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His criticism of the cross product seems more poignant than his criticism of quaternions in computer programming. One might ask -- why not teach bivectors in in
by scythe 7y ago
His criticism of the cross product seems more poignant than his criticism of quaternions in computer programming. One might ask -- why not teach bivectors in introductory math instead of cross products?
Historically it seems like 3D geometry and particularly cross products in the context of electromagnetism fomented the primary demand in mathematics education for students to be taught vectors. Unfortunately the mathematics curriculum (in Western countries) has not really been updated in decades to better prepare students for the jobs of today; we still enroll all students in a sequence that culminates in differential equations and particularly in second-order linear differential equations, which just so happen to be crucial to control problems in electrical and mechanical engineering. While many people's jobs involve some kind of mathematics somehow, only a few jobs involve the mathematics of electrical engineering, and I suspect that is part of the reason why so many students are bored in math class.
- BlueTemplar 7y agoPuzzles me too. And even further : IIRC, you don't need cross-product for electrical engineering, and IIRC it (thankfully) isn't (generally?) taught in high school. Furthermore, later, in college, it would seem that electromagnetics get easier when taught through bivectors rather than cross products (and you avoid the traps with pseudo-vectors and, later, gimbal lock with Euler angles ?). Maxwell's multiple equations seem to condensate to a single one under GA ! (What if we teach GA it will open the possibility of teaching EM in high school ?)