> Needing to "understand" root construction before "being able to use" is just procrastination. since I feel personally attacked by that statement (I say in je

> Needing to "understand" root construction before "being able to use" is just procrastination. since I feel personally attacked by that statement (I say in jest), it's more charitably viewed as a risky investment. Understanding now might help you use it more efficiently later. 3D Rotations are traditionally very tricky to represent in a computer! It's only in "modern" times that basically everyone has settled down on quaternions as the best parameterization. I think the comparison to anything about real numbers misses the point. It's not about rotors themselves, or real numbers themselves, it's about how they model something we care about. Money isn't a real number, but we model a balance in an account using one. And an accountant definitely needs to understand operations such as "debiting", "crediting", "accruing interest". So they need to understand addition, negative numbers, and multiplication. But that's just because of the choice of the model. funny enough, it seems like lots of accounting existed a while before negative numbers were obvious, so there are all sorts of to-me funny ways of representing negative numbers, or subtraction (I don't have any clear evidence to back this up). Everyone was doing accounting just fine before, but really it just feels more obviously elegant to use a negative number to represent a deficit.