3 ms·
I don't think this distinction is often made in practice, even though it might be useful. As far as I can tell, combining Tao's approach here with a Clifford al
by r0uv3n 3y ago
I don't think this distinction is often made in practice, even though it might be useful. As far as I can tell, combining Tao's approach here with a Clifford algebra approach (where energy is a scalar and torque a bivector) would be entirely possible and solve this problem.
- mikhailfranco 3y agoYes, this is the correct answer. The Gibbs formulation of 3D vector analysis/calculus was certainly useful, but forgets most of the spatial structure. Using Clifford Algebra (Geometric Algebra) fixes everything.
- ajkjk 3y agodaily chance to inject my opinion on GA: Almost all of the value in GA comes from the use of multivectors and the wedge product. It's very hard to find a justification for the "geometric product", and there's no real geometric interpretation of it. Therefore treating it as fundamental is a difficult-to-justify choice. "Exterior Algebra" on its own has everything you want without the objectionable parts.