[JadeNB]

> Saying quaternions require thinking in 4 dimensions seems like a lie with no proof.

How could one even subject a statement like that to proof? If you insist that you thought about quaternions without thinking in 4D, and the author insists that you're just so used to thinking in 4D that you didn't even notice it, then who's to arbitrate that dispute?

(I'm sensitive to these issues because I'm a mathematician of the "visualizing 4D is just visualizing n dimensions and setting n = 4" variety, so I have no idea when I'm particularly thinking in 4, or any other specific number, of dimensions ….)

[koolala]

I think of dimensions like 3D space. Normal people dimentions. Math calls independent variables 'dimensions' but it's a overloaded naming convention that causes people to think it has something to do with normal everyday dimensions like space. Math may as well use a different term than 'dimension' similar to Rank and there would be no confusion. Using the everyday dimention term makes a harmful misconception about quaternions for normal people because they are associated with understanding everyday geometry.

So the dispute is just using words differently. For quaternions, I think its very important to understand how they apply to everyday space / reality / imagination / intuition / Geometry. I wish it was something everyone understood.

To prove that statement to a normal person in the normal dimension way you'd need to define your 4 dimensions like space, time, or scale and explain examples of quaternions.