Hyperspace, cosmic strings, God, and the origin of all life, if our universe is the bi-product of the 4th dimension, what would that visually look like, and could we even comprehend it?
Humans reside in a 3-dimensional world, we can visualize objects in both 2 (length/width) and 3 (length/width/height) dimensions. Humans are limited in our perspective of the universe, let alone higher dimensions. But what if we could fathom the possibility of a 4th dimension and what it would look and be like; scientists and researchers at Duke University might have the answer.
“Living in a 3-dimensional world, we can easily visualize objects in 2 and 3 dimensions. But as a mathematician, playing with only 3 dimensions is limiting,” said Dr. Anthony Segerman Assistant Professor of Mathematics at Oklahoma State University. According to Anika Radiya-Dixita of Duke University, Dr. Segerman spoke to Duke students and faculty on 4-dimensional hyperspace in a series of PLUM lectures.
What Is 4th Dimensional Hyperspace?
Start with 2-dimensional space, where we have two variables in the world of physics and mathematics, X and Y, according to Dixit. If we visualize objects in an XY plane, such as a rectangle drawn on a piece of paper, the data we get is the length and width. Now take a 3-dimensional space, and visualize a globe, where we have an added variable have X (Length), Y (Width), and Z (Height). When we attempt to visualize 3-dimensional geometry on a 2-dimensional space, we use a right-angle marker and place it on the geometry to infer what it would look like in a 3-dimensional space. We can see a 3-dimensional object visualized on a 2-dimensional plane, such as our computer screen or cellphone. The right-angle method is essential in discovering what 4-dimensional objects would look like in a 2 or 3-dimensional space.
How To Visualize The 4th Dimension
Scientists and researchers are able to see a 4-dimensional space using this same method of placing a right-angle marker but this time on a 3-dimensional object. Likewise, we can describe a point in 4-dimensional space with four numbers – x, y, z, and w – where the purple w-axis is at a right angle to the other regions; in other words, we can take our human understanding of 3-dimensions by squishing the 4-dimensional variables down to three. The hypercube is similar to a cube in 3 dimensions, just like a cube is to a square. XYZW coordinate system can be used to discern what this object may be. A commonly explored experiment, the hypercube, is a 4D object we can make using this method. A hypercube is analogous to a cube in 3 dimensions, just as a cube is to a square.
What Is A Hypercube, And How Do We Make It
To create a 1D line, we make a point, make a copy, move the copied point parallel to some distance away, and then connect the two points with the line, according to Dr. Segerman. In a similar fashion, by making a copy of a line, and connecting them to add the second dimension, we can make a square. So, to create a hypercube, we move identical 3D cubes parallel to each other and then connect them with four lines.
When you try to create an n-dimensional cube, we take two copies of the (n−1)–dimensional cube and connect the corners that match up. This concept is a daunting task to understand. Even with the assistance of a 3D-printed model, trying to visualize the hypercube can get confusing. A possible hypercube created by Bathsheba Grossman attempts to help people understand this concept.
“How can we make a better picture of a hypercube,” said an interview by Anika Radiya-Dixit of Duke University.
“You sort of cheat, One way to cheat is by casting shadows. Parallel projection shadows, depicted in the figure below, are caused by rays of light falling at a right angle to the plane of the table. We can see that some of the edges of the shadow are parallel, which is also true of the physical object,” replied Dr. Segerman.
Answers Are In The Shadows
Just like our minds, our minds only detect light in 2-dimensions and then use our brain to computationally reconstruct the 3D world around us by using previous experience and information from the 2D images such as light, shade, and parallax. Then we can use a stereographic projection of a 4D object on a 3D world to visualize how that would appear.
The 4th dimension is almost incomprehensible, but the brightest minds of our society have found a way to make that a little easier.
