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It looks like we may have come a complete circle, from paper to digital and finally back to paper. Something that I recently stumbled across leads me to say this (although I really don't believe it).
In the Sherlock Holmes stories, for example, Holmes often gives his card to people to introduce himself. Maybe that's only in the Granada TV version of the stories. I can't quite keep straight the details of what I saw on TV and what I read because it's been so long since I read or saw either of them. In any event, Holmes certainly didn't send email or ask people to become his Facebook friends. He definitely didn't use Twitter. That sort of thing came much later. Holmes was definitely focused on printed ways to communicate.
It looks like Knock Knock, a store that sells that paper and paper products now has a paper-based answer to Twittter: Paper Tweet, pads of note paper that are marked with a grid of 140 characters so that your paper-based notes will have the same constraints as your tweets.
Maybe these are just meant to be clever gifts. I'm not sure that I'd want to leave an important message for someone on a piece of paper that's clearly labeled "PAPER TWEET." That's what Post-It Notes (preferably yellow) are for, after all.