In this article that talks about some history of hamilton
There is a snippet that says this:
Multiplication is very sneaky. You can only set up rules for multiplication that let you divide in dimensions 1, 2, 4 and 8. This is just a mysterious fact about the universe. Well, if you study maths it's not mysterious because you can see exactly why, but it's mysterious in the sense that when you hear about it first it just sounds completely crazy!
What are they talking about here? What type of division is possible in 2 dimensions but not 3? Could you give me an example of the division in two dimensions?