One of my PhD advisors—my official advisor—was Roger Blandford (now at Stanford). Blandford, being old-school, responded to a tweet thread I started by sending me email. I am trying to move over to always describing tensors and rotation operators and Lorentz transformations and the like in terms of unit vectors, and I realized that the most enlightened community along these lines are the quantum mechanics. Probably because they work in infinite-dimensional spaces often! Anyway, there are deep connections between vectors in a space and functions in a Hilbert space. I'm still learning; I think I will never fully get it.
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