It’s not easy to imagine dimensions higher than the three that we exist in, but in math, higher dimensions are used all the time.
What are higher dimensions?
In mathematics dimension refers to the number of coordinates needed to specify the object in question. It refers to the intrinsic property of an object, independent of the space in which the is. Wikipedia explains dimension by referencing a line: A line has a dimension of one, because only one coordinate is needed to specify a point on it.
Higher dimensions refer to abstract spaces and can be independent of the physical space humans live in.
Visualizing the geometry
As pointed out in this video from 3Blue1Brown, there are some downsides to the fact that we can’t visualise these dimensions. Putting math into geometric form helps us see how different mathematical ideas connect and discover novel ways to solve problems. How can we do that with higher dimensions that we can’t imagine?
This video presents one idea. Using number lines to represent axes, we can plot a certain point on a shape regardless of how many dimensions its in. From there, 3Blue1Brown explains how this idea can reveal truths about shapes in higher dimensions.
Image and video credit: 3Blue1Brown
This article was originally written for and published by Popular Mechanics USA.