Question: Question On Tensors

I apologize if the forum is strictly for undergrad students. I'm now on the section of Arfken's text "Mathematical Methods..." that deals with tensors, and I'm having a little trouble. My problem is how to physically or intuitively, picture (for lack of a better word) tensors. This also adds to the problem of not fully understanding and appreciating the difference between covariance and contravariance, other than it seeming to be arbitrarily subscripting or superscripting the tensor elements. Thanks, dc
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