Articles by HAS Members

What are "Dimensions"?

by Jonathan Park

This article appeared in the August 2023 HAS newsletter.

We live in a universe with three dimensions of space (spatial dimensions) and one of time (a temporal dimension). But what exactly is a “dimension”? Let’s concentrate on the dimensions of space here and look at one-, two-, and three-dimensional space. Put simply, the number of dimensions tells you how many numbers (coordinates) you need to define the location of an object. If you want to learn about the geometry of the universe (flat, curved or negatively curved), these concepts are an excellent starting point.

A one-dimensional "object" is a line – it has length but no width and no height. Picture the line along which two walls meet, or a wall meets a ceiling – no matter how much you zoom in, you will only see a length, but the width is always zero. In a space with only one dimension, you only need one number to define a position relative to another. You could say that a point is 5 units in front of you, so its coordinate is simply “5”; or 5 units behind you, so its coordinate is “–5” (minus 5). One-dimensional space would be a dull place to live – you can only move forwards or backwards – there is no “left and right” and no “up and down”. And you would be one-dimensional, so you wouldn't be able to do much of anything.

A map on a piece of paper is a good way to understand a two-dimensional space – you can go forwards and backwards or left and right, but there is no “up and down”. Here, two coordinates are needed to pinpoint any location. For instance, your position could be described as three steps in the x direction and four in the y direction, forming the coordinates (3, 4). The coordinates x and y might be East and North or anything else you define your map with. To get an accurate idea of a two-dimensional space (or two-dimensional universe), think about the surface of a sheet of paper. Not the piece of paper itself, because that has a thickness (a third dimension), but just imagine the boundary (the surface) where the paper meets the air. If you were a two-dimensional creature in such a universe, you would have as much trouble picturing a third dimension as we do picturing a fourth dimension in space.

And finally, in our three-dimensional Universe, we need three numbers to explain where something is. These are often called the x, y and z directions. Picture a helicopter hovering 800 metres above the ground, 500 metres North, and 700 metres East; from your perspective. You would describe its position by coordinates (500, 700, 800). Other types of coordinate systems can be used, but they still require three coordinates.

When it comes to thinking about four-dimensional space and four-dimensional objects - don't worry if you can't imagine these. Our three-dimensional brains struggle to grasp additional dimensions because we live in a universe of three spatial dimensions. On the other hand, often in cosmology, you will see one dimension removed to make it easier to grasp the concepts. For example, sometimes you might see galaxies drawn on the surface of a sphere (the surface of a sphere is two-dimensional). Though not a true representation (the universe is not a sphere, and not two-dimensional), the two-dimensional representation aids us in understanding some concepts.

Armed with this knowledge, we can begin to learn about spacetime diagrams, look at the geometry of our Universe (what does it mean to have a flat or a curved universe), and more in future articles.