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.