Author: Anthony Baio
Length, depth, height: these are the fundamental measurements we use to describe our three dimensional world. Just using these three, anyone from a child building a Lego set to an astrophysicist describing the very nature of a planet can specify any object in the three dimensions. However, scientists soon came to realize there is more than just the limited 3rd dimension that we live in today. There are theorized to be as many as 26 dimensions, according to theoretical physicists and mathematicians who are pioneering new mathematics in hopes of proving string theory to be genuine. As we can mentally descend to the 1st and 2nd dimensions (those of only length, and length and width) we can picture what it may be like to be one who lives in one of these dimensions, or more commonly referred to as a flatlander. A being who is traveling through one dimension can only perceive length, therefore only being able to travel in a straight line. A flatlander venturing through two dimensions will experience length and width, therefore having the ability to turn left and right and back and forth. However, a human in our three dimensional world can travel, front to back, side to side, and up and down*. Though humans may manifest the brainpower to perceive the 1st and 2nd dimensions, what about focusing on higher dimensions? Students learn early how to find lengths to one dimensional objects (rays), areas of two dimensional objects (squares), and volumes of three dimensional objects (cubes). But how can one determine the dimensional analysis of a fourth dimensional figure while abiding by the three- dimensional laws of nature? It has come to my attention that a new theory is to be named to ensure full perception of all descending dimensions upon the one which the current life-form exists in. The N+1 dimension is necessary to fully perceive the N** and the N’s descending dimensions.
I. Visual Perception
For a moment, assume the position of a flatlander on an even piece of computer paper. This 2-D being has the potential to maneuver up and down and left and right throughout the boundaries of the page. Now, if a square is drawn on said piece of paper the flatlander will have no option but to shift up and around the square. Although a human in the third dimension can associate the four connected lines at 90 degree angles with being a square, a flatlander can only distinguish the figure by bumping into it (as its edges has no depth) and going up and down until it can find a way around. Although a square may indeed be a two dimensional figure, it cannot be fully perceived as a square by a two dimensional flatlander. It necessarily involves the third dimension to apprehend the descending second dimension. The added depth measurement in the third dimension enables humans to view the entirety of the 2nd dimension from a distance, something that flatlanders cannot do. Juggling the 2nd and 3rd dimension may seem an easy feat to comprehend, but higher dimensions can be a bit trickier to imagine. For example, take the cube shape. It is one of the most elementary three dimensional shapes known. Viewed from the naked eye, one can observe its edges, faces, and vertices, but not all at once. There are two approaches to how one can view the entirety of the cube. One way is use the added 4th dimension of time (three special dimensions plus one of time). Using this method*, one can simply rotate around the cube, hence through time, and view all parts of the cube, but not all in one instant as it takes multiple periods of time to view the whole shape. As using time as the fourth dimension though, one cannot see the whole object in a single moment. However, just as a 3rd dimensional being can perceive the totality of the second dimension; the fourth special dimension can also apprehend every side and edge of the cube instantaneously. Humans cannot do this n the universe we live in today, but a possible 4th dimension can envision the entire cube at first glance. The dimension in which we current exist does not allow humans to even fully observe it; this is why any dimension above the third is required to envision it as a whole.
II. Hypershape Geometry
Geometry: a branch of mathematics applying to the measurements and relationships of shapes in space. Early in childhood, teachers instruct students on the various sectors of geometry including, but not limited to, area and volume. These properties are of the second and third dimensions and are common to everyday studies. However, a new kind of geometry is on the rise: hypergeometry. This kind of math is relative to normal geometry except in the sense that it pertains to higher dimensional shapes. What can these higher dimensional shapes look like? Although we may not have the ability to visualize the extra fourth special dimensions, physicists and mathematicians have used objects and concepts known as tesseracts to help “visit” these extradimensional shapes. For a moment, imagine a two dimensional cross divided into six cubes. When folded and fit together, it forms a cube. In doing this, we have used a two dimensional figure and folded it into a three dimensional shape. In the same manner, if one were to use a three dimensional cross, with six cubes instead of squares, and fold them together the result would be a hypercube. Since humans cannot perceive this, it is merely only a way to imagine what a fourth dimensional shape would be somewhat like. In attempting to define a hypercube, let us first look at the descending dimensional shapes. For example, finding the volume of a cube involves multiplying it’s three dimensional measurements (length, width, and height) and concluding the area of a square is equal to multiplying its two dimensional measurements (length and width). Following this pattern, a theoretical scientist can assume to take the product of all four dimensions. Although it may seem obvious, how can mathematicians be so sure, using only special dimensions (not time), that a three dimensional life form can give the correct answer for the volume of a cube? A perfect three dimensional cube will have perfect symmetry and uniformity. However, the only way one can perceive its uniformity is by rotating the cube to ensure it is symmetrical and even throughout. But, in rotating the cube, sub sequential moments of time are integrated together to allow for the motion of the cube. Now, let us take time out of the equation. The remaining feat is to determine the volume of the cube. Since one cannot simply rotate the cube to concur is to be exact, an extra dimension of space is needed to fully perceive the geometrical perfection of the cube. The fourth dimension is needed to fully perceive the descending dimensions.
*Four including time
**Also known as a wormhole