[taneq]

I had a similar 'aha' moment a few years ago about inner product (aka dot product) and the choice of '.' as an operator to access elements of a structure.

    struct Example {
      int elem1;
      int elem2;
      ...
    };
    
    Example ex1 = { 1, 2, ... };
    int a = ex1.elem1;
    int b = ex1.elem2;
    ...

If we think of ex1 as a vector, and elem1 as a constant vector [1, 0, 0...] (and elem2 as a constant vector [0, 1, 0, ...] and so on) then ex1.elem1 is literally the inner product of ex1 and the constant elem1.

I have no idea if that was the original thinking behind dot notation but it's neat and I like it.