Many of you may have heard of an object called the Tesseract.
Being able to perceive a tesseract is clearly impossible, as we cannot see beyond the number of dimensions we live in. We as humans clearly are and live in a three-dimensional world and there are three coordinate axes x, y and z, so we perceive directions left/right, forwards/backwards and up/down.
Imagining four spacial dimensions is very difficult so we can try something simpler with three-dimensional objects. Let’s imagine we were a two-dimensional species living in a two-dimensional world called Flat land, named by Edwin Abbott. We walk about in the two-dimensional space unaware of the other dimension which is the z-axis and that’s completely okay, just like how humans can live perfectly without knowing about the fourth dimension. We’re doing fine, minding our own business on Flat Land, but suddenly someone sees an unusual thing that changes its form from time to time and after a while it suddenly disappears through utter randomness. To the 2D us it may make us think we’re hallucinating but in reality it’s only just a three-dimensional shape passing through our overly boring world, for example if a three-dimensional sphere was to pass through Flat land we would see something quite strange – when first in contact with the surface it appears as a single point, then the circle would get increasingly larger reaching its maximum then recede in size shrinking back to a point which vanishes, thus only a two-dimensional cross-section of the three-dimensional object can be seen at once and that is its point of contact with the 2D plane.
In Flat Land three-dimensional beings would be like gods and have the ability to do things no 2D being could do, like magically remove an object from a locked room or perform supposed teleportation/ invisibility – appearing and disappearing out of thin air. It is now not counter-intuitive to say that a potential four-dimensional being may be able to manipulate things in our 3D world like how we could in Flat land.
Wouldn’t it be beneficial to interact with the other dimension? Maybe through that we could work out many unsolved mysteries of the modern world. Recapping on the beginning of this post, I mentioned that we cannot see beyond our limited dimensions which seems slightly hopeless, so let me explain by going back to the flatness of Flat Land. For simplicity let’s imagine the two-dimensional us to be geometric shapes like triangles. A 3D being again messes around in Flat land and sends a triangle flying into a new dimension, the triangle is obviously in shock and confusion as it realises it can see bizarre things like the insides of locked rooms and the bodies of other fellow triangles. It realises that it can suddenly see in two dimensions (perceive shapes) rather than in one dimension which was what it was like through its eyes living on Flat land. Then after a while the triangle comes to a safe landing back on Flat land. From the perspectives of the other triangles it appears out of nowhere, and they demand the little triangle to show them the mystical dimension “up”- to point to the direction and as we know there is no way for the triangle to do so because of the nature of Flat Land. We are unable to perceive a tesseract because we are trapped within the limitations of a three-dimensional world.
However what we can do is try to understand four dimensions and even extra higher dimensions. A line is one-dimensional, a square has four lines connected to each other by right angles which is two-dimensional, a cube has six squares connected to each other also by right angles in the z projection. So this means a tesseract would involve three-dimensional cubes connected to each other by right angles through the fourth dimension.
A three-dimensional cube is able to be represented in 2D through its shadow, though as you can see it is not an accurate representation as not all the angles are of 90 degrees, it’s as if removing a dimension sacrifices the cube’s form. Thus a fourth dimensional tesseract can also be represented through its three-dimensional “shadow”:the Hyper Cube. Its form is distorted through the lost of a dimension.
Is there existence of a four-dimensional plane in the universe? Who knows. Because we are physically trapped in three dimensions we wouldn’t know if there is one or not. We can analyse any number of higher dimensions theoretically using the power of mathematics and there is also a popular “Theory of everything” – Super string theory which even theorizes the possibility of ten space-time dimensions. Despite this, currently there is still no experimental evidence to confirm the concept of string theory or a four-dimensional plane.
The idea of extra dimensions always intrigues me and makes me ponder a few things such as what would happen if we somehow interacted with the fourth physical dimension, if we are potentially the shadows of four-dimensional beings, and the possibilities of dimension manipulation etc. As a high school student and only just starting calculus in maths class I acknowledge that I certainly have too long of a mathematical journey to make before I can even partially grasp complex ideas like extra dimensions and string theory but these comprehension barriers do not and would never eliminate my ardent and curiosity.
This post does not mention the other popular interpretation of four dimensions which is three spacial dimensions plus one time dimension, though I may cover some related content at a later date.
Author – Susan Chen
Susan is a 5th year high school student currently studying three STEM subjects at Scottish Higher level-Mathematics, Physics and Chemistry (Crash Course). She particularly loves ideas in astrophysics and hopes to embark on an academic journey in the area of theoretical physics.