system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: why isn't quaternion multiplication commutative?
gpt
Quaternions are used to describe rotation in 3D space. Multiplying by i, j or k is just a 90° turn about an axis. Hold an object in front of you, then turn it 90° to the right, then flip it up 90°. Take note of what its orientation is. Now put the object back to where it started and then flip it up 90° before turning it to the right 90°. If you did it right, the object should not be in the same orientation as the first set of instructions. This is why quaternion multiplication isn't communitative. Numberphile recently did a video explaining this more clearly.