system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5, what is a quaternion?
gpt
Imagine you're standing on a number line. All [real] numbers are in front of you and behind you on that line. If you take a step forward you increase by +1. If you take a step back, you decrease (-1). What happens if you take a step to the left or right, though? You increase or decrease by *i*, the imaginary number. Contrary to its name, imaginary numbers do very much exist. If you combine your forward and side steps you get a complex number.

Ok, so all real numbers are in front or behind you, all imaginary numbers are to your left and right. Your position anywhere on this 2-dimensional plane can be described as some combination of real and imaginary numbers. What happens if you go *up or down*? Now, you're in a 3D space and you need another set of numbers to describe where you are. You have to add *j* and *k*.

A quaternion is the combination of all of these numbers: a+b*i*+c*j*+d*k*. And, in fact, you can continue adding dimensions and add even more types of numbers. For complicated math reasons, the more dimensions you add, the more types of numbers you have to add.