What if you could pick up a printed newspaper, but instead of a handful of stories hand-picked by a secret cabal of senior editors in a dingy newsroom somewhere, it had pieces that were selected based on what was being shared — either by your social network or by users of Facebook, Twitter etc. as a whole? Would you read it? More importantly, would you pay for it? You can’t buy one of those yet, but The Guardian (see disclosure below) is bringing an experimental print version it has been working on to the United States for the first time: a printed paper that is generated entirely — or almost entirely — by algorithms based on social-sharing activity and other user behavior by the paper’s readers. Is this a glimpse into the future of newspapers? According to Digiday, the Guardian‘s offering — known as #Open001 — is being rolled out later this week. But you won’t be able to pick one up at the corner store: only 5,000 copies will be printed each month, and they are going to the offices of media and ad agencies. In other words, it’s as much a marketing effort at this point for the Guardian (which isn’t printed in the U.S.) as it is a publishing experiment.