Quite possible. But that's in no small measure because I have yet to find an actual cogent definition of "tensor" that distinguishes a tensor from an array. (I have a similar problem with monads.)
> So what I mean when I talk about the reality of the tensor I mean whatever it is the tensor is expressing in the physical universe
OK, but then "the reality of a tensor" not depending on the coordinate system has nothing to do with tensors, and becomes a vacuous observation. It is simply a fact that actual physical quantities don't depend on how you write them down, and hence don't change when you write them down in different ways.
No it’s very important for physics to have a mathematical object that doesn’t change so that you can represent these characteristics of the universe that don’t change. For every observer in every reference frame even though they will use different basis vectors and different components, the combination of basis vectors and components will be the same. That’s extremely powerful. Try the video I linked a few posts above for what I think is a really excellent explanation of what a tensor is (using practical household objects to illustrate everything practically). I think you’ll get it.
I don't understand them. None of the introductory materials I've read on them ever made any sense to me. I kinda sorta understand "state" and "maybe" but the general idea that links these two things together and (I am given to understand) leads to other cool stuff just eludes me.
Easiest way to understand is to write code using them IMO. (Writing a parser for some language with a parser-combinator library is a good place to start.) Otherwise it's like trying to understand how to play a board game by reading the rulebook. It's easier to just try playing the game
Quite possible. But that's in no small measure because I have yet to find an actual cogent definition of "tensor" that distinguishes a tensor from an array. (I have a similar problem with monads.)
> So what I mean when I talk about the reality of the tensor I mean whatever it is the tensor is expressing in the physical universe
OK, but then "the reality of a tensor" not depending on the coordinate system has nothing to do with tensors, and becomes a vacuous observation. It is simply a fact that actual physical quantities don't depend on how you write them down, and hence don't change when you write them down in different ways.