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1. In vector and higher order tensor fields, what does it mean to "observe the field from point (x,y,z)?" I fully understand how to use the equations to get a column (or row) vector, and how to draw a vector from it, but the vector seems to change depending on what point I plug in (with most equations). I understand how this works mathematically, but I would love to know how it works applied to a real-life vector field so I can understand it better.

2. What just doesn't make sense to me is a 3rd-order tensor. Again, I understand it as a mathematical concept, but not at all as a concept applied to real-life physics.

3. This one is fairly straight foreword: Does the curl of a vector field change depending on the point it is measured at? From what I understand the answer is yes, but I just want to check.