“Remixing is the adoption, alteration, and recombination of pre-existing cultural texts (songs, literature, paintings, etc.) to create something new.” (Wikipedia)
Remixing is not inherently a negative word. It has become one for many people due to it’s often used association with copying and plagiarism.
Copying something is directly reproducing the existing work with no new interpretation and no credit to the original artist. This does nothing to move things forward. It is duplication.
Remixing is paying homage. It’s being aware of the elements of a prior work that inspire you and being untroubled (on purpose or unexpectedly) of those that don’t.
If someone came to you after giving a presentation on a new idea, product, service you were developing and said, “That’s just a remix of Picasso and thermodynamics.” it would be considered negative. This is because someone used the word remix using the negative definition; of copying and plagiarism.
It would also be rude to approach anyone after a presentation with negative laden criticism, but that’s another story.
If someone came to you after presenting your work and said, “That’s an interesting approach. I never thought to combine Picasso and thermodynamics.”. That would be a complement. The critic would have made the connection (explicit or implicit in your presentation) between two previous works and seen the unique value of combining the two inspirations.
All work is influenced by prior work. Which in turn was inspired by even older prior work. Continuing ad infinitum. No new work exists without influence – even if that influence is to do the exact opposite!
I see remix (and the surrounding culture) the penultimate way of expressing how we’re all interconnected – that every action ripples out and causes new twists and turns down unexplored paths. This is comforting, positive and powerful. It moves things forward and is an intrinsic part in making anything new.
Another recently oft-cited example of remix at work: http://gizmodo.com/343641/1960s-braun-products-hold-the-secrets-to-apples-future
Side note: I chuckled to myself while writing this. I just remixed the negative language of remix to come up with a positive definition of remix. I remixed remix.