Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

Comments on Complex numbers in 2D, quaternions in 4D, why nothing in 3D?

Post

Complex numbers in 2D, quaternions in 4D, why nothing in 3D?

+10
−0

I'm just trying to understand why quaternions are necessary. If I understand right, first off please check me on this, Hamilton kept trying to find ways to multiply triplets and found something satisfactory only when he escalated to four dimensions.

So game coders and spacecraft engineers extend a vector into four dimensions, then rotate it by a conjugation that takes it out of 3-D space with the first multiplication and pulls it back with the second. (And please check me on that too).

Is there an intuitive way to understand why that's necessary? Or is it one of those things that can only be explained formally?

History
Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

1 comment thread

3D surface embedded in a 4D space (1 comment)
3D surface embedded in a 4D space
Peter Taylor‭ wrote about 2 years ago

Rather than thinking about going "out of 3D space", it may be helpful to think about it as working with the surface of a 3D unit hypersphere embedded in a 4D space.