# Fourth Dimension: Definition & Overview

Instructor: Sergey Segal

Sergey has a Masters in Biomedical Engineering and has taught science and mathematics courses at the University of Wisconsin-Madison.

The fourth dimension is a mathematical construct used by scientists to describe certain types of phenomena. Learn more about it, subsequently testing your knowledge with a quiz.

## The Fourth Dimension Defined

Have you ever wondered what it would be like to live in a world with four spatial dimensions? It's a very difficult thought experiment since we're so used to our three dimensional world. So let's start with something simple.

Imagine living in a two dimensional world, similar to old video games like Pac-Man or Super Mario Brothers. You would only be able to move on a flat plane, which you can think of as an infinitely thin sheet of paper. You wouldn't have any understanding of what it means to move above and below it. For example, if you were walking on the street and saw a large tree branch in front of you, there would be no way to step over it, and you would have to go around it.

Before proceeding, it's important to note that scientists sometimes talk about non-spatial dimensions. You might have heard about the Theory of Relativity, where Einstein mentioned the fourth dimension to be temporal instead of spatial. For the purposes of this lesson, we're only going to discuss spatial dimensions, which are often utilized by scientists as the medium in which phenomena occur.

Living in a three dimensional world, we can move above and below objects, in addition to the other directions on a two dimensional plane. Well, introducing another dimension would be similar to going from two to three dimensions. The fourth dimension is an extension of the geometry of space that would give us more ways to move from one place to another.

Let us take a closer look at the fourth dimension from a mathematical perspective.

## The Fourth Dimension: A Mathematical Perspective

If we were to draw a zero-dimensional world, how would it look? Well, all we would need to draw is one little dot. Zero dimensions implies that there is no freedom of movement, so all objects would exist at the same exact location in such a world, which is represented by a point.

How about a one-dimensional world? In this case, objects would be able to move in only one particular way. Imagine drawing a point on a piece of paper to represent a zero dimensional world. To add another dimension, you would draw one more point, and then connect the two of them. The resulting drawing is a line, which represents the medium along which objects can move in this one-dimensional world.

Similarly, representing a two dimensional world would be achieved by drawing a parallel line, and connecting the two of them. Objects would now be able to move along a plane.

To represent three dimensions, we would take two parallel planes and connect them together. It would look like a box, and objects would be able to move along and between different planes.

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