To be honest, my question is much more practical, and much naiver too. I work with people who use Euler angles to express rotations, and it's a horrible world.

To be honest, my question is much more practical, and much naiver too. I work with people who use Euler angles to express rotations, and it's a horrible world. I learned quaternions in my day, and there are some obvious advantages. When I discovered GA some years ago, it was really eye opening. It makes quaternions an easy to explain concept, even intuitive, and I've used it since then, not only in my own work but also to teach other people. Then, I learned about differential forms, and it's also very interesting, I think I could base my "intuitive explanations" in this other paradigm, but I'm not sure I should. I do not think it makes a big difference in my particular case, but as I said I find this "competition" a bit frustrating, and am trying to understand it better. I cannot discuss with a mathematician if the Hodge star is a GA or a DFs concept, but I have found it all over the place when reading about DFs, and not so in GA related material (though I have a vague idea about how the Hodge star operator can easily be defined in GAs using the pseudoscalar). But is this really my choice? I have listened opinions about which one is more general, but not really convincing arguments (at least not arguments that are obvious to me). Thanks for your explanation. I think I need to have a deeper look at this stuff. I like to get lost in these rabbit holes, but sometimes it goes a bit over my head.