cube has a length, a width, and a height, and each of its faces is a 2D square.
But what if we add another dimension, perpendicular to the other three? This is hard to imagine, because we have no experience of such a direction in our 3D world. But mathematically, we can extend the concept of 3D space to 4D space, just like we can extend the concept of 2D space to 3D space.
One way to visualize 4D objects is to use analogies with lower dimensions. For example, a 4D cube is called a tesseract, and it is made by connecting two 3D cubes with lines. Just like a cube has six square faces, a tesseract has eight cubic cells. Each cell is at a right angle to the other cells, but we can't see that in our 3D perspective.
Use projections or shadows. For example, if we shine a light on a cube, we can see its shadow on a flat surface. The shadow is a 2D projection of the 3D cube. Similarly, if we shine a light on a tesseract, we can see its shadow on a flat or curved surface. The shadow is a 3D projection of the 4D tesseract.โ
So, what would a 4D object look like to a human being? It would look like a distorted or moving 3D object, because we can't see the full shape or structure of the object in our 3D vision. We can only see parts or slices of the object at different angles or times. To see the whole object, we would need to have a 4D vision, which is beyond our human capabilities.
