The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott explores the concept of physical dimensions through characters who encounter higher-dimensional beings. The protagonist, “A. Square,” lives in a two-dimensional world called Flatland. When the three-dimensional “Sphere” visits him, Square realizes that a whole world exists that he never could have imagined. Eventually, his interactions with Sphere open his mind to the possibility of even higher dimensions.
Still popular after 140 years, the book showcases humanity’s fascination with higher dimensions, as well as our struggle to understand the concept of a universe where higher-dimensional beings, like aliens, might exist. Let’s be clear: at this point, aliens inhabiting any dimension are purely hypothetical, let alone the fourth dimension. But that fact hasn’t stopped scientists and philosophers from exploring the idea of what a higher dimension would be like. And plenty of thought experiments have already extended our mathematical knowledge of higher dimensions, allowing us to conceptualize four-dimensional creatures interacting with our three-dimensional space.
Higher dimensions are a necessary feature in mathematics as the only way to understand certain concepts. For example, string theory—so far, our best explanation for how the tiniest particles in the universe behave—requires the existence of higher physical dimensions. Otherwise, the behavior of vibrating “strings” that theorists think make up all particles cannot work. Today’s physicists accept the theoretical possibility that our universe started out with as many as 11 dimensions.
Over the years, experiments and mathematical modeling have provided some inkling of four-dimensional characteristics. For example, two-dimensional experiments in both the U.S. and in Europe 2018 showed evidence of a four-dimensional existence because scientists could make logical inferences based on how electrons behave while undergoing a specific change in their electric charge. First, the electrons moved in one direction through an electrically conductive material. When researchers put a magnetic field perpendicular to the material, it forced the electrons to divert either to the left or to the right. The electrons were essentially stuck in two dimensions. Physicists involved in the experiment extrapolated that a comparable effect would occur in the fourth dimension, and that we would see its effects in our familiar third dimension.
In other words, we can see evidence of the fourth dimension in our own. As three-dimensional beings, we cast a two-dimensional shadow. The same principle could be true for four-dimensional beings who could leave traces of themselves in our world. To understand how, let’s start with the basic concept of how different dimensions relate to one another.
As residents of a three-dimensional world, we easily perceive three dimensions: height (or length), width, and depth. We can travel up and down, left and right, and forward and backward. And we know the lower dimensions. The zeroth dimension is a point, which has no height, width, or depth. The first dimension branches out, becoming a line, with length only. Nothing would exist beyond this line to a one-dimensional creature. Two-dimensional shapes, like the characters in Flatland, are what we can draw on paper, like squares and circles. They have both width and length, and they can also travel in these directions. A two-dimensional creature wouldn’t be able to escape the piece of paper they live on, however, because they simply cannot perceive anything other than two dimensions. With the addition of a third dimension, a far richer reality emerges, because now the shape can travel up and down, leaping right off the paper. This is the shape of the universe we know and take for granted.
Now comes the tricky part. To step into higher dimensions, you’re basically making a right angle to the previous shape: first squaring the line for the second dimension, and then cubing the line to reach the third dimension. To step up to the fourth dimension, you need to do the same thing—make a right angle to the cube, extending it into a “hypercube,” or tesseract. Four lines connect to every point, and every surface is a cube. Sometimes physicists describe the fourth dimension as a space that’s perpendicular to a cube. (Feeling lost yet?) This description, while geometrically accurate, is not much help—no brain wired for a 3D world can understand what a tesseract or other higher-dimension object actually looks like. So theoretically, we would not be able to perceive a four-dimensional being with our senses—unless they somehow physically accessed our three-dimensional reality.
How would we see aliens from higher dimensions if they entered our three-dimensional world? “Well, it depends on what part of the 4D object is passing through our 3D space,” science communicator Toby Heny explains. She provides a neat visualization of what it would be like to see a four-dimensional object in our three-dimensional reality on her YouTube channel, Tibees. Supposing there is a four-dimensional ball, Hendy holds out her hand, and a little red ball of yarn pops into existence on it. “Right now, we see a small sphere, because this slice is near the edge of the 4D ball,” she says. As the ball moves through our world, it appears to grow. As it moves out of our plane of existence, it shrinks again, then disappears. “The 4D ball still exists, but our slice of space does not contain it,” Hendy concludes. On the other hand, a 4D being would be able to see the ball and know exactly where it is, she says.
In the same way, an alien from the fourth dimension may pass largely undetected through a “slice” of our three-dimensional universe. Only a part of it would appear, materializing out of nowhere, and then we would see more and more of its parts. But we’d never be able to see all of it at once, because we can’t actually see the fourth dimension with our senses. Finally, it would shrink down to nothing again.
If you can’t quite wrap your head around that (we don’t blame you) then think of it this way: The square in Flatland cannot comprehend the third dimension. So how would it perceive a sphere, a three-dimensional object, invading its two-dimensional plane of existence? Imagine you are the square on the sheet of paper. As the sphere descends onto the sheet in front of you, you start to see a small circle appearing (out of nowhere). This is the leading “slice” of the sphere that’s entering your two dimensions. Gradually, as the sphere continues passing through your two-dimensional plane, the circle—which indicates the diameter of the sphere’s body—gets larger and larger, until the middle of the sphere is fully in your plane. This slice of sphere then shrinks, until nothing is left. At this point, the sphere has traveled completely out of your 2D universe.
For us, that means aliens might be larger than they appear, because we would see only a three-dimensional slice of them at a time. This is exemplified in the games Miegakure and 4D Miner, where you can experience a four-dimensional world through our comprehensible three-dimensional perceptions. So, objects like trees and hills appear and disappear, since our perception of them changes as we move through three-dimensional space. The 4D “hyperspider” predators in 3D Miner are extra menacing because they can move through objects as they hunt us. That’s because a four-dimensional object can slide through gaps that we can’t perceive or access.
Once we hit higher dimensions, it becomes even more difficult to picture what the beings living in there would be like, and how they would interact with our three-dimensional lives. Mathematically, you can keep going with these dimensional iterations, and make cool-looking models. In the end, even models like these four-dimensional shapes are overly simple analogies for a complex reality that’s out of our reach.
So, what would a four-dimensional alien make of us if they visited our three-dimensional reality? Theory suggests they would be able to see inside of us. Just as we can see an array of objects scattered over a two-dimensional surface, all at once from our vantage point in the third dimension, a four-dimensional being would be able to see all of us at once. Kind of creepy.
Perhaps while they are studying us, we have no clue. Based on what we know about physical dimensions, it may be hard to detect an alien spacecraft popping into our space. Could it be that if any UFO sightings are truly related to aliens, they’re hard to prove because the aliens can easily slip away into a higher dimension?
