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+Two days ago, after running through Func Diff Geometry chapter, spent a while
+reading Carroll Spacetime+Geometry, in early chapters. Particularly relevant
+was the discussion of 1-forms ("dual vectors") and vectors and tensors. Tensor
+language isn't really even used in this book, except in Appendix C. Should
+probably work through that appendix in another week or two.
+
+---
+
+Starting on chapter 4, about basis fields (basic vector fields and basis
+one-form fields), both coordinate and non-coordinate.
+
+What is an example of a non-coordinate basis? Rotations! This will probably
+come back up as... Lorentz transforms? Rotations of spacetime, as a change of
+frame.
+
+Commutators!
+
+The commutator of two coordinate basis fields is zero. This is one way to tell
+if basis fields are coordinate or non-coordinate. Is this sufficient proof?