But when you said $$ \frac {\partial} {\partial x} $$ multiplied by a scalar is not a vector, you said it was "nonsense", you weren't misinterpreting what Penrose was saying? Because that's what he says in his book.Tach said:It is not that I disagree with Penrose, it is that you misinterpret what he's writing.
Actually what he says is the scalar should be a function of x (or whatever variable is being varied). But as others have noted that's a mere mathematical detail because a vector multiplied by any scalar is still a vector. That's something I learned in a linear algebra course.
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